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Abstract: The paper concerns the description and the validation of a constitutive model for concrete characterized by a combined plastic-hardening-damage-fracture dissipative criterion developed within the framework of the simple material model, so that its numerical implementation is easy and robust. Two different damage isotropic mechanisms associated with tensile and compressive strain processes are introduced and two hardening variables are used; the first rules the plastic hardening while the second controls the compaction of the material. The limit domain is defined through the envelope of three yield criteria presenting a strong and original coupling between plastic and damage dissipative mechanisms. It is demonstrated that the proposed framework allows the reproduction of some distinctive features of the behavior of concrete under multiaxial stress states, such as volumetric hardening in triaxial compression load processes, the increment of strength under confined compression, post-peak dilatancy, varying degradation of the elastic stiffness in tensile or compressive stress states, the increase of the limit strain in cyclic processes. A comparison of the numerical predictions with the literature experimental tests is presented. The limits of the proposed model are also discussed in the paper. [Copyright &y& Elsevier]

Abstract: The present paper is focused on constitutive modelling and identification of parameters of the relevant model of plastic strain-induced martensitic transformation in austenitic stainless steels at low temperatures. The model used to describe the FCC→BCC phase transformation in austenitic stainless steels is based on the assumption of linearization of the most intensive part of the transformation curve. The kinetics of phase transformation is described by three parameters: transformation threshold (p ξ ), slope (A) and saturation level (ξ L). It is assumed that the phase transformation is driven by the accumulated plastic strain p. In addition, the intensity of plastic deformation is strongly coupled to the phase transformation via the description of mixed kinematic/isotropic linear plastic hardening based on the Mori–Tanaka homogenization. The theory of small strains is applied. Small strain fields, corresponding to phase transformation, are decomposed into the volumic and the shear parts. The grade AISI 316L, stainless steel often used in cryogenic applications, has been chosen as a good example of the austenitic structure. The magnetic permeability of fine gauge stainless steel sheets (thickness 0.15–0.25mm) subjected to monotonic straining was measured as a function of strain. The detailed methodology of relevant measurements is presented in the paper. Tuning of the constitutive model is described and the relevant parameters are identified. The model has been applied in the design of thin-walled bellows expansion joints for the large Hadron Collider (LHC), at present under construction at CERN. [Copyright &y& Elsevier]

Shape-memory polymers (SMPs) represent a class of smart materials able to store a temporary shape and to recover the original shape upon an external stimulus, such as temperature. The present paper proposes a three-dimensional finite-strain phenomenological model for thermo-responsive SMPs, which distinguishes between two material phases presenting different properties and is based on a rule of mixtures. The proposed model is motivated by the earlier work of Reese et al. (2010) and it considers several significant material features that had not been addressed in previous phenomenological approaches. Specifically, the model reproduces both heating-stretching-cooling and cold drawing shape-fixing procedures and it takes into account the non-ideal behavior of realistic SMPs (i.e. imperfect shape-fixing and incomplete shape-recovery). Several numerical tests are reported to assess model performances, from simple uniaxial and biaxial tests to complex simulations of biomedical devices. Comparisons with experimental data taken from the literature are also provided to validate the model. The proposed improvements increase the model applicability over a wide range of polymer types and operating conditions. [ABSTRACT FROM AUTHOR]

Constitutive models for shape memory alloys have seen significant development in the last decades. They have evolved from uniaxial, mostly empirical, relations to full-fledged mathematical descriptions accounting for many of the effects observed in these materials with an ever-higher degree of detail. The models available today are constructed using various approaches ranging from micromechanics with or without scale transition, to statistical physics and particle dynamics, to methods of classical plasticity, to energy approaches coupled with thermodynamic and conservation principles. They have finally matured to the extent where they can be utilized in reasonably accurate numerical analysis of potentially complex shape memory alloy devices subjected to non-trivial thermomechanical loading. This paper aims at providing an up-to-date review of key constitutive models for shape memory alloys, with an attempt to track their evolution from their inception to their most recent versions. The models are categorized in terms of the approach they use in describing the behavior of shape memory alloys. [ABSTRACT FROM AUTHOR]

