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We present a simple theory of a strain pulse propagating as a solitary wave through a continuous two-dimensional population of cells. A critical strain is assumed to trigger a strain transformation, while, simultaneously, cells move as automata to tend to restore a preferred cell density. We consider systems in which the strain transformation is a shape change, a burst of proliferation, or the commencement of growth (which changes the shape of the population sheet), and demonstrate isomorphism among these cases. Numerical and analytical solutions describe a strain pulse whose height does not depend on how the strain disturbance was first launched, or the rate at which the strain transformation is achieved, or the rate constant in the rule for the restorative cell motion. The strain pulse is therefore very stable, surviving the imposition of strong perturbations: it would serve well as a timing signal in development. The automatous wave formulation is simple, with few model parameters. A strong case exists for the presence of a strain pulse during amelogenesis. Quantitative analysis reveals a simple relationship between the velocity of the leading edge of the pulse in amelogenesis and the known speed of migration of ameloblast cells. This result and energy arguments support the depiction of wave motion as an automatous cell response to strain, rather than as a response to an elastic energy gradient. The theory may also contribute to understanding the determination front in somitogenesis, moving fronts of convergent-extension transformation, and mitotic wavefronts in the syncytial drosophila embryo.

Transformations in cell shape and motility triggered by strain cues impinging on individual cells within a large population are shown to offer a distinct alternative to chemical cues as a pathway to periodic patterns or sequential segmentation. Interacting transformations can raise up solitary wave-like strain pulses that propagate across a population, providing the cells all the timing and positional information necessary for templating segmentation. Candidate strain-cued transformations include a cell transforming into a secretory state, wherein it changes the organ's geometry; a change in a cell's shape; the onset of proliferation; and surges in cell motility, being either a change in the rate at which cells minimize density gradients or the onset of positive velocity feedback. If the wave response excited by transformations is assumed to be nonlinear, biologically interesting solution spaces emerge. When multiple transformations are pinned to different strain levels by switching criteria in a nonlinear system, their transformation fronts propagate at different velocities. When positive velocity feedback acts between a pair of such fronts, a cycling system can arise, timed by jumps in the location of one of the pair. The period of the cyclic pattern is approximately λ = 1.43 L excl / e c , where L excl is a length scale related to velocity feedback and e c is the critical strain for the primary (driving) transformation. Remarkably but consistently with one small set of data, λ is independent of the velocity of the pulse system and the type of transformation that drives the system. Reasonable values of e c and the assumption that L excl must be at least the cell width if velocity feedback is effected by discrete cells yield an approximate lower bound for λ, free of adjustable parameters. The lower bound approximately predicts the lengths of rugae that form in palatal development in the mouse, somites that form during body axis extension in a bird embryo, and cell cohorts that form among pre-ameloblasts in the mouse or rat incisor.

The degradation of SiC-based ceramic matrix composites (CMCs) in conditions typical of gas turbine engine operation proceeds via the stress-rupture of fiber bundles. The degradation is accelerated when oxygen and water invade the composite through matrix microcracks and react with fiber coatings and the fibers themselves. We review micromechanical models of the main rate-determining phenomena involved, including the the diffusion of gases and reaction products through matrix microcracks, oxidation of SiC (in both matrix and fibers) leading to the loss of stiffness and strength in exposed fibers, the formation of oxide scale on SiC fiber and along matrix crack surfaces that cause the partial closure of microcracks, and the concomitant and synergistic loss of BN fiber coatings. The micromechanical models could be formulated as time-dependent coupled differential equations in time, which must be solved dynamically, e.g., as an iterated user-defined material element, within a finite element simulation. A paradigm is thus established for incorporating the time-dependent evolution of local material properties according to the local environmental and stress conditions that exist within a material, in a simulation of the damage evolution of a composite component. We exemplify the calibration of typical micromechanical degradation models using thermodynamic data for the oxidation and/or volatilization of BN and SiC by oxygen and water, mechanical test data for the rate of stress-rupture of SiC fibers, and kinetic data for the processes involved in gas permeation through microcracks. We discuss approaches for validating computational simulations that include the micromechanical models of environmental degradation. A special challenge is achieving validated predictions of trends with temperature, which are expected to vary in a complex manner during use.. This article is protected by copyright. All rights reserved.

Methods are presented for calibrating the local elastic properties of tow-scale material domains in virtual specimens of textile composites. A model of the tow geometry is calibrated using 3D tomographic data via previously published methods. The local elasticity is defined to vary with the local tow orientation and fiber volume fraction within tows. The accuracy of the tow geometry is assessed by comparing the surface geometry of virtual specimens with an alternative data source, viz. topographical data obtained by digital image correlation. Calibration of the elastic constants is validated by comparing measured surface strain distributions with computed strain distributions. An approach is also presented for extending the model to the non-linear regime, by simulating the response of virtual specimens in which the bonds between abutting tows are broken and the resulting fracture surfaces are frictionless. The latter results yield a better match to the measured strain distributions.

We argue in favor of representing living cells as automata and review demonstrations that autonomous cells can form patterns by responding to local variations in the strain fields that arise from their individual or collective motions. An autonomous cell’s response to strain stimuli is assumed to be effected by internally-generated, internally-powered forces, which generally move the cell in directions other than those implied by external energy gradients. Evidence of cells acting as strain-cued automata have been inferred from patterns observed in nature and from experiments conducted in vitro. Simulations that mimic particular cases of pattern forming share the idealization that cells are assumed to pass information among themselves solely via mechanical boundary conditions, i.e., the tractions and displacements present at their membranes. This assumption opens three mechanisms for pattern formation in large cell populations: wavelike behavior, kinematic feedback in cell motility that can lead to sliding and rotational patterns, and directed migration during invasions. Wavelike behavior among ameloblast cells during amelogenesis (the formation of dental enamel) has been inferred from enamel microstructure, while strain waves in populations of epithelial cells have been observed in vitro. One hypothesized kinematic feedback mechanism, “enhanced shear motility”, accounts successfully for the spontaneous formation of layered patterns during amelogenesis in the mouse incisor. Directed migration is exemplified by a theory of invader cells that sense and respond to the strains they themselves create in the host population as they invade it: analysis shows that the strain fields contain positional information that could aid the formation of cell network structures, stabilizing the slender geometry of branches and helping govern the frequency of branch bifurcation and branch coalescence (the formation of closed networks). In simulations of pattern formation in homogeneous populations and network formation by invaders, morphological outcomes are governed by the ratio of the rates of two competing time dependent processes, one a migration velocity and the other a relaxation velocity related to the propagation of strain information. Relaxation velocities are approximately constant for different species and organs, whereas cell migration rates vary by three orders of magnitude. We conjecture that developmental processes use rapid cell migration to achieve certain outcomes, and slow migration to achieve others. We infer from analysis of host relaxation during network formation that a transition exists in the mechanical response of a host cell from animate to inanimate behavior when its strain changes at a rate that exceeds 10(−4)–10(−3)s(−1). The transition has previously been observed in experiments conducted in vitro.

