Search

This paper deals with the formulation, calibration, and validation of the Lattice Discrete Particle Model (LDPM) suitable for the simulation of the failure behavior of concrete. LDPM simulates concrete at the meso-scale considered to be the length scale of coarse aggregate pieces. LDPM is formulated in the framework of discrete models for which the unknown displacement field is not continuous but only defined at discrete points representing the center of discrete particles. The size and distribution of the particles is obtained by idealizing the geometry of the concrete's internal structure. Discrete compatibility and equilibrium equations are used to formulate the governing equations of the LDPM computational framework. Particle contact behavior represents the mechanical interaction among adjacent aggregate particles through the embedding mortar. Such interaction is governed by meso-scale constitutive equations simulating meso-scale tensile fracturing with strain-softening,cohesive and frictional shearing, and nonlinear compressive behavior with strain-hardening. The present, Part I of this two-part study deals with model formulation leaving model calibration and validation to the subsequent., Submitted for publication in Cement and Concrete Composites. Sponsored in part by U.S. Army Engineer Research and Development Center (RDEC). Prepared in cooperation with Engineering and Software System Solutions, Inc., San Diego, CA. Government or Federal Purpose Rights License. The original document contains color images.

The Lattice Discrete Particle Model (LDPM) formulated in the preceding Part I of this study is calibrated and validated in the present Part II. Calibration and validation is performed by comparing the results of numerical simulations with experimental data gathered from the literature. Simulated experiments include uniaxial and multiaxial compression, tensile fracture, shear strength, and cycling compression tests., Submitted for publication in Cement & Concrete Composites. Sponsored in part by U.S. Army Engineer Research and Development Center (ERDC), Vicksburg, MS. Prepared in cooperation with Engineering and Software Systems Solutions, Inc., San Diego, CA; and ERDC, Vicksburg, MS.

The Mori-Tanaka micromechanics method is used to predict the effective properties of composite materials consisting of a polymer matrix reinforced by a fiber made of a transformation shape memory effect (SME) material. The composite response is plotted for combinations of the following scenarios: (1) isothermal longitudinal and transverse stress input, (2) stress- free thermal loading, (3) constant fiber thermoelastic properties, and (4) thermoelastic fiber properties that vary with the martensite volume fraction. For the case of an isothermal stress input, the composite transformation stress, the maximum transformation strain, and the hysteresis are all reduced vis-a-vis the monolithic SME material. In contrast to a monolithic SME material, stress- free thermal loading of a SME composite can produce a transformation strain. It is shown that closed form solutions for the effective martensite and austenite start temperatures can be derived, that they are sensitive to the stress-free reference temperature of the fiber, and that the stress-free austenite and martensite start temperatures are higher than those of the monolithic SME material.

The 3-D formulation of flexible rods with embedded line actuators is presented in this paper. Both the rods and the line actuator are assumed to be initially curved and relatively positioned in an arbitrary way. The deformed configurations of the rod and actuator are connected by assuming that the principal planes of the rod remain in plane and inextensible in the deformed configuration. The resultant forces and moments in the rod and actuator are found by solving the equilibrium equations for both the rod and actuator and applying continuity of tractions on the rod-actuator interface. The formulation is reduced to 2-D and applied to the case of a Shape Memory Alloy (SMA) fiber embedded in a cylindrical rod. The deformed shapes of the rod under repeated thermal actuation and the resulting shape memory loss due to the development of residual stresses are-evaluated. Finally, the inverse problem of finding the required actuation force and initial curvature, to acquire a predetermined deformed shape, is solved in closed form for the 2-D cases.