Elevated temperature has significant effect on the mechanical response of metals and alloys. Industrial processes often use high temperature forming to fabricate components of complex shape from alloys such as aluminum or magnesium that have low room temperature formability. Accurate forming models to integrate warm forming in computer aided engineering (CAE) in production environment has been hampered by a lack of constitutive relations at elevated temperatures, forcing one to rely on experimental data for such integration. In this paper, a new thermo elasto-viscoplastic (TEV) constitutive relation is developed to model the behavior of face-centred cubic (FCC) polycrystals, especially aluminum alloys, at elevated temperatures. The model takes into account the temperature dependence of the single crystal elastic coefficients, single slip hardening parameters, thermal softening, rate sensitivity, and the total deformation. The TEV framework has been implemented into the commercial finite element code LS-DYNA to study the effects of temperature on metal forming. Uniaxial tension simulations at six different temperatures ranging from 25 °C to 260 °C have been performed and calibrated with published experimental results. Equations for the variation of single-slip hardening parameters with temperature have been developed for the AA5754 aluminum alloy. Shear test simulations at different temperatures have been used to validate the model. The proposed framework for the single slip parameters for uniaxial tension accurately predicts the shear stress-shear strain data without the need for any further fitting parameter. Temperature dependence of texture evolution, single slip hardening and hardening rates, thermal softening, and slip activity in AA5754 sheet alloy during temperatures corresponding to warm forming temperatures are investigated. [ABSTRACT FROM AUTHOR]

Deformation twinning and texture evolution in hexagonal close-packed (HCP) metals lead to evolving flow stress asymmetry/anisotropy and evolving plastic anisotropy. These phenomena cause a significant change in the shape of the yield surface with accumulated plastic deformation which cannot be modeled accurately with traditional hardening laws. In this paper, an anisotropic continuum-based plasticity model is proposed to capture the large strain cyclic hardening behavior of magnesium alloys. Key in the current formulation is the incorporation of distortional hardening to model the evolving asymmetric/anisotropic hardening response of magnesium alloys for both monotonic and reverse loading paths. The hardening behavior is classified into three deformation modes: Monotonic Loading [ML], Reverse Compression [RC], and Reverse Tension [RT]. The deformation modes correspond to the different loading regimes of the cyclic hardening curve. Specifically, the ML mode corresponds to the initial in-plane tension and the initial in-plane compression from the annealed state, the RC mode corresponds to the in-plane compression following previous tension and the RT mode corresponds to the in-plane tension following previous compression. Three separate hardening laws are used to define the hardening response within each deformation mode. Moreover, a multi-yield surface modeling approach is used where a CPB06 type anisotropic yield surface is assigned to each deformation mode. The evolution of the anisotropy coefficients involved in the expression of the yield function, is considered to model distortional hardening within each deformation mode. The evolving anisotropy parameters are found by minimizing the difference between the model predictions and the experiments, together with the interpolation technique proposed by Plunkett et al. (2006) . The proposed model is calibrated using monotonic and reverse loading experimental data for AZ31B and ZEK100 magnesium alloys. A strain rate independent elasto-plastic formulation is used to implement the proposed constitutive model as a user material subroutine (UMAT) in the commercial finite element software LS-DYNA ® . The predictions of the model are compared against the experimental monotonic and cyclic (CTC and TCT) flow stresses and r-values of AZ31B and ZEK100 sheets along different test directions. An excellent agreement is found between the simulated and experimental results. [ABSTRACT FROM AUTHOR]