The physics of crack initiation in a polymer matrix composite are investigated by varying the modeling choices made in simulations and comparing the resulting predictions with high-resolution in situ images of cracks. Experimental data were acquired using synchrotron-radiation computed tomography (SRCT) at a resolution on the order of 1 pm, which provides detailed measurement of the location, shape, and size of small cracks, as well as the crack opening and shear displacements. These data prove sufficient to discriminate among competing physical descriptions of crack initiation. Simulations are executed with a high-fidelity formulation, the augmented finite element method (A-FEM), which permits consideration of coupled damage mechanisms, including both discrete cracks and fine-scale continuum damage. The discrete cracks are assumed to be nonlinear fracture events, governed by reasonably general mixed-mode cohesive laws. Crack initiation is described in terms of strength parameters within the cohesive laws, so that the cohesive law provides a unified model for crack initiation and growth. Whereas the cracks investigated are typically 1 mm or less in length, the fine-scale continuum damage refers to irreversible matrix deformation occurring over gauge lengths extending down to the fiber diameter (0.007 mm). We find that the location and far-field stress for crack initiation are predicted accurately only if the variations of local stress within plies and in the presence of stress concentrators (notches, etc.) are explicitly computed and used in initiation criteria; stress redistribution due to matrix nonlinearity that occurs prior to crack initiation is accounted for; and a mixed-mode criterion is used for crack initiation. If these factors are not all considered, which is the case for commonly used failure criteria, predictions of the location and far-field stress for initiation are not accurate.

Data acquired from synchrotron-based X-ray computed tomography provide complete descriptions of the stochastic positions of each fiber in large bundles within composite samples. The data can be accumulated for distances along the nominal fiber direction that are long enough to reveal meandering or misalignment. Data are analyzed for a single fiber bundle consolidated as a mini-composite specimen and a block of fibers embedded within a single ply in a tape laminate specimen. The fibers in these materials differ markedly in their departure from alignment and the patterns formed by fiber deviations. The tape laminate specimen exhibits evidence of fibers that have slipped laterally through the bundle in narrow shear bands, which may be a mechanism of bundle deformation under transverse compression and shear. This pattern is absent in the single-tow specimen, which was not subject to transverse loads in processing. We propose a combination of topological and Euclidean metrics to quantify these and other stochastic bundle characteristics. Topological metrics are based on the neighbor map of fibers, which is constructed on cross-sections of the bundle by Delaunay triangulation (or Voronoi tessellation). Variations of the neighbor map along the fiber direction describe fiber meandering, twist, etc. Euclidean metrics include factors such as local fiber density and fiber orientation. The metrics distinguish bundle types, enable quantification of the effects of the manufacturing history of bundles, and provide target statistics to be matched by virtual specimens that might be generated for use in fiber-scale virtual tests.

Generating realistic 3D tow-level finite element (FE) models of textile weaves and impregnated textile composites poses a challenge because of the complexity of the 3D architecture and the need for achieving high quality finite elements and nonintersecting tow volumes. A common approach sweeps a constant tow cross-section along a smooth and continuous centerline that repeats over a unit cell length. However actual microstructures of dry fabrics and textile composites are often aperiodic and non-deterministic. In this study, we present a novel method to generate realistic virtual microstructures of fabrics and textile composites using a “thermal growth” approach. This involves a series of orthotropic volumetric expansions and shrinkages of the tow cross-sections and centerlines that are artificially induced by prescribed thermal loads, along with mechanics-driven tow deformations in order to grow or form the tows into their final realistic configurations within the weave. Contact-pairs are defined between interlacing tow surfaces to prevent tow inter-penetrations. The final virtual microstructures are generated through a series of simulations executed using LSDYNA. Two case studies are presented. The first is a plain-weave Kevlar fabric used in protective structures. The second is an angle-interlock PIP-CVI processed C/SiC ceramic matrix composite used in high temperature structures. The virtual microstructures are validated against experimental microstructures obtained from SEM, optical, and microCT characterization. Relatively fine features are generated correctly, including variations in tow shapes and the distribution of spacings that are left between tows. This novel thermal growth approach to generate 3D tow-level meshes of weave architectures can be applied towards any 2D, 2.5D, and 3D woven, braided, and knit architectures. The generated virtual microstructures are at the core of Teledyne’s ICME-based virtual testing toolset to predict the linear thermoelastic and non-linear thermostructural damage behavior of textiles, PMCs, and CMCs.

Recent theoretical simulations of amelogenesis and network formation and new, simple analyses of the basic multicellular unit (BMU) allow estimation of the order of magnitude of the strain energy density in populations of living cells in their natural environment. A similar simple calculation translates recent measurements of the force–displacement relation for contacting cells (cell–cell adhesion energy) into equivalent volume energy densities, which are formed by averaging the changes in contact energy caused by a cell׳s migration over the cell׳s volume. The rates of change of these mechanical energy densities (energy density rates) are then compared to the order of magnitude of the metabolic activity of a cell, expressed as a rate of production of metabolic energy per unit volume. The mechanical energy density rates are 4–5 orders of magnitude smaller than the metabolic energy density rate in amelogenesis or bone remodeling in the BMU, which involve modest cell migration velocities, and 2–3 orders of magnitude smaller for innervation of the gut or angiogenesis, where migration rates are among the highest for all cell types. For representative cell–cell adhesion gradients, the mechanical energy density rate is 6 orders of magnitude smaller than the metabolic energy density rate. The results call into question the validity of using simple constitutive laws to represent living cells. They also imply that cells need not migrate as inanimate objects of gradients in an energy field, but are better regarded as self-powered automata that may elect to be guided by such gradients or move otherwise.

We present a methodology for characterizing and reconstructing in-plane weave variability in textile composites. Surface topography of a partially processed C-fiber/SiC matrix composite panel was measured using digital image correlation. The centroids of tow segments that appear periodically on the fabric surface were located by image analysis and used as fiducial markers. Stochastic deviations of the fiducial markers from the ideal periodic weave structure indicate geometrical variance. Fourier analysis shows that spatial wavelengths of the deviations range from the size of one unit cell to the dimensions of the entire panel. Long-range deviations are attributed principally to fabric deformation after manufacture, during handling. Short-range fluctuations, extracted by computing spatial derivatives of the positions of the fiducial markers, are attributed to variations in tow packing density that arises during weaving. A simple set of statistics for these deviations is presented and its use in generating stochastic virtual specimens is demonstrated.

