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The present paper revisits a stress update procedure for the Hoek-Brown plasticity model enhanced by a Rankine type of tension cut-off failure criterion. Limiting tensile stresses not only supports the behavior of weak rock masses with a very low tensile strength but in combination with the original Hoek-Brown model improves robustness of the stress update procedure, i.e. the stress return mapping algorithm. Herein, the primary focus is on the stress return from a space of inadmissible trial stresses for which neither the Hoek-Brown yield surface nor its derivative can be evaluated. All potential scenarios are thoroughly discussed both in the framework of single- and multi-surface plasticity. The presented procedures were implemented and verified with the help of the Geo5 FEM software.

Glued laminated timber beams exposed to fire of a variable duration were tested in three point bending. Three types of model geometries taking into account the effect of burning were created. Each model was examined for five material data sets. The maximum deflection obtained from FEM simulations was compared with the corresponding deflection wel derived from a three point bending test of burnt beams. The analysis was performed with the help of Ansys® software limiting attention to a liner elasticity with the maximum applied force Fel selected at the proportionality limit observed experimentally. Majority of FEM models provided smaller deflections compared to measurements except for the material set adopting Young’s moduli from the compression test. The best fit was observed for the material data set obtained from homogenization. No predominant preference among individual geometries was found promoting the computational model based on reduced cross-section as sufficiently accurate.

Laminated glass has been introduced to improve the mechanical performance, in particular impact resistance, of float glass while maintaining its transparency. However, its rate-dependent behaviour has not been sufficiently understood and various methods have been used to model it. This study compares the response of three material models commonly used to model glass cracking implemented in industry-standard LS-DYNA software: a smeared fixed crack model with the Rankine failure criterion, the nonlocal failure criterion by Pyttel et al., and the Johnson-Holmquist model. The input parameters are taken from several published studies, so each model was tested in multiple validated settings. The response of the models is compared with values measured during the earlier experimental campaign, the results of which were published in proceedings of the preceding conference. The reference experiments involved freely hanging full-scale samples, which eliminated the effect of structural supports and allowed more accurate validation of the numerical models. The response of two types of glass, i.e. annealed or heat-strengthened, and two types of interlayer, i.e., polyvinyl butyral or ethylene-vinyl acetate, was tested and is simulated herein. The time evolution of the contact force, specimen accelerations, and fracture patterns are discussed, demonstrating the main shortcomings of the three models in simulating destructive tests on laminated glass samples under low-velocity impact.

A comparative study of the viscous response of polymer matrix based fibrous composites predicted by the Mori-Tanaka method and finite element simulations based on the 1st order homogenization theory is presented. Aligned basalt and carbon fibers embedded into a polymeric matrix are considered to represent a quasi isotropic and transversely isotropic two-phase systems. While differences in the prediction of the macroscopic elastic response are attributed merely to the properties of the fiber phase, the viscoelastic behavior is largely affected by the selected homogenization method. A stiffer response predicted by the Mori-Tanaka method for both creep and relaxation tests is observed for both material systems and supports similar finding found in the literature. Thus suitable modifications of the original formulation of such two-point averaging schemes are needed for them to be applicable in the multi-scale modeling of generally anisotropic yarns in plane weave textile composites.

Masonry is a heterogeneous composite material made of bricks bonded by a mortar matrix. Modeling such a material on macroscale typically calls for homogenization adopting a suitable constitutive model capable of capturing its quasi-brittle behavior. The present contribution concentrates on comparison and potential application of classical isotropic and orthotropic damage models in the framework of strain based first order numerical homogenization. As an illustrative example, a representative volume element in terms of a periodic unit cell is constructed to address the response of an unreinforced masonry (URM) structure typical of “Placa” buildings (mixed masonry-reinforced concrete buildings) built in Portugal. The performance of the two models is examined on the basis of macroscopic stress-strain curves constructed for both tensile and compressive loading. The selected geometrical constraints clearly identify the differences in the predictive capabilities of the two models.