The finite deformation response of an epoxy resin is investigated in the glassy regime using a constitutive relation that accounts for thermally activated yielding, pressure-sensitivity, strain softening and molecular chain reorientation. A previous formulation of this macromolecular model is modified so as to decouple the onset of yielding from the peak nominal stress, and enable accurate modeling of temperature and strain-rate effects concurrently. The latter cannot be modeled adequately with existing models when the temperature dependence of elastic moduli is accounted for. Tension and compression experiments are carried out on Epon 862 across a range of temperatures and strain rates. Special care is taken to extract the intrinsic material behavior from the recorded mechanical responses using a new technique of video-based extensometry, which is well adapted to cylindrical geometries. Key features of the data include a temperature dependence of elastic moduli and a tension–compression asymmetry that goes beyond differences in peak yield. The experimental data is divided in two sets for model calibration and assessment. The first set contains sufficient data to identify all model parameters following a procedure outlined in the paper. The second data set is used to assess the predictive capabilities of the model for test conditions not used in the calibration step. It is shown that when the tension and compression cases are treated separately, with respect to post-peak softening, model predictions are excellent over the investigated ranges of temperature and strain rate. [ABSTRACT FROM AUTHOR]

Abstract: The elastic–plastic response of sheet materials during non-proportional paths is seldom incorporated in constitutive equations used for routine sheet forming simulation, but can have a significant effect on formability and springback. Monotonic tension and compression, coaxial tension–compression (T–C), coaxial compression–tension (C–T), and two-stage/non-coaxial tensile tests were performed for three grades of dual phase steels: DP590, DP780, and DP980. The reverse flow curves have three characteristics: reduced yield stress (Bauschinger effect), rapid transient strain hardening over a few percent strain, and long-term or “permanent” softening. The departure of the reverse hardening curves from monotonic ones is larger than with other typical sheet forming alloys, presumably because of the effects of large second-phase martensite particles in dual-phase steels. A Modified Chaboche type model was applied in this paper to simulate the elastic–plastic behavior of DP steels. In addition to one or more standard nonlinear components of the back stress, a linear term was added to represent the “permanent” offset of hardening following a stress reversal. The parameters for the model were fit using the monotonic and reverse tensile test results only, and the model predictions were then compared with large-strain balanced biaxial bulge test, non-coaxial, two-stage tensile tests, and draw-bend springback tests. The Modified Chaboche model captured the response following a path change much better than isotropic hardening models, but there is a fundamental difference between large-strain hardening after a path change that occurs between path reversals and changes of principal strain axis. The Chaboche model can reproduce either behaviors, but not both simultaneously. [Copyright &y& Elsevier]

Abstract: This paper presents a complete theoretical accounting of the thermomechanical coupling within a viscoplastic model to predict the time, temperature, and stress state dependent mechanical behavior of amorphous glassy polymers. The foundational model formulation (Bouvard et al., 2010), developed to predict the time dependent behavior of amorphous glassy polymer, departed from the Haward and Thackray (1968) spring-dashpot representation widely used to model the mechanical behavior of polymers. Instead, the model equations were derived from within a large deformation kinematics and thermodynamics framework based upon the approach proposed by Coleman and Gurtin (1967) in which physically-based internal state variables (ISVs) were selected to accurately represent the underlying physics of the polymer deformation mechanisms. The updated model presented includes the distinction of temperature dependence. Hence, the present material model accounts for (i) the material strain softening induced by the polymer chain slippage; (ii) the material strain hardening at large strains induced by chain stretching between entanglement points; (iii) the time, temperature, and stress state dependence exhibited by polymers under deformation. The model also accounts for heat generation induced by plastic dissipation that leads to the thermal softening of the material under large deformation at medium strain rates. The material model response was compared to experimental data for an amorphous polycarbonate deformed at different strain rates, temperatures, and stress states. The simulations account for fully coupled thermomechanical applications. Good agreement was observed between the model correlation and the experimental data in compression (for both loading and unloading responses), creep, tension, and torsion for different strain rates and temperatures. Moreover, finite element simulations of a Split Hopkinson Pressure Bar compression device accurately captured the mechanical response of the material deformed under high strain rate conditions. [Copyright &y& Elsevier]