In-plane centroids of textile composites are simulated as cross-correlated random fields. Each tow position is defined as an average trend quantified from experimental data, added with zero-mean deviations produced as a stochastic field. Realisations of these fields are generated using a framework based on the Karhunen-Lo`eve series expansion that is calibrated with experimental information from prior work. Positional deviations are obtained that are correlated along the tow and between neighbouring tows. The application is a 2/2 twill woven carbon fibre reinforced epoxy consisting of multiple unit cells. Generated in-plane deviations of the warp and weft tows resem-ble the experimental fluctuations with similar wavelengths. Simulation of thousand specimens demonstrates that the virtual in-plane positions possess the experimental standard deviation and correlation lengths on average. ispartof: Composite Structures vol:116 issue:1 pages:75-83 status: published

High-fidelity strength prediction of composites requires advanced numerical methods that can explicitly resolve the multiple damage processes and their nonlinear coupling at various scales. Nonlinear fracture models such as cohesive zone models are critical for damage descriptions and need to be properly embedded in a numerical framework so that correct coupling between different damage process zones can be guaranteed. This paper reviews the recent developments in advanced numerical methods that have the potential to address the important issue of progressive damage evolution in composites. Candidate FE-based numerical methods, including X-FEM, A-FEM, and phantom node methods, are reviewed and their capabilities in handling the multiple damage coupling in composites are assessed. Successful simulations of composites at various scales using the framework of A-FEM are presented and the numerical and material issues associated with these high-fidelity analyses are highlighted. Finally, we address the question of how to integrate all these different scale analyses into a single multiscale numerical framework by using the Arlequin coupling method.

Ceramic matrix composites are the emerging material of choice for structures that will see temperatures above ~1,500 °C in hostile environments, as for example in next-generation gas turbines and hypersonic-flight applications. The safe operation of applications depends on how small cracks forming inside the material are restrained by its microstructure. As with natural tissue such as bone and seashells, the tailored microstructural complexity of ceramic matrix composites imparts them with mechanical toughness, which is essential to avoiding failure. Yet gathering three-dimensional observations of damage evolution in extreme environments has been a challenge. Using synchrotron X-ray computed microtomography, we have fully resolved sequences of microcrack damage as cracks grow under load at temperatures up to 1,750 °C. Our observations are key ingredients for the high-fidelity simulations used to compute failure risks under extreme operating conditions.

A novel magnetically actuated scaffold was used to explore the effects of strain stimulus on the proliferation and spatial distribution of smooth muscle cells and improve cell viability in the scaffold interior by pumping nutrients throughout the structure. Magnetically actuable scaffolds were fabricated in a tube shape by winding electrospun sheets of a biodegradable polymer modified with magnetic Fe(2)O(3) nanoparticles. Prior to rolling, the sheets were seeded with smooth muscle cells and wound into tubes with diameter 5.2 mm and wall thickness 0.2 mm. The tubular scaffolds were actuated by a magnetic field to induce a cyclic crimping deformation, which applies strain stimulus to the cells and pumps nutrient fluid through the porous tube walls. Comparison with non-actuated controls shows that magnetic actuation increases the total cell count throughout the scaffold after 14 days of incubation. Furthermore, whereas cell density as a function of position through the tube wall thickness showed a minimum in the mid-interior in the controls after 14 days due to cell starvation, the actuated scaffolds displayed a maximum cell density. Comparison of cell distributions with the expected spatial variations in strain amplitude and nutrient flux implies that both strain stimulus and nutrient pumping are significant factors in cell proliferation.

Recent work presented a Monte Carlo algorithm based on Markov Chain operators for generating replicas of textile composite specimens that possess the same statistical characteristics as specimens imaged using high resolution x-ray computed tomography. That work represented the textile reinforcement by one-dimensional tow loci in three-dimensional space, suitable for use in the Binary Model of textile composites. Here analogous algorithms are used to generate solid, three-dimensional (3D) tow representations, to provide geometrical models for more detailed failure analyses. The algorithms for generating 3D models are divided into those that refer to the topology of the textile and those that deal with its geometry. The topological rules carry all the information that distinguishes textiles with different interlacing patterns (weaves, braids, etc.) and provide instructions for resolving interpenetrations or ordering errors among tows. They also simplify writing a single computer program that can accept input data for generic textile cases. The geometrical rules adjust the shape and smoothness of the generated virtual specimens to match data from imaged specimens. The virtual specimen generator is illustrated using data for an angle interlock weave, a common 3D textile architecture.

A Monte Carlo algorithm is defined for generating replicas of textile composite specimens that possess the same statistical characteristics as specimens imaged using high resolution computed tomography. The textile reinforcement is represented by one-dimensional tow loci in three-dimensional space, which are easily incorporated into the Binary Model of textile composites. A tow locus is expressed as the sum of non-stochastic, periodic variations in the coordinates of the tow centroid and stochastic, non-periodic deviations. The non-stochastic variations have period commensurate with the dimensions of the unit cell of the textile, while the stochastic deviations, which describe geometrical defects, exhibit correlation lengths that may be incommensurate with the unit cell. The model is calibrated with data deduced in prior work from computed tomography images. The calibration obviates the need for assuming any ideal shape functions for the tow loci, which can take very general form. The approach is therefore valid for a wide range of textile architectures. Once calibrated, a Markov Chain algorithm can generate numerous stochastic replicas of a textile architecture very rapidly. These virtual specimens can be much larger than the real specimens from which the data were originally gathered, a necessary feature when real specimen size is limited by the nature of high resolution computed tomography. The virtual specimen generator is illustrated using data for an angle interlock weave.

Three-dimensional (3-D) images of two ceramic-matrix textile composites were captured by X-ray micron-resolution computed tomography (lCT) on a synchrotron beamline. Compared to optical images of sections, CT data reveal comprehensive geometrical information about the fiber tows; information at smaller scales, on matrix voids, individual fibers, and fiber coatings, can also be extracted but image artifacts can compromise interpretation. A statistical analysis of the shape and positioning of the fiber tows in the 3-D woven architecture is performed, based on a decomposition of the spatial variations of any geometrical characteristic of the tows into non-stochastic periodic trends and non-periodic stochastic deviations. The periodic trends are compiled by exploiting the nominal translational invariance of the textile, a process that maximizes the information content of the relatively small specimens that can be imaged at high resolution. The stochastic deviations (or geometrical defects in the textile) are summarized in terms of the standard deviation of any characteristic at a single point along the axis of a tow and correlations between the values of deviations at two different points on the same or different tows. The tow characteristics analyzed consist of the coordinates of the centroids of a tow, together with the area, aspect ratio, and orientation of its cross-section. The tabulated statistics are sufficient to calibrate a probabilistic generator (detailed elsewhere) that can create virtual specimens of any size that are individually distinct but share the statistical characteristics of the small specimens analyzed by X-ray lCT. The data analysis presented herein forms the first step in formulating a virtual test of textile composites, by providing the statistical information required for realistic description of the textile reinforcement.