Two groups of small-size single edge notched beams (SENB) made of European spruce (Picea abies) were tested in three-point bending (3PB) until failure under displacement control. The first group comprised of eight solid and two glued laminated (GL) timber beams manufactured with (a) the single edge notch at the bottom of the mid-span and (b) the reduced ligament depth. The second group consisted of four GL timber beams with the single edge notch only. We employed digital image correlation (DIC) to quantify strains and displacements, capture the damage evolution, and track the sequence of failure patterns. In this work, we present response of the beams in terms of load vs. crosshead displacement of the moving crosshead and load vs. crack tip opening displacement (CTOD).

The paper describes a finite element simulation of the response of a real underground structure subjected to earthquake using GEO5 FEM program. It concentrates on the influence of material damping with respect to a specific type of boundary condition prescribed at the bottom of the analyzed domain. It is seen that considering material damping is inevitable particularly in case of so called fixed boundary conditions to arrive at meaningful results. This is demonstrated on an artificial earthquake generated according to a design spectrum defined in Eurocode 8. A viscous damping ratio combined with the results of eigenvalue analysis is used to derive parameters of Rayleigh damping for three specific scenarios promoting the approach based on the lowest natural frequency as sufficiently accurate for the present task.

Laminated glass composed of several layers of glass plies bonded to a polymer interlayer enjoys ever growing interest in modern architecture. Being often used in impact protection designs requires understanding of both pre- and post-breakage behavior of these structures. This paper contributes to this subject by examining an application of an explicit phase field dynamic model to the description of fracture in a laminated glass subjected to a low velocity impact. The achieved results indicate the ability of the proposed model to successfully describe the onset of damage and subsequent crack propagation. It has, however, been observed that a relatively fine mesh is needed to interpolate a sharp discontinuity accurately, which makes this approach computationally demanding. The model is first validated against experimental results obtained for a single-layer float glass. Next, the usability of the phase-field damage model as a crack predictor in individual layers of the composite is investigated. The dependence of the results on residual stiffness, element type, and initial tensile strength is examined and discussed.

The paper deals with the prediction of the response of a real underground structure subjected to earthquake. A fully dynamic analysis is carried out in the GEO5 FEM program using the Finite Element Method. Limiting our attention to a two-dimensional analysis we focus on the implementation of special boundary conditions along the vertical edges of the computational model. A simple study is carried out first to show that incorrectly applied boundary conditions may significantly influence the actual design of underground structures loaded by vertically propagating shear waves. This study promotes the combination of so called free-field and static boundary conditions as demonstrated on a simple example.

The paper deals with the evaluation of tunnel construction subjected to earthquake using a pseudostatic analysis combined with the finite element method. The initial stage of calculation is concerned with the design of computational model and subsequent analysis of the actual excavation process. The case study of the response of a selected construction to earthquake follows next. To that end, the so called 1D free filed dynamic analysis is performed first to generate appropriate loading conditions in terms of a layered-wise constant shear strain. Therein, two particular boundary conditions, termed the fixed and absorbing boundary, are examined. The corresponding loading conditions are finally introduced in a 2D plane strain analysis to yield the internal forces developed in the tunnel lining. The results clearly show inadequacy of the fixed boundary and promote the use of absorbing boundary conditions for the present soil profile.

The present paper is concerned with two types of periodic unit cell of composite yarn with different geometry but the same material properties. Their macroscopic response under tensile and compressive loading in the transverse direction and their combination are plotted in the graphs. Based on stress-strain curves the failure envelopes are constructed. A simple maximum stress criterion and linear softening law is used in the adopted progressive damage analysis to outline the softening part of stress-strain diagrams. Finally the impact of selected representative volume element is observed through the comparison of results gained for both designed periodic unit cells in the microlevel, meaning the level of yarn.