Abstract: In this paper, the experimental response of oxygen free high conductivity (OFHC) copper under multiaxial loading conditions is presented, along with quasi-static and dynamic response under uniaxial compression loading. The multiaxial experiments were performed under non-proportional loading conditions, where the sample was subjected to uniaxial loading for a predetermined strain followed by biaxial loading. These experimental results provide a comprehensive data set for constitutive modeling of the material response at finite strains, over a wide range of strain-rates and temperatures. The observed strain-rate and temperature dependent responses under uniaxial loading are shown to correlate closely using the Khan–Huang–Liang (KHL) constitutive model; the model is shown to be in close agreement with other published experimental results [Khan, A.S., Liang, R., 1999. Behavior of three BCC metal over a wide range of strain rates and temperatures. International Journal of Plasticity 15, 1089–1109; Nemat-Nasser, S., Li, Y., 1998. Flow stress of F.C.C polycrystals with applications to OFHC Cu. Acta Materialia 46 (2), 565–577]. This constitutive model is further demonstrated to predict the observed material response accurately, using the material constants determined from uniaxial loading results during proportional and non-proportional loading experiments. The micro-texture characterization of as-extruded, annealed and deformed samples was performed to investigate the effect of temperature and strain-rate on texture evolution of OFHC copper. Grain average misorientation (GAM) was used to reveal the deformation heterogeneity and orientation gradients in deformed samples. [Copyright &y& Elsevier]

Abstract: In this paper, modifications are proposed to a phenomenological plasticity model to account for the evolution of recrystallization and the resultant softening behavior. The novel model includes internal state variables representing dislocation density and the spacing between geometrically necessary subgrain boundaries. In order to capture both single and multiple peak recrystallization, the model tracks the evolution of recrystallized volume fractions for multiple cycles of recrystallization, and has a set of state variables for each volume fraction. A rule of mixtures is used to determine the average stress. The model is capable of capturing static recrystallization as well as both single and multiple peak dynamic recrystallization. Material parameters are fit to data from monotonic compression tests on copper for a wide range of temperatures and strain rates. The model is then validated by using the same parameter set to predict multiple-stage response in which samples are compressed, held at temperature for various lengths of time, and then compressed further. The model predicts both the static recrystallization that occurs between loading stages as well as the dynamic recrystallization occurring during the second loading stage. [Copyright &y& Elsevier]

Abstract: This paper deals with the modeling of the plasticity of extruded aluminum 6260-T6 at the macroscopic level. The model is based on the framework of classical polycrystalline plasticity. A Reduced Texture Methodology (RTM) is used to provide the computational efficiency needed for industrial applications. The RTM approach involves a significant reduction of the number of representative crystallographic orientations. Furthermore, a special hybrid experimental–numerical procedure is used to identify all model parameters (including texture) from mechanical experiments. The experimental program includes uniaxial tensile experiments for different material orientations. Due to the heterogeneity in texture and grain size along the thickness direction of the 2mm thick extruded material, specimens of full- and reduced thickness are prepared. Uniaxial compression–tension experiments are completed with the help of an anti-buckling device. The mechanical response of full-thickness specimens is modeled using 12 crystallographic orientations. Only eight distinct grain orientations are required to obtain satisfactory predictions for the reduced-thickness specimens with the same set of hardening parameters. The models describe well the stress–strain curves and Lankford ratios for all directions. It is found that the computed reduced textures are in good agreement with EBSD measurements. The 8-grain model is also validated for non-proportional loading paths in the space of tension and shear. Simulations of punch experiments are performed to further validate the model and to demonstrate the computational efficiency of the RTM based polycrystalline plasticity model in structural applications. [Copyright &y& Elsevier]