The augmented finite element method (A-FEM) is used to study the fundamental composite failure problem of delamination and associated damage events spreading from a stress concentrator during tensile loading. The solution exploits the ability of A-FEM to account for coupled multiple crack types that are not predetermined in shape or number. The nonlinear processes of each fracture mode are represented by a cohesive model, which provides a unified description of crack initiation and propagation and can also describe crack coalescence and bifurcation. The study problem is an orthogonal double-notched tension specimen, in which delaminations interact with transverse ply cracks, intra-ply splitting cracks, non-localized fine-scale matrix shear deformation, and fiber breaks. Cohesive laws and constitutive laws for matrix shear deformation are calibrated using literature data from independent tests. The calibrated simulations are mesh independent and correctly reproduce all qualitative aspects of the coupled damage evolution processes. They also correctly predict delamination sizes and shapes, the density of transverse ply cracks, the growth rate of splitting cracks, softening of the global stress–strain curve, and the ultimate strength. A sensitivity analysis relates variability in cohesive law parameters to predicted deviance in engineering properties. Given the known variability in cohesive law parameters, the predicted deviance in ultimate strength agrees with that in experimental data. The importance of including the interactions between different crack systems and non-localized shear deformation is demonstrated by suppressing the presence of separate mechanisms; the predicted delamination shapes, splitting crack growth rate, and the stress–displacement relationship fall into significant error.

The development of ceramic composites with three-dimensional fiber reinforcement architectures formed by textile methods has led to the potential for active shape-morphing surfaces that can operate in high temperature and variable pressure environments. This technology is of particular interest for hypersonic applications, where SCRAM jet engines require variable inlet geometry to achieve efficient flight over realistic flight profiles and variable flight conditions. The experiments reported here show that significant shape morphing can be achieved and good control of the shape sustained even in the presence of large temperature and pressure gradients. Experiments were carried out using a subscale morphing hypersonic inlet with rectangular cross-section in a Mach 8 wind tunnel facility with a total temperature of 800 K. The upper surface of the inlet consisted of a C–SiC composite plate (0.7 mm thick, 37.5 cm long, and 11 cm wide) connected to five actuators through a triangular truss support structure. The lower surface was a flat plate instrumented with an array of pressure taps along the flow centerline. As the shape varied, the surface contour was reliably controlled for high efficiency, low loss compression. A factor of six inlet area ratio variation was achieved and good agreement with model predictions was observed.

We demonstrate that traditional cohesive zone (CZ) elements cannot be accurate when used in conjunction with solid elements with arbitrary intra-element cracking capability, because they cannot capture the load transfer between cohesive interfaces and the solid elements when crack bifurcation or coalescence occurs. An augmented cohesive zone (ACZ) element based on the augmented finite element method formulation is therefore proposed. The new element allows for arbitrary separation of the cohesive element in accordance with the crack configuration of the abutting solid elements, thus correctly maintaining the non-linear coupling between merging or bifurcating cracks. Numerical accuracy and effectiveness of the proposed ACZ element are demonstrated through several examples. Copyright 2011 John Wiley & Sons, Ltd.

A recent theory has suggested that populations of migrating and proliferating cells can create network structures by responding to strain cues associated with the cell density variations that arise during network formation. Unlike prior theories of network formation, the strain-cue mechanism leads to nonfractal networks, consisting of closed loops rather than tree-like morphologies. In this paper, the possibility is suggested of developing a synthetic process for fabricating networks that mimic the mechanisms present in the theory. Such a biomimetic process should replicate three phenomena: (1) the extension of the existing network domain should be governed by the strain field that exists just outside the existing domain, rather than the strains within the domain; (2) the process should be stochastic; and (3) a relaxation mechanism must be present by which the strains that induce network extension at any location will fade with time. Simulations imply values for the key parameters of these mechanisms to achieve useful networks. Possible routes to realizing a biomimetic system are discussed.

As part of the quest to add the infraply scale to high-fidelity simulations of damage evolution in composites, a model of the phenomenon of delamination jumping across transverse plies is formulated by using nonlinear cohesive fracture models in the augmented finite element method (A-FEM). The nonlinearity of the fracture process zone and the interaction between multiple cracks combines to determine the details of how the delamination jump occurs. Simulations reveal that the jumping process starts with the triggering of a sequence of kinking cracks branching from the propagating delamination crack into the transverse plies. The first few kinking cracks arrest within the transverse plies just above the further interface because of the crack-retarding effects of the nonlinear process zone and the effects of material heterogeneity. Eventually, one kinking crack reaches the interface and initiates a new delamination crack, a step that is accom- panied by a significant load spike. The competition between delamination and kinking cracks shows global-local coupling: kinking cracks are triggered when the local stress satisfies a critical condition, but a kinking crack does not reach the second interface and initiate the new delamination crack until the global energy release rate reaches the kinking crack toughness. This suggests that the jumping process is con- trolled more by deterministic load and geometrical factors than by stochastic flaw populations. DOI: 10.1061/(ASCE)AS.1943-5525 .0000008. © 2011 American Society of Civil Engineers.

First introduced over a decade ago, the Binary Model has evolved into a computationally efficient tool for predicting the properties of textile composites. Key to the formulation is the question of what details of the textile composite and the distributions of stress, strain, temperature, etc., are necessary and sufficient to represent the physics of the problem adequately and to ensure useful engineering predictions. This paper is concerned specifically with the prediction of the ultimate strength in cases where failure follows a single substantial local damage event, such as the rupture or kinking of a tow or the creation of a shear band mediated by matrix damage, without further increase in the external load. The accuracy of predictions is assessed for some triaxially braided carbon/epoxy composites. A gauge length is introduced that is suggested by the micromechanics of the failure mechanisms. Predictions are made by reference to strains that are averaged over a volume whose sides are commensurate with this gauge, but nevertheless retain spatial variations associated with the textile architecture. Failure criteria for tow rupture and matrix shear failure are taken from a single un-notched tensile test; the calibrated model then successfully predicts the failure mechanism (matrix shear or fiber rupture) and ultimate strength in un-notched and open-hole tension tests for any orientation of the textile fabric relative to the load axis, as well as bending and simple shear tests. The successful predictions are made using strains calculated for an entirely elastic representation of the material, which is possible because of the brittle character of the stress–strain curves. Predictions are also attempted using strains computed under the assumption that the textile material is homogeneous. These predictions are significantly inferior.