This paper is concerned with the determination of hygroexpansion coefficients of wood. Wood is a naturally hygroscopic material, attracting moisture from its surroundings. Its dimensions change depending on the actual moisture content. This dependence is characterized by the coefficient of hygroexpansion. For complex microstructures, this coefficient can be determined, similarly to the coefficient of thermal expansion, either from analytical or numerical homogenization. The homogenization procedure, used in this paper, comprises several steps corresponding to the wood structural composition. Accuracy of this approach is governed by correctness of the chosen input parameters. One of the most important parameters are the volume fractions of the earlywood and latewood. Ascertained dependence of the earlywood and latewood volume fractions on dry wood density is also presented.

Laminated glass, consisting of glass layers connected with transparent foils, has found its applications in civil, automotive, or marine engineering. Due to a high contrast in layer properties, mechanical response of laminated glass structures cannot be predicted using classical laminate theories. On the other hand, engineering applications demand easy-to-use formulas of acceptable accuracy. This contribution addresses such simplified models for free vibrations of laminated glass beams, with the goal to determine their natural frequencies and modal damping properties. Our strategy is to approximate the complex behavior of a laminated structure with that of an equivalent monolithic beam. Its effective thickness is determined by the variational method proposed by Galuppi and Royer-Carfagni for static problems, which we extended for modal analysis. We show that this new approach overcomes inaccuracies of the currently used dynamic effective thickness model by López-Aenlle and Pelayo.

This paper is concerned with the evaluation of microfibril angle of spruce. The microfibril angle is defined as an inclination of microfibrils from the longitudinal axis, the direction of lumens. It is well known and further supported by the present study that the microfibril angle has a great influence on the final mechanical properties of wood. This angle could be measured either directly using, e.g. polarisation microscopy, X-ray diffraction, infrared spectroscopy, or indirectly, as used in this study, by employing the nanoindentation measurements. Therein, the measured indentation modulus is compared with that obtained numerically using the anisotropic theory of indentation. The latter one depends on the entire stiffness matrix derived through homogenization and the searched microfibril angle. In view of the cell wall microstructure, the effective cell properties were found using the two-step micromechanical homogenization adopting both the Self-consistent and Mori-Tanaka methods.

The present paper is concerned with the analysis of a ceramic matrix composite, more specifically the plain weave textile fabric composite made of basalt fibers embedded into the pyrolyzed polysiloxane matrix. Attention is paid to the determination of effective elastic properties of the yarn via homogenization based on the Mori-Tanaka averaging scheme and the 1st order numerical homogenization method adopting a suitable representative computational model. The latter approach is then employed to simulate the response of the yarn when loaded beyond the elastic limits. The required mechanical properties of individual material phases are directly measured using nanoindentation with in-build scanning probe microscopy. Applicability of the proposed computational methodology is supported by the analysis of a unidirectional fibrous composite, representing the yarn, subjected to a macroscopically uniform strain.

The paper is concerned with our ongoing research effort devoted to the development of reliable computational tools for the calibration of advanced constitutive models of soils. At present, such software is available for the hypoplastic model of clays applicable to soft soils. This software provides a stepping stone for the determination of potential links between individual model parameters and fundamental characteristics of soils. Identifying such links would allow for tuning the model without performing time consuming experiments, particularly in the case of an initial design. Some preliminary results are presented in the paper.

The purpose of this paper is to present a simple micromechanics-based model to estimate the effective thermal conductivity of macroscopically isotropic materials of matrix-inclusion type. The methodology is based on the well-established Mori-Tanaka method for composite media reinforced with ellipsoidal inclusions, extended to account for imperfect thermal contact at the matrix-inclusion interface, random orientation of particles and particle size distribution. Using simple ensemble averaging arguments, we show that the Mori-Tanaka relations are still applicable for these complex systems, provided that the inclusion conductivity is appropriately modified. Such conclusion is supported by the verification of the model against a detailed finite-element study as well as its validation against experimental data for a wide range of engineering material systems.