Abstract: In the concurrent multiscale analysis, it is difficult to have truly seamless transition between the atomistic and continuum scale. This situation is even worse when defects pass through the boundary between different scales. For example, there is a lack of effective methods to handle the dislocation passing through scale boundaries which is important to investigate plasticity at the nanoscale. In this paper, the generalized particle (GP) method proposed by the first author is further developed so that a seamless transition and dislocation passing between different scales can be realized. Specifically, the linkage between different scales is through material neighbor-link cells (NLC) with scale duality. This indicates that material elements can be high-scale particles through a lumping process and can also be atoms via decomposition depending on the needs of the simulation. At the interface, the information transfer from bottom scale-up or from top scale-down is through the particles or atoms in the NLC. They are with the same material structure, all possess nonlocal constitutive behavior; thus, the smooth transition at the interface between different scales can be attained and validated to avoid non-physical responses. To save degrees of freedom, atoms are lumped together into a generalized particle in the domain in which the deformation gradient is near homogeneous. On the other hand, when defects such as dislocations in the atomistic domain are near the particle domain, the particles along dislocation propagation path and its surrounding region will be decomposed into atoms so dislocations can freely pass through the scale boundary and propagate inside the model just as it propagates in the deformed atomistic crystal structure. The method is verified first for seamless transition of variables at the scale boundary by a one-dimensional model and then verified for dislocation nucleation and propagation passing through scale boundaries in two cases, one is near the free surface and the other is inside of the copper nanowire. All the validations are through comparisons with fully atomistic analyses under same conditions. The comparison is satisfactory. [Copyright &y& Elsevier]

Abstract: In this paper, a constitutive model for the unified description of rate dependent and rate independent material behavior is proposed. It is applicable to isotropic metals subjected to arbitrary thermomechanical loading conditions at small strains. The focus of the model formulation is its validity for the full range of thermal and mechanical loading conditions to be covered in an industrial context by e.g. modern aero-engine designs. Consequently, the proposed model describes the material behavior on a macroscopic level covering the full temperature range from room temperature to the upper application limit under monotonic as well as cyclic loading. Special emphasis is also put on the correct representation of the observed ratcheting behavior. The most prominent features of the model are the combined treatment of both, rate dependent, as well as rate independent inelasticity through a limit surface concept, the description of primary, secondary and tertiary creep behavior and the application of an appropriate backstress evolution equation. A fully implicit integration algorithm for the proposed model is developed and implemented in connection with uniaxial integration point drivers as well as three alternative Finite Element packages. The parameters of the proposed model can be identified based on a limited number of complex cyclic tests and monotonic creep tests. After reporting on the fitting results for such tests for the Nickel-base superalloy IN718 the predictive capabilities of the proposed model are assessed for a number of isothermal and nonisothermal tests. Finally, the performance of the algorithmic implementation into the Finite Element packages is briefly addressed. [Copyright &y& Elsevier]

Abstract: The deformation behavior of two unfilled engineering thermoplastics, ultra high molecular weight polyethylene (UHMWPE) and polycarbonate (PC), has been investigated in creep test conditions. It has been found that a loading history (prior to the creep test) comprising of loading to a maximum stress or strain value followed by partial unloading to arrive at the target stress value can greatly modify the strain-time behavior. Under such a test protocol, while the expected increase in strain during creep (constant tensile load) is observed, at relatively low creep stresses specimens have also demonstrated a monotonic decrease in strain. In an intermediate stress range, specimens have demonstrated time dependent behavior comprising of a transition from decreasing to increasing strain during creep in tension. This paper presents experimental results to delineate these findings and explore the effect of prior strain rate on the qualitative and quantitative changes in the output (strain-time) behavior. Furthermore, modification of the viscoplasticity theory based on overstress (VBO) model into a double element configuration is introduced. These changes confer upon the model the ability to yield non-monotonic behavior in creep, and supporting simulation results have been included. These changes, therefore, allow the model to simulate strain rate sensitivity, creep, relaxation, and recovery behavior, but more importantly address the issue of non-monotonic changes in creep and relaxation when a loading history involves some degree of unloading. [Copyright &y& Elsevier]