The shape change of a stress free cylindrical flexible rod with embedded SMA actuators is modeled in this paper for rods with single or multiple SMA actuators placed parallel to the long axis of the rod for the first heating the SMA actuators. The distributed axial compressive force, transverse normal force, and bending moments that act on the rod due to the shape recovery of the SMA actuators have been given by Lagoudas and Tadjbakhsh. The deformed shape of the rod is found by solving the nonlinear equations of equilibrium of the rod. For multiple actuators the resultant forces and moments are considered. A design analysis is performed for the active rod with a single SMA actuator. Key design variables are Erod, the thermal bond strength of the rod to the SMA actuator, and the rod dimensions. Key design parameters are: maximum rod/actuator interfacial shear stress, rod strain, rod slenderness ratio, and rod deflection. An analysis is then performed which investigates the influence of the design variables on each of the design parameters.

The variational theory of three dimensional deformations of curved twisted and extensible elastic rods is obtained based entirely on the kinematical variables position and rotations. The constitutive relations that define the resistive couples and the axial force as gradients of the strain energy function are established. A candidate for the strain energy function on the basis of classical assumptions is presented.

A comprehensive research effort was conducted on constitutive and micromechanical modelling of granular soil. This includes: (1) the development of a new constitutive relation for granular media based on the contact law between two spheres; (2) an experimental investigation on the stress-strain response of a glass bead material with 46 monotonic and cyclic experiments on hollow cylinder specimens, most of them constant mean stress tests to measure deviatoric response and behavior of initial and subsequent yield loci; and (3) numerical simulations of the behavior of granular media using the discrete element method. The proposed constitutive law captures a number of key aspects of the observed stress-strain behavior of granular soils, and it predicts well the experiments on glass beads. Novel aspects of the proposed model include yield cones parallel to the failure envelope, and a basic relation between the field of elastoplastic moduli and the elastic constants of the material., See also Volume 3, AD-A238 158.

A comprehensive research effort was conducted on constitutive and micromechanical modelling of granular soil. This includes: (1) the development of a new constitutive relation for granular media based on the contact law between two spheres; (2) an experimental investigation on the stress-strain response of a glass bead material with 46 monotonic and cyclic experiments on hollow cylinder specimens, most of them constant mean stress tests to measure deviatoric response and behavior of initial and subsequent yield loci; and (3) numerical simulations of the behavior of granular media using the discrete element method. The proposed constitutive law captures a number of key aspects of the observed stress-strain behavior of granular soils, and it predicts well the experiments on glass beads. Novel aspects of the proposed model include yield cones parallel to the failure envelope, and a basic relation between the field of elastoplastic moduli and the elastic constants of the material., See also Volume 2, AD-A238 092.

This volume contains a selection of recent work by leading researchers in micromechanics that was presented at the IUTAM Symposium on Inelastic Deformation of Composite Materials at Rensselaer. The Symposium was made possible by the generous support of AFOSR, ARO, NSF, IUTAM and RPI. Thanks are due to the sponsors and to the local organizing committee for their support and work on behalf of the symposium. Composite materials, Inelastic deformation, Micromechanics

Nonlinear discrete element simulations were used to provide an insight on the nonlinear modelling of granular soil. These simulations were based on an incremental solution to the nonlinear problem of two spheres in contact, incorporated into discrete element TRUBAL which was further optimized for vector and parallel processing on the IBM 3090 supercomputer. It was found that this approach not only interprets successfully nonlinear behavior of soil, but also provides a wealth of information on the fabric changes during the loading. The yield surface of a granular medium, needed for defining the constitutive relation of such a medium, distorts by forming an apex in the direction of loading while becoming flatter in the opposite direction. This contrary to the practice followed in modelling granular media where the yield surface of soils are typically assumed to retain the same shape. Origin of this distortion phenomenon lies in the texturing (or fabric anisotropy) which occurs in the direction of prestraining, as well as in the redistribution of interparticle contact forces in the absence of significant particle movement during the small strain probes needed to define the yield surface. These phenomena cause certain slip systems to be activated which produce the characteristic apex which appear in the yield surface in the loading direction. Therefore, distribution and magnitude of the contact forces are critical for a good understanding of the macroscopic response of the medium. Accurate modelling of the contact force distribution can be achieved only if the behavior at the contact is fully understood and rigorously modelled., See also Volume 1, AD-A238 091.