A comparison of substantial published data for 3D woven, stitched and pinned composites quantifies the advantages and disadvantages of these different types of through-thickness reinforcement for in-plane mechanical properties. Stitching or 3D weaving can either improve or degrade the tension, compression, flexure and interlaminar shear properties, usually by less than 20%. Furthermore, the property changes are not strongly influenced by the volume content or diameter of the through-thickness reinforcement for these two processes. One implication of this result is that high levels of through-thickness reinforcement can be incorporated where needed to achieve high impact damage resistance. In contrast, pinning always degrades in-plane properties and fatigue performance, to a degree that increases monotonically with the volume content and diameter of the pins. Property trends are interpreted where possible in terms of known failure mechanisms and expectations from modelling. Some major gaps in data and mechanistic understanding are identified, with specific suggestions for new standards for recording data and new types of experiments.

In this paper nonlinear cohesive fracture models with cohesive parameters and laminar elasticity typical of polymer composites are used to study the initiation and propagation of a transverse intra-ply crack that is coupled to possible delaminations at the ply interfaces in a [0/90/0°] laminate. The evolution of the transverse crack is found to be more complex than previously described, involving initial growth, growth along the ply in a tunneling mode, and expansion across the thickness of the ply in a plane strain mode. For the coupled crack system, two failure modes are distinguished: (1) complete tunneling propagation of the transverse crack before any delamination occurs, followed by delamination initiation and propagation; and (2) simultaneous propagation of the transverse and delaminations cracks. The former process is always stable, is favored by large values of the mode II to mode I toughness ratio and low values of the cohesive strength, and is predicted to be the prevalent failure sequence for polymer composites. The latter process is often unstable, because it tends to occur when the cohesive strength is so high that the stress for initiating the transverse crack exceeds the stress required for its tunneling propagation. The nonlinear fracture models provide a unified description of the entire process of initiation and crack propagation. If the delamination cracks are modeled by linear elastic fracture mechanics, substantially inaccurate predictions result for the onset of delamination cracking and for the tunneling crack initiation from a pre-existing flaw.

An augmented finite element method (“A-FEM”) is presented that is a variant of the method of Hansbo and Hansbo (Comput Methods Appl Mech Eng, 193: 3523–3540, 2004), which can fully account for arbitrary discontinuities that traverse the interior of elements. Like the method of Hansbo and Hansbo, the A-FEM preserves elemental locality, because element augmentation is implemented within single elements and involves nodal information from the modified element only. The A-FEM offers the additional convenience that the augmentation is implemented via separable mathematical elements that employ standard finite element nodal interpolation only. Thus, the formulation is fully compatible with standard commercial finite element packages and can be incorporated as a user element without access to the source code. Because possible discontinuities include both elastic heterogeneity and cracks, the A-FEM is ideally suited to modeling damage evolution in structural or biological materials with complex morphology. Elements of a multi-scale approach to analyzing damage mechanisms in laminated or woven textile composites are used to validate the A-FEM and illustrate its possible uses. Key capabilities of the formulation include the use of meshes that need not conform to the surfaces of heterogeneities; the ability to apply the augmented element recursively, enabling modeling of multiple discontinuities arising on different, possibly intersecting surfaces within an element; and the ease with which cohesive zone models of nonlinear fracture can be incorporated.

A new paradigm for ceramic composite structural components enables functionality in heat exchange, transpiration, detailed shape, and thermal strain management that significantly exceeds the prior art. The paradigm is based on the use of three-dimensional fiber reinforcement that is tailored to the specific shape, stress, and thermal requirements of a structural application and therefore generally requires innovative textile methods for each realization. Key features include the attainment of thin skins (less than 1 mm) that are nevertheless structurally robust, transpiration holes formed without cutting fibers, double curvature, compliant integral attachment to other structures that avoids thermal stress buildup, and microcomposite ceramic matrices that minimize spalling and allow the formation of smooth surfaces. All these features can be combined into structures of very varied gross shape and function, using a wide range of materials such as all-oxide systems and SiC and carbon fibers in SiC matrices. Illustrations are drawn from rocket nozzles, thermal protection systems, and gas turbine engines. The new design challenges that arise for such material/structure systems are being met by specialized computational modeling that departs significantly in the representation of materials behavior from that used in conventional finite element methods.

The uncertain quality of composites, due to variability in the mechanical response, forces design engineers to employ high safety margins to ensure that the design requirements are met. Especially for textile composites, an improved assessment of the quality of any composite material is achieved by identification and simulation of the inherent uncertainty in the reinforcement geometry. This paper presents such a comprehensive multi-scale strategy to develop realistic stochastic replicas of a composite material, with emphasis on the identification step. First, the scatter in the tow reinforcement is characterised on the short-range (meso-scale) and long-range (macro-scale) from high-resolution images. Next, a probabilistic uncertainty quantification method is proposed to analyse the variability of each path parameter in terms of average trend, standard deviation and correlation information. This set of statistical information is essential to reproduce the random textile geometry in a numerical simulation approach. The multi-scale framework delivers representative models in the WiseTex format and is demonstrated for a carbon-epoxy 2/2 twill woven composite produced by resin transfer moulding. ispartof: Composites Science and Technology vol:122 pages:122-129 status: published

The quality of high-performance composite structures is difficult to predict. Variability in the macroscopic performance is dominated by the spatial randomness in the geometrical characteristics of the reinforcement, especially for textile composites. This work provides a roadmap for generating realistic virtual textile specimens spanning multiple unit cells, which are required to perform high-fidelity simulations. First, the geometrical variability in the reinforcement structure is experimentally quantified on the meso- and macro-scale in terms of average trends, standard deviations and correlation lengths. Next, each reinforcement parameter is modelled by the sum of its average trend and its zero-mean deviations, which are both determined by analysing experiments. Virtual specimens are then created using advanced simulation techniques that match the experimental statistics. Depending on the nature of measured correlations, the simulation technique is either a Monte Carlo Markov Chain method, a cross-correlated Karhunen–Loeve Series Expansion technique or a Fourier Transform method used in combination with a Markov ` Chain algorithm. In a last step, a virtual representation of the textile geometry is constructed in geometrical modelling software, such as the commercially available WiseTex software. The multi-scale framework is validated using data for a carbon–epoxy 2/2 twill woven composite produced by resin transfer moulding: the simulated tow deviations trends replicate the target statistics. ispartof: Computer Methods in Applied Mechanics and Engineering vol:310 pages:906-934 status: published

Previously published experimental data for the fracture of bone are analysed using cohesive zone models to deal with the non-linear processes of material failure. Non-linear effects dominate tests; linear-elastic fracture mechanics cannot give an internally consistent account of the data. In contrast, the same cohesive traction law can account accurately for substantial differences in the fracture data for normal (non-diseased or aged) adult human humeral cortical bone taken at two laboratories, where different specimen configurations were used. Further model calculations illustrate more general characteristics of the non-linear fracture of bone and demonstrate in particular that the fracture toughness of bone deduced via LEFM from test data is not a material constant, but will take different values for different crack lengths and test configurations. LEFM can be valid only when the crack is much longer than a certain length scale, representative of the length of the process zone in the cohesive model, which for human cortical bone ranges from 3 to 10 mm. Naturally-occurring bones and the specimens used to test them are not much larger than this dimension for most relevant orientations, implying the necessity of non-linear fracture models. The analysis of fracture data also requires proper representation of the approximately orthotropic elasticity of the bone specimen. The fracture test data show that human humeral cortical bone is much more compliant in shear in the plane of the test specimen than would be inferred from the relevant Young’s moduli, if the material were isotropic in that plane, as is often assumed. If the specimen is incorrectly assumed to be isotropic in that plane, the initial measured compliance cannot be reproduced to within a factor of four and the fracture toughness deduced from the measured work of fracture will be overestimated by ∼30%.