Abstract: This paper describes a numerical, hierarchical multiscale modeling methodology involving two distinct bridges over three different length scales that predicts the work hardening of face centered cubic crystals in the absence of physical experiments. This methodology builds a clear bridging approach connecting nano-, micro- and meso-scales. In this methodology, molecular dynamics simulations (nanoscale) are performed to generate mobilities for dislocations. A discrete dislocations numerical tool (microscale) then uses the mobility data obtained from the molecular dynamics simulations to determine the work hardening. The second bridge occurs as the material parameters in a slip system hardening law employed in crystal plasticity models (mesoscale) are determined by the dislocation dynamics simulation results. The material parameters are computed using a correlation procedure based on both the functional form of the hardening law and the internal elastic stress/plastic shear strain fields computed from discrete dislocations. This multiscale bridging methodology was validated by using a crystal plasticity model to predict the mechanical response of an aluminum single crystal deformed under uniaxial compressive loading along the [421] direction. The computed strain-stress response agrees well with the experimental data. [Copyright &y& Elsevier]

Abstract: The constitutive model for the unusual asymmetric hardening behavior of magnesium alloy sheet presented in a companion paper (Lee, M.G., Wagoner, R.H., Lee, J.K., Chung, K., Kim, H.Y., 2008. Constitutive modeling for anisotropic/asymmetric hardening behavior of magnesium alloy sheet, Int. J. Plasticity 24(4), 545–582) was applied to the springback prediction in sheet metal forming. The implicit finite element program ABAQUS was utilized to implement the developed constitutive equations via user material subroutine. For the verification purpose, the springback of AZ31B magnesium alloy sheet was measured using the unconstrained cylindrical bending test of Numisheet (Numisheet ’2002 Benchmark Problem, 2002. In: Yang, D.Y., Oh, S.I., Huh, H., Kim, Y.H. (Eds.), Proceedings of 5th International Conference and Workshop on Numerical Simulation of 3D Sheet Forming Processes, Jeju, Korea) and 2D draw bend test. With the specially designed draw bend test the direct restraining force and long drawn distance were attainable, thus the measurement of the springback could be made with improved accuracy comparable with conventional U channel draw bend test. Besides the developed constitutive models, other models based on isotropic constitutive equations and the Chaboche type kinematic hardening model were also considered. Comparisons were made between simulated results by the finite element analysis and corresponding experiments and the newly proposed model showed enhanced prediction capability, which was also supported by the simple bending analysis adopting asymmetric stress–strain response. [Copyright &y& Elsevier]

Abstract: This paper describes a combined fracture–plastic model for concrete. Tension is handled by a fracture model, based on the classical orthotropic smeared crack formulation and the crack band approach. It employs the Rankine failure criterion, exponential softening, and it can be used as a rotated or a fixed crack model. The plasticity model for concrete in compression is based on the Menétrey–Willam failure surface, the plastic volumetric strain as a hardening/softening parameter and a non-associated flow rule based on a nonlinear plastic potential function. Both models use a return-mapping algorithm for the integration of constitutive equations. Special attention is given to the development of an algorithm for the combination of the two models. The suggested combination algorithm is based on a recursive substitution, and it allows for the two models to be developed and formulated separately. The algorithm can handle cases when failure surfaces of both models are active, but also when physical changes such as crack closure occur. The model can be used to simulate concrete cracking, crushing under high confinement and crack closure due to crushing in other material directions. The model is integrated in a general finite element package ATENA and its performance is evaluated by comparisons with various experimental results from the literature. [Copyright &y& Elsevier]