A description of equipment purchased under an AFOSR equipment grant is provided. This equipment is being used to extend the capabilities of the existing MTS servohydraulic axial-torsional testing machine to allow high precision tests on hollow cylinder soil specimens at constant mean stress levels, especially for specimens undergoing very small strains. The principal equipment items acquired are a computer based data acquisition and control system, a new hollow cylinder triaxial cell, a number of transducers and associated electronics, and mechanical hardware, including a new hydraulic power supply. In addition, several equipment items have been acquired with the RPI matching funds for the existing 100 g-ton geotechnical centrifuge, including a container for holding models during testing and a fork lift for model transport. Keywords: Laboratory/test equipment; Soil mechanics; Hollow cylinder tests; Data acquisition and control system; Geotechnical centrifuge; Soil dynamics.

A summary of results is presented on the subject of damage development in metal and polymer matrix composite laminates. The following technical developments are described: (i) Evaluation of crack densities, stiffness changes, and fiber stresses caused by cyclic loading in three 6061-0 AlB laminates, with O8 (0/90)2s, and (o/+ or - 45/90/0 + or - 45/1/290s) layers. This problem is solved in an incremental way, with regard for interaction between plastic deformation and matrix crack growth in individual plies. Saturation damage states are predicted at different levels of steady cyclic loading. Good comparison is obtained with available experimental data, (ii) Analysis of first ply failure in polymer matrix composites. The influence of ply thickness on strength is predicted in terms of flaw nucleation mechanisms, and (iii) Analysis of distributed damage caused in a composite ply by either transverse cracks or fiber breaks. Several methods, such as self-consistent estimates, shear lag approximations, crack array models, and finite element analysis of cracks in an embedded ply were employed. It was found that these methods give very similar predictions of stiffness reductions of plies and laminates, and that these predictions are in good agreement with available experimental data.

Modeling of gun propellant combustion requires reliable input data on the kinetics of individual reactions involved. In this work the HTP (high-temperature photochemistry) technique is used to provide such data over wide temperature ranges. Detailed studies of the H + NH3 yields NH2 + H2 and H + N2O yields N2 + OH reactions have been made. In both systems quantum mechanical tunneling is found to contribute significantly to the overall reaction. For the latter reaction it is shown that a second channel leading to NH + NO contributes less than 7 percent below 2000 k. Keywords: Atomic hydrogen; Nitrogen oxides; Ammonia; Gun propellant reactions; High-temperature kinetics; Non-Arrhenius kinetics; Quantum-mechanical tunneling.

The need for a micromechanical approach to modeling the stress-strain response of granular soil is discussed and justified. The report focuses on the small shear strain (gamma or = 0.01%) behavior, and investigates the validity of analytically modeling uniform, rounded-grained quartz sands by arrays of identical elastic quartz spheres. First the stress-strain properties of 6 regular arrays of spheres are studied, focusing on isotropic and transversely isotropic boundary loading. An analytical procedure is established for determining the elastic moduli of a random assemblage of equal elastic spheres of arbitrary mean porosity, subjected to isotropic confining pressure. The procedure uses the properties of the regular arrays already described, accounts for the spatial distribution of porosity, and calculates the macroscopic moduli through the self consistent method. The procedure was applied to compute the shear and bulk moduli of assemblages of quartz spheres which were then compared with static and dynamic measurements on quartz sands from the literature. The theoretical sands are significantly stiffer than actual soils due to the lower number of effective contacts in actual sands. However, excellent agreement was found with resonant column shear modulus measurements on Ottawa sand, after subjecting it to a large number of cycles of shear prestraining which increased the number of contacts toward the theoretical value.

Granular soil is presented in this work by 2-D random arrays of elastic, rough, quartz sphere using the 'distinct element' method. The original 3-D computer code TRUBAL, originally developed by Peter Cundall, has been modified at RPI by the introduction of a general solution to the Hertz-Mindlin contact problem. This was achieved by attaching a subroutine to the original code, which describes the nonlinear force-displacement relationship at the intergranular contacts, by means of plasticity theory and kinematic hardening. The above modified program (CONBAL-2) developed as part of another RPI project, can perform 2-D simulations and has already been used to study the dynamic small strain behavior as well as the large strain behavior of sand.