Methods are presented for creating biocompatible composites with magnetic functionality by incorporating magnetic nanoparticles in a biodegradable polymer matrix. A wide range of volume fractions for magnetic particle loading and therefore magnetization density are achievable. The nanoscale of the particles aids in achieving dispersion, so that variations in physical and chemical properties occur on scales much less than that of cells. Sufficient magnetization is achieved to enable actuation of the material, i.e., the generation of strains of biologically significant magnitudes using remotely applied magnetic fields. The magnitude of the actuation is demonstrated to enable fluid pumping and create local strains in cell aggregates that should be sufficient to stimulate cell growth and differentiation. The composite materials can be formed into random-pore scaffold materials with controlled porosity, pore shape, and pore connectivity. They can also be shaped by pressing, rolling, or drawing and joined by thermoplastic welding, so that ordered three-dimensional scaffold structures and various shell structures, such as tubes and toroids, can be fabricated. When the composite sheets are formed into tubes, the application of a moving magnetic field induces simulated peristalsis. When intestinal cells were seeded on the composite sheets, cells remained viable and grew rapidly in vitro.

This paper examines the effect of pinning on the flexural properties, fatigue life and failure mechanisms of carbon/epoxy laminates. Five-harness satin weave carbon/epoxy laminates were reinforced in the through-thickness direction with different volume fractions and sizes of fibrous composite pins. Microscopic examination of the laminates before flexural testing revealed that the pins caused considerable damage to the microstructure, including out-of-plane crimping, in-plane distortion and breakage of the fibres and the formation of resin-rich zones around each pin. The pins also caused swelling of the laminate that reduced the fibre volume content. Despite the damage, the pins did not affect the flexural modulus of the laminate. However, increasing the volume content or diameter of the pins caused a steady decline in the flexural strength and fatigue life, which appear to be governed by fiber rupture on the tensile side of the laminate. Property changes are discussed in terms of transitions in the dominant failure mechanisms due to the presence of pins.

The difficult challenge of simulating diffuse and complex fracture patterns in tough structural composites is at last beginning to yield to conceptual and computational advances in fracture modeling. Contributing successes include the refinement of cohesive models of fracture and the formulation of hybrid stress-strain and traction-displacement models that combine continuum (spatially averaged) and discrete damage representations in a single calculation. Emerging hierarchical formulations add the potential of tracing the damage mechanisms down through all scales to the atomic. As the models near the fidelity required for their use as virtual experiments, opportunities arise for reducing the number of costly tests needed to certify safety and extending the design space to include material configurations that are too complex to certify by purely empirical methods.

The effect of through-thickness reinforcement by fibrous pins on the static tensile strength, fatigue life and failure mechanisms of single lap joints made of carbon/epoxy composite is investigated. Pinning is highly effective in increasing the ultimate strength, elongation limit and fatigue life. Improvements to the monotonic and fatigue properties are attributed to transitions in the failure mechanisms, from unstable joint debonding in the absence of pins to stable debonding in the presence of pins followed by ultimate failure by pin pull-out or shear fracture or tensile laminate rupture. Which mechanism induces ultimate failure in the presence of pins depends on their volume content and diameter. The trends with volume content and diameter can be predicted qualitatively using analytical results from a previously published model of the deformation mechanics of pins loaded in mixed mode.

The effects of through-thickness reinforcement of carbon/epoxy laminates with thin pins on the in-plane tensile properties, tensile fatigue life and failure mechanisms are investigated. Tensile studies in the 0 fibre direction are performed on unidirectional and quasiisotropic laminates reinforced with different volume contents and sizes of fibrous composite z-pins. Microstructural analysis reveals that z-pinning causes several types of damage, including out-of-plane fibre crimping, in-plane fibre distortion, mild dilution of the in-plane fibre volume fraction due to laminate swelling, and clusters of broken fibres. In unidirectional composites, resin pockets form around pins and coalesce into continuous resin channels at higher z-pin contents. Young’s modulus falls only a few percent at most, due partly to in-plane fibre dilution and partly to fibre waviness. Monotonic tensile strength is degraded more significantly, falling linearly with both pin content and pin diameter. Comparison with prior data shows that the rate of degradation is evidently a strong function of the particular pin insertion method used. Failure mechanisms include fibre rupture, presumably affected by broken fibres, and, in unidirectional laminates, longitudinal splitting cracks emanating from resin pockets. Whereas non-pinned laminates show very modest fatigue effects, the pinned laminates exhibit strong fatigue effects, with strength falling by as much as 33% at 10 6 cycles. The slope of the fatigue life (S–N) curve tends to increase in magnitude with pin content and density. Limited evidence and prior literature suggest that the dominant fatigue mechanism may be progressive softening and fibre damage in misaligned segments of in-plane fibres. 2005 Elsevier Ltd. All rights reserved.

A simple and efficient computational approach is presented for analyzing the benefits of through-thickness pins for restricting debond failure in joints. Experiments have shown that increases in debond resistance and ultimate strength depend on the material, size, density, location, and angle of deployment of the pins and the mechanisms of pin deformation, which are complex and strongly affected by the mode ratio of the debond crack. Here the mechanics problem is simplified by representing the effects of the pins by tractions acting on the fracture surfaces of the debond crack. The tractions are prescribed as functions of the crack displacement, which are available in simple forms that summarize the complex deformations to a reasonable accuracy. The resulting model can be used to track the evolution of competing failure mechanisms, including tensile or compressive failure of the adherends, joint debonding (creating leak, for example, if the joint is in a pipeline), and ultimate failure associated with pin rupture or pullout. Calculations illustrating complex mode ratio variations are presented for a lap joint specimen comprising curved laminate segments cut from pipes.