Abstract: This paper presents a new approach using Artificial Neural Networks (ANNs) models to simulate the response during nanohardness tests of a variety of materials with nonlinear behavior. The ANNs continuous input and output variables usually include material parameters, indentation deflection, and resisting force. Different ANN models, including dimensionless input/output variables, are generated and trained with discrete finite-element (FE) simulations with different geometries and nonlinear material parameters. Only the monotonic loading part of the load–displacement indentation response is used to generate the trained ANN models. This is a departure from classical indentation simulations or tests where typically the unloading portion is used to determine the stiffness and hardness. The experimental part of this study includes nanoindentation tests performed on a silicon (Si) substrate with and without a nanocrystalline copper (Cu) film. The new ANN models are used to back-calculate (inverse problem) the in situ nonlinear material parameters for different copper material systems. The results are compared with available data in the literature. The proposed FE–ANN modeling approach is very effective and can be used in calibrating and predicting the in situ inelastic material properties using the monotonic part of the indentation response and for depths above 50nm where the overall resisting force represents a continuum response. [Copyright &y& Elsevier]

This paper describes a stress–strain interpolation method to model the macroscopic anisotropic elasto-plastic behavior of polycrystalline materials. Accurate analytical descriptions of yield loci derived from crystallographic texture [Int. J. Plasticity 19 (2003) 647; J. Phys. IV France 105 (2003) 39] are an interesting alternative to finite element models, where the macroscopic stress is provided by an averaging of microscopic stresses computed on a set of representative crystallites [Acta Metal 22 (1985) 923; Int. J. Plasticity 5 (1989) 67]. The parameters of the analytical functions modeling the yield locus are identified by comparison with a high number of stress tensors computed, for instance, by the well-known Taylor model [J. Inst. Metal 62 (1938) 307]. This identification method depends on the crystallographic texture and should be applied each time that the plastic strain has induced a significant texture evolution. The stress–strain interpolation method accurately describes the anisotropic material behavior in a narrow stress direction defined by only five stress points. The cost of texture updating is then greatly reduced compared to a full analytical function of the yield locus. After the mathematical description of the stress–strain interpolation method, its validity is demonstrated on two non-radial strain paths. The simulations of a deep drawing experiment allow comparing model predictions and measurements. Accuracy and CPU time of the interpolation stress–strain method are judged against two other models, respectively based on a complete analytical yield locus and on the averaging of crystallite stresses. [Copyright &y& Elsevier]

The silica-filled rubber material presented in this paper exhibits nonlinear elasticity, nonlinear rate dependence and stress-softening effect under cyclic loading. In order to model the material behavior in a finite element code, the internal state variable concept is considered for finite deformation viscoelasticity. Moreover, the so-called Mullins'' effect is taken into account by using a discontinuous damage concept. A total Lagrangian formulation with incompressibility constraint is adopted in the finite element code. The constitutive equations with their optimized set of parameters are validated by comparing the simulated results with experimental data. This result is very useful for the fatigue lifetime analysis of the investigated silica-filled rubber material. [Copyright &y& Elsevier]

Ultrasonic wave velocities propagating in a plastically deformed medium are known to depend upon its microstructural material properties. Therefore, the authors have proposed the theoretical modeling of an ultrasonic nondestructive method to evaluate plastically deformed states. In the present paper, we verify the proposed theoretical modeling of an ultrasonic nondestructive method and examine its accuracy by comparing the experimental results with the simulated subsequent yield surfaces, the longitudinal and transverse wave velocities under combined stress states of an aluminum alloy using internal state variables of an anisotropic distortional yield model which were determined to achieve a good fit for the experimental results of the longitudinal and transverse wave velocity changes under uniaxial tension test. As a special case, the velocity changes of longitudinal wave under pure shear state subjected to the combinations of tension and compression are also studied, it shows a different result compared with that of longitudinal wave velocity under torsional tests of thin thickness cylinders, i.e., simple shear state. The effects on ultrasonic wave velocity changes due to texture and cross slip under simple and pure shear states are studied via a finite element polycrystal model (FEPM). [Copyright &y& Elsevier]