We present an application of the Mori-Tanaka micromechanical model for a description of the highly nonlinear behavior of asphalt mixtures. This method is expected to replace an expensive finite element-based fully-coupled multi-scale analysis while still providing useful information about local fields on the meso-scale that are not predictable by strictly macroscopic simulations. Drawing on our recent results from extensive experimental and also numerical investigations this paper concentrates on principal limitations of the Mori-Tanaka method, typical of all two-point averaging schemes, when appliedto material systems prone to evolving highly localized deformation patterns such as a network of shear bands. The inability of the Mori-Tanaka method to properly capture the correct stress transfer between phases with increasing compliance of the matrix phase is remedied here by introducing a damage like parameter into the local constitutive equation of reinforcements (stones) to control an amount of stress taken by this phase. A deficiency of the Mori-Tanaka method in the prediction of creep response is also mentioned particularly in the light of large scale simulations. A comparison with the application of macroscopic homogenized constitutive model for an asphalt mixture is also presented.

AbstractLaminated glass units exhibit complex response as a result of different mechanical behavior and properties of glass and polymer foil. We aim to develop a finite element model for elastic laminated glass plates based on the refined plate theory by Mau. For a geometrically nonlinear description of the behavior of units, each layer behaves according to the Reissner-Mindlin kinematics, complemented with membrane effects and the von Kármán assumptions. Nodal Lagrange multipliers enforce the compatibility of independent layers in this approach. We have derived the discretized model by the energy-minimization arguments, assuming that the unknown fields are approximated by bi-linear functions at the element level, and solved the resulting system by the Newton method with consistent linearization. We have demonstrated through verification and validation examples that the proposed formulation is reliable and accurately reproduces the behavior of laminated glass units. This study represents a first step to the development of a comprehensive, mechanics-based model for laminated glass systems that is suitable for implementation in common engineering finite element solvers.

We have discovered a mistake in our original derivation related to the definition of the apparent conductivity due to orientation averaging.

The influence of elevated temperatures on mechanical behavior of glued laminated timber beams is examined on the basis of tensile tests. Dog bone samples prepared from beams exposed to fire of variable duration were categorized with respect to the type and position of the failure crack, type and number of discontinuities such as knots, and the level of browning. The acquired experimental results suggest that the wood variability and the effect of growth discontinuities are probably more significant than the effect of elevated temperatures. To support this conclusion, further study is currently under way, exploring samples from the second series of the fire tests.

This paper examines the possibility of using the Mori-Tanaka micromechanical model describe the rate dependent behavior of the polymer matrix based fibrous composites. The generalized Leonov model is adopted to capture the time and rate dependent character of the selected matrix, while fibers are assumed elastic. The performance of the Mori-Tanaka method is tested against the finite element simulations carried out in the framework of first-order homogenization. For simplicity, the periodic hexagonal array model is chosen to represent the microstructural arrangement of fibers in the yarn cross-section. To match the predictions provided by the two approaches a suitable modification to the original Mori-Tanaka method is proposed. An extensive parametric study is presented to illustrate a considerable improvement of the predictive capability of the modified Mori-Tanaka method.

This paper revisits the issue of a potential substitutions of the Hoek-Brown failure model by the standard Mohr-Coulomb model in the stability analysis of rock masses. The derivation of equivalent shear strength parameters of the Mohr-Coulomb proposed by Hoek et al. [1] is addressed with emphases on the suitable range of stresses for which the equivalence of the two failure criteria applies. To that end, a simple numerical analysis of the oedometric test is carried out. It is seen that a correct choice of the upper limit of the minimum compressive principal stress is crucial for the Mohr-Coulomb model to provide predictions comparable to the Hoek-Brown model. This issue is addressed next in the light of the solution of slope stability problem. All the presented results were derived with the help of the GEO5 FEM finite element software [2].