This report presents a brief summary of the principal results obtained in a research program on damage development in fibrous composite laminates. The following technical subjects are described: (i) Effect of transverse cracks and fiber breaks on stiffness changes in unidirectional and laminated plates. (ii) Effect of ply thickness on initial failure and on progressive cracking in brittle matrix laminates, and (iii) Analysis of progressive cracking in metal and polymer composite laminates. Work in progress is discussed as well. Keywords: Composite materials, Cracking, Damage accumulation.

The goal of this study was to develop a constitutive law for granular soil based on the particulate nature of the material. This is accomplished by a systematic, mostly analytical approach to the problem, starting from the response of the contact between two elastic rough spheres subjected to arbitrary normal and tangential forces, and continuing with the response of regular and random arrays of spheres. The following tasks were completed: a) study and compilation of the differential stress-strain relationships of several regular arrays of identical quartz spheres; b) use of the Self Consistent and Nonlinear Finite Element methods to calculate the small strain, monotonic and cyclic stress-strain behavior of random/regular arrays of identical quartz spheres loaded isotropically and anisotropically, including wave velocity predictions; and c) use of Nonlinear Distinct Element simulations of two-dimensional random arrays of quartz spheres to determine their small and large strain response, including the initial position and subsequent translation and distortion of yield surfaces. The main features of a proposed constitutive law for granular media are discussed. The law is basically the stress-strain equivalent of the force-deformation model for the contact between two spheres, enhanced to incorporate dilation and the distortion of yield surfaces due to prestrain which has been observed in granular media. The proposed stress-strain law includes an infinite number of yield surfaces of conical shape initially parallel to each other.

Exact relationships are derived between instantaneous overall thermal stress or strain vectors and instantaneous overall mechanical stifness or compliance, for two binary composite systems in which one of the phases may deform plastically. Also the local instantaneous thermal strain and stress concentration factors are related in an exact way to the corresponding mechanical concentration factors. The results depend on instantaneous thermoelastic constants and volume fractions of the phases. They are found for fibrous composites with two distinct elastically isotropic or transversely isotropic phases, and for any binary composite with elastically isotropic phases. The results indicate that in the plastic range the thermal and mechanical loading effects are coupled even if the phase properties of not depend on changes in temperature. The derivation is based on a novel decomposition procedure which indicates that spatially uniform elastic strain fields can be created in certain heterogeneous media by superposition of uniform phase eigen-strains with local strains caused by piecewise uniform strss fields which are in equilibrium with prescribed surface tractions. The method is extended to discretized microstructures, and also to analysis of moisture absorption and phase transformation effects on overall response and on local fields in the two composite materials. (Author)

This report summarizes recent results of studies on progressive ply cracking in fibrous laminates. Evaluation of stiffness changes caused by systems of aligned slit cracks which are parallel to the fiber direction in a unidirectional composite lamina is discussed. Results obtained by the self-consistent method are presented. Next, a procedure for estimating instantaneous crack densities and stiffness changes in a lamina subjected to a prescribed strain history is outlined. These results are extended to analysis of laminated composite plates under in-plane stresses. Specific examples and comparisons of analytical and experimental results are presented for two graphite-epoxy systems. Keywords: Composite materials; Cracking; Damage accumulation.