A study to test the correlations among neat-resin and composite properties was performed, to identify possible ways of reducing the number of tests necessary to screen candidate resins for use in aerospace structures. Neat-resin and composite tests were conducted for four different resin matrices, whose neat properties varied over a wide range, allowing reasonably strong tests of correlations. Since different fiber architectures and fiber types are often of interest to a designer, tested correlations included those between composite coupons containing the same resin but with different fibers and lay-up. Composite structural properties were represented by unnotched tension, open-hole tension, unnotched compression, and open-hole compression. Correlations were sought between these and neat-resin properties, composite shear strength, and Mode I composite delamination toughness. Strong linear correlations, which are proposed to be the most useful because they discriminate best between different resin systems, were found in certain cases, but not others. Most significantly, an Iosipescu shear test for a [0°/90°] composite of one fiber type was shown to be a good predictor, for the tested resins, of open-hole compression and unnotched compression in composites with different fibers and architecture; and a fair predictor of open-hole tension. Open-hole tension strength was shown to correlate better with neat-resin fracture toughness, but neat-resin properties were otherwise inferior indicators of most composite properties. While data for further resins are needed to enrich the statistical base, some rationalizations can be found for the presence of the stronger correlations that were observed. The correlations described here suggest that reduced test matrices, containing tests for only Iosipescu composite shear and either neat-resin toughness or Mode I delamination toughness, may suffice to evaluate the likely structural performance of composites containing new candidate resins. The tests could be performed on a standard fiber type and architecture, yet be predictors for other fiber types and architecture.

Data for fracture in human humeral cortical bone are re-analyzed to assess the validity for this material of linear-elastic fracture mechanics (LEFM), which is the standard method of analyzing toughness and one basis for analyzing clinical data relating to bone quality. A nonlinear fracture model, which is based on representing the damage zone in the bone by a cohesive model, is calibrated against a number of sets of test data for normal (not diseased or aged) human cortical bone taken from cadavers. The data consist of load vs. load-point displacement measurements from standard compact-tension fracture tests. Conventional LEFM is unable to account for the shape of the load-displacement curves, but the nonlinear model overcomes this deficiency. Calibration of the nonlinear model against one data curve leads to predictions of the peak load and the displacement to peak load for two other data curves that are, for this limited test set, more accurate than those made using LEFM. Furthermore, prior observations of damage mechanisms in bone are incompatible with the modeling assumption of LEFM that all nonlinearity is confined to a zone much smaller than the specimen and the crack length. The predictions of the cohesive model and the prior observations concur that the length of the nonlinear zone in human cortical bone varies in the range 3-10 mm, which is comparable to or larger than naturally-occurring bones and the specimens used to test them. We infer that LEFM is not an accurate model for cortical bone. The fracture toughness of bone deduced via LEFM from test data will not generally be a material constant, but will take different values for different crack lengths and test configurations. The accuracy of using LEFM or single-parameter fracture toughness for analyzing the significance of data from clinical studies is called into question. The nonlinear cohesive zone model is proposed to be a more accurate model of bone and the traction-displacement or cohesive law is hypothesized to be a material property. The cohesive law contains a more complete representation of the mechanics of material failure than the single-parameter fracture toughness and may therefore provide a superior measure of bone quality, e.g., for assessing the efficacy of therapy for osteoporosis.

This paper deals with the elastic interaction of multiple through-width delaminations in laminated plates subject to static out of plane loading and deforming in cylindrical bending. A model has been formulated utilizing the classical theory of the bending of beams and plates and accounting for non-frictional contact along the delamination faces. Strong interaction effects arise between the delaminations including shielding and amplification of the energy release rate and modification of the mode ratio as compared to a structure with only a single delamination. Such behavior has been summarized in maps that completely characterize the response of a system of two delaminations in a cantilever beam. The quasi-static propagation of the system of delaminations is also strongly controlled by the delamination interactions, which lead to local snap-back and snap-through instabilities, crack arrest and crack pull-along. The results show similarity to those for cracked infinite bodies, but the finite-thickness of the plate plays an important role and gives rise to more complex behaviors. The stability of the equality of length of a system of n delaminations is controlled by their spacing. Finite element calculations confirm that the model proposed here is accurate, except when the difference in the length of the interacting delaminations is less than a few times the separation of their planes.

The problem is considered of a fibre that is driven dynamically, by compression at one end, into a matrix. The fibre is not initially bonded to the matrix, so that its motion is resisted solely by friction. Prior work based on simplified models has shown that the combination of inertial effects and friction acting over long domains of the fibre–matrix interface gives rise to behaviour that is far more complex than in the well-known static loading problem. The front velocity may depart significantly from the bar wave speed and regimes of slip, slip/stick and reverse slip can exist for different material choices and loading rates. Here more realistic numerical simulations and detailed observations of dynamic displacement fields in a model push-in experiment are used to seek more complete understanding of the problem. The prior results are at least partly confirmed, especially the ability of simple shear-lag theory to predict front velocities and gross features of the deformation. Some other fundamental aspects are newly revealed, including oscillations in the interface stresses during loading; and suggestions of unstable, possibly chaotic interface conditions during unloading. Consideration of the experiments and two different orders of model suggest that the tentatively characterized chaotic phenomena may arise because of the essential nonlinearity of friction, that the shear traction changes discontinuously with the sense of the motion, rather than being associated with the details of the constitutive law that is assumed for the friction. This contrasts with recent understanding of instability and ill-posedness at interfaces loaded uniformly in time, where the nature of the assumed friction law dominates the outcome.

A trend in the last decade towards models in which nonlinear crack tip processes are represented explicitly, rather than being assigned to a point process at the crack tip (as in linear elastic fracture mechanics), is reviewed by a survey of the literature. A good compromise between computational efficiency and physical reality seems to be the cohesive zone formulation, which collapses the effect of the nonlinear crack process zone onto a surface of displacement discontinuity (generalized crack). Damage mechanisms that can be represented by cohesive models include delamination of plies, large splitting (shear) cracks within plies, multiple matrix cracking within plies, fiber rupture or microbuckling (kink band formation), friction acting between delaminated plies, process zones at crack tips representing crazing or other nonlinearity, and large scale bridging by through-thickness reinforcement or oblique crack-bridging fibers. The power of the technique is illustrated here for delamination and splitting cracks in laminates. A cohesive element is presented for simulating three-dimensional, mode-dependent process zones. An essential feature of the formulation is that the delamination crack shape can follow its natural evolution, according to the evolving mode conditions calculated within the simulation. But in numerical work, care must be taken that element sizes are defined consistently with the characteristic lengths of cohesive zones that are implied by the chosen cohesive laws. Qualitatively successful applications are reported to some practical problems in composite engineering, which cannot be adequately analyzed by conventional tools such as linear elastic fracture mechanics and the virtual crack closure technique. The simulations successfully reproduce experimentally measured crack shapes that have been reported in the literature over a decade ago, but have not been reproduced by prior models.