This paper outlines prediction of the macroscopic response of unidirectional fibrous composites made either from basalt or carbon fibers impregnated by a polymeric epoxy matrix. The viscoelastic response of the matrix phase was represented by the Maxwell chain model. A series of creep tests performed at several stress levels served as a stepping stone for the model calibration. The macroscopic behavior of both composites was first examined via computational homogenization. Attention was accorded to computational cells with variable size extracted from large representative images. We observed that selecting the computational model as a sufficiently large test window should be approached with caution. Because initial designs often need a large parametric study to test various material and geometrical patterns, this study was then supported by computationally much more effective Mori-Tanaka averaging scheme, clearly showing its potential even if loading the composite beyond its elastic limit.

This paper investigates a time-stepping procedure of the Newmark type for dynamic analyses of viscoelastic structures characterized by a generalized Maxwell model. We depart from a scheme developed for a three-parameter model by Hatada et al. [1], which we extend to a generic Maxwell chain and demonstrate that the resulting algorithm can be derived from a suitably discretized Hamilton variational principle. This variational structure manifests itself in an excellent stability and a low artificial damping of the integrator, as we confirm with a mass-spring-dashpot example. After a straightforward generalization to distributed systems, the integrator may find use in, e.g., fracture simulations of laminated glass units, once combined with variationally-based fracture models.

An adequate understanding of the response of laminated glass structures to impact loading becomes essential to rationalise their design, which has been proven by several studies that appeared in the last years. Our study focuses on the behaviour of three-layer laminated glass plates subjected to the low-velocity impact of a steel impactor. Using combined experimental and computational analysis, we study the influence of the laminated glass composition on the response of laminated glass, crack initiation and the final fracture pattern. A polyvinyl butyral or ethylene-vinyl acetate interlayer merges annealed or heat-strengthened soda-lime-silica glass panes together so that the tested panels have the same cross-section layout. As the boundary conditions of the plate largely influence the impact performance of glass panels, the samples were suspended on thin steel ropes to avoid the effect of supports on the laminated glass response. The finite element model of this contact-impact problem, accounting for the time/temperature-dependent behaviour of two polymer interlayers, is presented and validated. Finally, we discuss the effect of the glass and foil type on the contact force and response of laminated glass plates.

Laminated glass fulfills the demands on safety and security in transparent structural elements used in architecture and other fields of engineering. It can be constructed as forced-entry, bullet, or blast resistant. The basic three-layer configuration consists of two glass panes connected with a polymer or ionomer interlayer; the advanced products contain also other layers. The foil ensures shear coupling and provides post-breakage resistance and damping. For the design of laminated glass structures and their analysis, knowledge of mechanical properties of interlayers is essential. In numerical simulations, the interlayer is most typically described by the generalized Maxwell chain ‒ a classical viscoelastic model which can capture the time/temperature-dependent response of polymers under shear. Its parameters can be found for common interlayer types in the literature. However, they differ even for the same material, because of a slightly different content of additives, different test setups, and different data processing procedures. In this contribution, the dependence of the response of a laminated glass element on the material parameters of the polymer interlayer is studied by means of numerical modelling and experiments. Two examples are shown and discussed, i.e., quasi-static analysis of a simply-supported beam and modal analysis of a free-free beam. Numerical predictions are obtained by a layer-wise model based on the finite element method. These predictions are validated against the detailed experimental data. We demonstrate that using the Maxwell model parameters from the literature determined even for the same material type but not for the concrete foil may lead to unrealistic predictions.

An efficient approach to the evaluation of effective elastic properties of plain weave textile composites using the Mori-Tanaka method is presented. The method proves its potential even if applied to real material systems with various types of imperfections including the non-uniform waviness of the fiber-tow paths, both along its longitudinal direction and through the laminate thickness. The influence of the remaining geometrical parameters is accounted for by optimal calibration of the shape of the equivalent ellipsoidal inclusion. An application of the method to a particular sample of the carbon-carbon composite laminate demonstrates not only its applicability but also its efficiency particularly when compared with finite element simulations. [ABSTRACT FROM AUTHOR]