A cyclic strain approach to pore pressure buildup and liquefaction during earthquakes of saturated choesionless soils has been proposed and developed. One of the key findings has been the existence, for every potentially liquefiable site and sand layer, of a 'threshold ground surface acceleration,' a sub t, below which there is no pore pressure buildup. The value of a sub t is mainly a function of two soil parameters: the 'threshold shear strain' of the sand, gamma sub t, and its maximum shear modulus, G sub max. The existence of a sub t has been detected by several researchers in a number of laboratory studies. Also, the existence of gamma sub t and its range of values for quartz sands has been predicted from simple particulate mechanics considerations. The work presented herein was performed at RPI and constitutes an extension of the experimental study by Ladd and focuses on the effects of anisotropic consolidation and of very low relative densities on gamma sub t and on the rate of pore pressure buildup at cyclic strains slightly above gamma sub t. Two sands, Montery No. 0 sand and Banding Sand, were tested and the results are reported herein. The effect of anisotropic consolidation is important because NC sands in the field are typically anisotropically consolidated, and also because any attempt to extend the cyclic strain approach to earth structures and slopes must necessarily consider the effect of consolidation shear stresses. Testing very loose sand, D sub r = 20 percent, is important because very loose sand deposits in the field are usually the most susceptible to pore pressure buildup and liquefaction during earthquakes.

This report presents a detailed overview of the impact of read-only memory (ROM) chips on computing, and more specifically, numerical analysis. A review of the impact of VLSI technologies is given to indicate the role of ROM chips. A review of available ROM technologies is presented including ROM, PROM, and EPROM chips. A discussion of data storage on ROM is presented covering the mechanics of ROM usage, potential speed increases, programming interfaces, and preparation of data ROM chips through down-line loading. Software on ROM, known as firmware, is discussed similarly and two commercial examples of firmware are presented. Final conclusions highlight the importance of ROM chips for the numerical analyst.

Nine strong motion accelerograms recorded at rock and soil stations during two California earthquakes are analyzed using recently developed processing techniques. These techniques study the characteristics of the records in the time domain, including graphs of the buildup of energy of the horizontal acceleration with time, the variation with time of the RMS horizontal acceleration, and the variation with time of the angle between the principal axis of the ground acceleration and the vertical axis. The comparisons of the graphs showed that the wave arrivals are generally consistent between stations during the strong part but that some soil accelerograms have additional significant motions after t sub 2. The consistency of wave arrivals during the strong part was especially good for the 1971 San Fernando records in the Pasadena Area. There, the strongest wave arrival occurred at all four stations considered, approximately 3 seconds after the first S-wave arrival. Several one-dimensional site response simulations were performed at some of the soil stations studied, using the equivalent linear approach. The results showed that the simulated soil accelerations essentially preserve the time domain features of the input rock motion. One consequence of this was that the simulations predicted reasonably well the characteristics of soil motions in the strong part, but did not predict the additional soil motions after T sub 2.

Dynamic behavior of flexible components of mechanisms is prone to instabilities which create resonant speed barriers. By considering small deformations superimposed on the steady dynamic state equations governing evolution of disturbances can be obtained. For the case of mechanisms driven by periodic inputs these equations reduce to a system of coupled Mathieu-Hill equations for the amplitudes of modes of vibrations. Application of the Floquet theory determines the critical conditions of speed, geometry and material properties causing dynamic instability. (Author), This article is from 'Transactions of the Army Conference on Applied Mathematics and Computing (2nd) Held at Washington, DC on 22-25 May 1984,' AD-A154 047, p105-116.

Static stability of an elastic system composed of a flexible and a rigid link leads to a nonlinear eigenvalue problem with a single buckling load or infinite buckling loads when the flexible link is in tension or compression, respectively. Integration of equations of equilibrium leads to nonlinear singular integral equations which can be analyzed and solved numerically. (Author), This article is from 'Transactions of the Army Conference on Applied Mathematics and Computing (2nd) Held at Washington, DC on 22-25 May 1984,' AD-A154 047, p597-610.

The hydrodynamic theory of foil bearings is reviewed. The relationship between fluid pressure and film thickness is discussed. The compressibility of gas is included in the analysis. It is shown that the basic equation for determination of pressure distribution becomes a third order boundary value problem in terms of film thickness. A simple numerical scheme for solution of the nonlinear boundary value problem is developed and some examples are considered and discussed. (Author), This article is from 'Transactions of the Army Conference on Applied Mathematics and Computing (1st) Held at Washington, DC on 9-11 May 1983,' AD-A139 224, p659-677. Prepared in cooperation with Clarkson Coll., Potsdam, NY. Dept. of Mechanical and Industrial Engineering.