Engineering tests and full-field strain measurements are used to assess the accuracy of predictions made by the Binary Model, a computational tool for textile composites. The test case is a carbon fiber/SiC matrix composite, in which the reinforcement is a three-dimensional angle-interlock weave. The test composites are thin, having been designed for heat exchanger applications. The thinness leads to strong variations in local strains and strong effects of tow waviness upon macroscopic elasticity. The model performs well in predicting both local variations in strain and macroscopic elasticity. The effect of averaging local strains over variable gauge lengths is explored. Strains averaged over an appropriate gauge length have recently been proposed as the preferred measures of strain for use in local failure criteria.

The field of dynamic fracture has been enlivened over the last 5 years or so by a series of remarkable accomplishments in different fields—earthquake science, atomistic (classical and quantum) simulations, novel laboratory experiments, materials modeling, and continuum mechanics. Important concepts either discovered for the first time or elaborated in new ways reveal wider significance. Here the separate streams of the literature of this progress are reviewed comparatively to highlight commonality and contrasts in the mechanics and physics. Much of the value of the new work resides in the new questions it has raised, which suggests profitable areas for research in the next few years and beyond. From the viewpoint of fundamental science, excitement is greatest in the struggle to probe the character of dynamic fracture at the atomic scale, using Newtonian or quantum mechanics as appropriate (a qualifier to be debated!). But lively interest is also directed towards modeling and experimentation at macroscales, including the geological, where the science of fracture is pulled at once by fundamental issues, such as the curious effects of friction, and the structural, where dynamic effects are essential to proper design or certification and even in manufacture.

Integrally formed ceramic matrix composite structures are being developed for a range of hot-structure applications involving active cooling. Integral textile structures offer several advantages: 1) Joints between ceramicand other materials in hot zones can be avoided. 2) Thin skins (

Experiments are reported that explore the mechanics of single pins or rods that bridge a delamination crack in a miniature model specimen. The effects of material and geometrical parameters are determined by varying the angle of the rod, its material, and the material in which it is embedded. Different tests represent mode I and mode II loading, with respect to a pre-existing delamination crack. Many observed mechanisms are similar to those previously reported for stitches and in limited studies on rods. They include debonding and sliding of the rod relative to the substrate, lateral deflection of the rod into the substrate (when mode II is present), rod pullout, and rod rupture. Sliding in mode I can be explained by assuming that pullout is resisted by uniform friction, which has a modest value (, 1 – 20 MPa). However, when mode II loading is present and the rod deflects laterally, a more complicated friction behaviour is suggested. Peak load occurs well after the whole rod has begun to slide out of the specimen, implying that the pullout process is stable in mode II to large displacements. This, together with the high values observed for the peak loads and displacements suggest the presence of an enhanced friction zone (snubbing effect) extending over the segment of the rod that has been laterally deflected by mode II loading. This zone can grow under increasing shear displacements even after the whole rod begins to slide, leading to increasing shear loads (stable pullout). Various characteristics of the pullout experiments are consistent with this model. q 2004 Published by Elsevier Ltd.

Elementary analyses of a standard compression test and a new test configuration for combined compression and shear illuminate the mechanisms of deformation of dry fiber bundles in fiber preforms under multi-axial loads. Such stress states are central to fiber bundle behavior in thick preforms that are being manipulated in pressurized tools. Sliding, buckling, compression, and shear deformation mechanisms are observed to operate at the single fiber bundle (tow) level. Shear includes deformation transverse to the axis of a tow (changes in cross-sectional shape) and axial shear (shear deflection of a tow segment acting as a short beam). Not all of these mechanisms have been addressed before in the extensive literature on textile deformation. The presence of multiple mechanisms complicates the quest for simple experiments that could be treated as standards for data acquisition. The need for new tests to be invented and standardized is highlighted.

A previously published computational model of textile composites known as the Binary Model is generalized to allow systematic study of the effects of mesh refinement. Calculations using different meshing orders show that predictions of local strains are mesh independent when the strains are averaged over gauge volumes whose dimensions are greater than or equal to approximately half the width dimensions of a single tow. Strains averaged over such gauges are favored for use in failure criteria for predicting various mechanisms of failure in a textile composite, including transverse cracking within tows, kink band failure in compression, tensile tow rupture, and shear failure. For the highest order representations (infinitely dense meshes), the generalized formulation of the Binary Model necessarily approaches conventional finite element meshing strategies for textile composites in its predictions. However, the work reported here implies that usefully accurate predictions of spatially averaged strains can be obtained even at the lowest level of mesh refinement. This preserves great simplicity in the model set-up and rapid computation for relatively large features of structural components. Calculations for some textile structures provide insight into the strength or relative absence of textile effects in local strains for different loading configurations.@DOI: 10.1115/1.1605117#

Prior experiments have revealed exceptionally high values of the work of fracture (0.4– 1.1 MJm −2 ) in carbon/epoxy 3D interlock woven composites. Detailed destructive examination of specimens suggested that much of the work of fracture arose when the specimens were strained well beyond the failure of individual tows yet still carried loads ∼1 GPa . A mechanism of lockup amongst broken tows sliding across the final tensile fracture surface was suggested as the means by which high loads could still be transferred after tow failure. In this paper, the roles of weave architecture and the distribution of flaws in the mechanics of tow lockup are investigated by Monte Carlo simulations using the so-called Binary Model. The Binary Model was introduced previously as a finite element formulation specialised to the problem of simulating relatively large, three-dimensional segments of textile composites, without any assumption of periodicity or other symmetry, while preserving the architecture and topology of the tow arrangement. The simulations succeed in reproducing all qualitative aspects of measured stress–strain curves. They reveal that lockup can indeed account for high loads being sustained beyond tow failure, provided flaws in tows have certain spatial distributions. The importance of the interlock architecture in enhancing friction by holding asperities on sliding fibre tows into firm contact is highlighted.

Inertial effects in the mechanism of fibre pullout (or push-in) are examined, with emphasis on how the rate of propagation of stress waves along the fibre, and thence the pullout dynamics, are governed by friction and the propagation of companion waves excited in the matrix. With a simple shear lag model (assuming zero debond energy at the fibre/matrix interface), the effect of uniform frictional coupling between the fibre and the matrix is accounted for in a straightforward way. Analytical solutions are derived when the pullout load increases linearly in time. The process zone of activated material is generally divided into two or three domains along the axis of the fibre. Within these domains, slip in the sense implied by the load, slip in the opposite sense (reverse slip), and stick may be observed. The attainable combinations define three regimes of behavior, which are realized for different material parameter values. The elastodynamic problem is also solved more accurately using a plane stress finite element method, with friction represented by an interfacial cohesive zone. The predictions of the shear lag theory are broadly confirmed.