A cylindrical cell model based on continuum theory for plastic constitutive behavior of short-fiber/particle reinforced composites is proposed. The composite is idealized as uniformly distributed periodic arrays of aligned cells, and each cell consists of a cylindrical inclusion surrounded by a plastically deforming matrix. In the analysis, the non-uniform deformation field of the cell is decomposed into the sum of the first order approximate field and the trial additional deformation field. The precise deformation field are determined based on the minimum strain energy principle. Systematic calculation results are presented for the influence of reinforcement volume fraction and shape on the overall mechanical behavior of the composites. The results are in good agreement with the existing finite element analyses and the experimental results. This paper attempts to stimulate the work to get the analytical constitutive relation of short-fiber/particle reinforced composites. [Copyright &y& Elsevier]

The r-value of a sheet metal is a measure of plastic anisotropy frequently used for prediction of performance in deep-drawing. It has also figured prominently in the literature for validation of theories where the predicted angular dependence of r is compared with the measured dependence. As plastic anisotropy in sheet metals is caused mainly by the preferred orientations of grains within the polycrystalline metal, it is natural to ask how r would depend on the orientation distribution function (ODF) w which defines the crystallographic texture of the polycrystal. In this paper a general formula relating r to w is derived for textured sheet metals whose plastic flow behavior is governed by a plastic potential f(σ, w), the anisotropic part of which depends linearly on the texture coefficients; here σ denotes the deviator of the Cauchy stress. Specific forms of this formula for orthorhombic sheets of cubic and of hexagonal metals are explicitly given. [Copyright &y& Elsevier]

It is essential to model the Bauschinger effect correctly for sheet metal forming process simulation and subsequent springback prediction when material points are subjected to cyclic loading conditions. The combined nonlinear hardening model for time independent cyclic plasticity, proposed by Chaboche and co-workers, is examined and a simple modification is suggested for the isotropic part of the hardening rule to utilize the conventional tensile test data directly. This modification is useful for the materials whose reverse loading curves saturate to the monotonic loading curve. In addition, an anisotropic nonlinear kinematic hardening model (ANK model) is proposed in an attempt to represent the Bauschinger effect more realistically. Possible offset in flow stress is modeled by treating the back stress evolution during reverse loading differently from the initial loading. This strategy coupled with the modified isotropic hardening rule seems to provide a way to model the Bauschinger effect consistently over multiple cycles. Two types of auto-body alloys are examined in this paper. Associated material parameters are determined by employing available tension-compression test data and multi-cycle bend test data. A developed finite element formulation is applied to analyze simple validation type of problems. The cyclic stress–strain curves generated from the proposed ANK model match remarkably well with measured data. [Copyright &y& Elsevier]

Superplastic forming is a valuable metal working technique because of the extreme ductility that can be achieved. However, it is limited in application due to the presence of small voids that grow and coalesce during the forming process, often causing premature failure. In order to understand and control this phenomenon accurate constitutive models must be developed which account for void parameters that affect the macroscopic behavior of the material. This paper looks specifically at the effect of void size and spacing on the ductility and flow stress of viscoplastic materials. Based on the gradient-dependent theory of plasticity, a model is proposed that accounts for size effects by incorporating strain gradient terms into a continuum based constitutive equation. Both experimental testing and finite element (FE) modeling were performed on Pb–Sn, tensile specimens with small holes drilled in them in random patterns. The experimental tests indicate that a decrease in void size results in an increase in ductility. The FE results demonstrate that the gradient terms strengthen the material by diffusing the strain in areas of high strain concentration and delay failure by slowing void growth. In addition, the model predicted an increase in ductility and flow stress with decreasing void size. [Copyright &y& Elsevier]