A probabilistic procedure is presented that can be used for the design of new flood levees as well as the assessment of the safety of levee systems that are already in operation. The various steps involved in the procedure are briefly outlined, with emphasis placed in the identification and description of possible failure modes, and the determination of the corresponding values of the probability of failure. The latter is achieved with the aid of an approximate method based on point estimates of the statistical moments of the levee failure functions (safety margins). The developed procedure is illustrated in two examples and the obtained results are presented and discussed. Example I involves the determination of the probability of failure of a given levee in slope (both upstream and downstream) sliding and piping. The likelihood for the occurrence of the latter is found under the assumption that the levee material is strong enough to allow the mechanism of piping (roofing) to develop. Example II involves the selection of a levee cross-section and type of fill for a desired value of the probability of failure (P sub f), and the determination of the corresponding value of the conventional factor of safety (FS). This is achieved by developing a relationship (in the form of nomographs) between P sub f and FS for a range of values for the levee geometry., This article is from 'Proceedings, Seminar on Probabilistic Methods in Geotechnical Engineering Held at Vicksburg, Mississippi on 21 September 1982,' AD-A136 497.

The need for a micromechanical approach to modeling the stress-strain response of granular soil is discussed and justified. This work focuses on the small shear strain behavior, and investigates the validity of modeling analytically uniform, rounded-grained quartz and by arrays of identical elastic, rough, quartz spheres. As a first step, the stress-strain properties of six regular arrays of spheres are studied in some detail, with focus on isotropic and biaxial boundary loading. Keywords: Particular mechanics; Regular arrays of spheres; Self consistent method; Stress-strain relationships; Isotropy, Transverse isotropy; Small strains; Threshold strain/P-waves; Shear modulus.

This report presents a brief summary of results obtained in our research program on damage development in fibrous composite laminates. The following technical subjects are described: (i) Effect of fiber breaks on stiffness changes in unidirectional composites. (ii) Stress analysis of transverse cracks. (iii) Progressive transverse cracking of 0/90 laminates. (iv) Analysis of cracks approaching a boundary between two materials. (v) Fatigue of B/Al laminates. Keywords: Composite materials; Epoxy laminates; Laminates; Crack propagation; Cracking(Fracturing); Aluminum; Boron; Balnium.

The purpose of this research program was to establish experimentally verified constitutive relations for isothermal elastic-plastic behavior of metal matrix fibrous composite materials. The theoretical part of the work was concerned with development of new constitutive models of elastic-plastic fibrous composite materials. Our goal was to identify modeling techniques which would permit derivation of overall instantaneous mechanical properties of the aggregate in terms of microstructural geometry and the properties of the phases. Since most fibers remain elastic until failure, the inelastic overall strains are caused by plastic deformation of the matrix. Therefore, an important objective was to find connections between the elastic-plastic deformation of the neat matrix and the composite, and to develop models which would utilize such connections in predictions of the overall response. Also, among the possible approaches to the problem, it was necessary to identify those which would offer a guarantee of accuracy in applications involving incremental loading which could be verified experimentally.

A new 2-D model of the stress-strain behavior of granular soil at small strains is presented. The model is based on an incremental solution to the contact problem and is implemented through nonlinear finite element techniques. The results of numerical experiments conducted on this idealized aggregate are compared to laboratory data on the static and cyclic small strain behavior of actual sand, as well as to recent compressional wave velocity measurements on anisotropically consolidated dry sand, with good agreement. These measurements, performed at the large cubic triaxial facility at the University of Texas, have shown that the P-wave velocity depends only on the principal stress parallel to the direction of wave propagation; this finding was also predicted by the simulation. A number of useful insight on the microscopic behavior of this idealized aggregate are also discussed. Keywords: Particulate mechanics; Stress-strain relationships; Small strains; P-wave velocity; Constrained modulus.