User Material Subroutine Research Articles

UMAT4COMSOL: An Abaqus user material (UMAT) subroutine wrapper for COMSOL

We present a wrapper that allows Abaqus user material subroutines (UMATs) to be used as an External Material library in the software COMSOL Multiphysics. The wrapper, written in C language, transforms COMSOL’s external material subroutine inputs and outputs into Fortran-coded Abaqus UMAT inputs and outputs, by means of a consistent variable transformation. This significantly facilitates conducting coupled, multi-physics studies employing the advanced material models that the solid mechanics community has developed over the past decades. We exemplify the potential of our new framework, UMAT4COMSOL, by conducting numerical experiments in the areas of elastoplasticity, hyperelasticity and crystal plasticity. The source code, detailed documentation and example tutorials are made freely available to download at www.empaneda.com/codes.

Cumulative fretting fatigue damage model for steel wire ropes

AbstractFretting fatigue contributes significantly to the fatigue failure process in steel wire ropes at the wire‐to‐wire trellis contact region with partial slip conditions. In this respect, this work demonstrates a new damage‐based fretting fatigue model for the prediction of such a failure process. The model is based on Lemaitre's damage equations for quasi‐brittle material with a damageable micro‐inclusion embedded in an elastic meso‐element. It incorporates the cyclic degradation of the elastic modulus of the drawn steel wire material. The fatigue life model acknowledges the mean stress effect. The constitutive and damage equations are formulated into user material (UMAT) subroutine for integration with Abaqus finite element analysis code. The localized fretting fatigue damage mechanism is simulated with an isolated two‐wire model. The effect of the contact condition with the coefficient of friction of 0.2 and 0.8 on the contact mechanics of the drawn wires is considered. The fretting fatigue mechanism map is established for each simulation case. The simulated results of N0 (no of cycles to initiate damage) and damage variable, D, confirm the fretting fatigue condition as the damage occurs in the slip region of the contact area for both the frictional conditions. The results were found in agreement with the previously establish Ruiz fretting parameter. This study will provide a base for the onward reliability assessment of steel wire ropes.

Modeling and simulation of dynamic compression of Bulk Metallic Glasses at room and elevated temperatures using split Hopkinson pressure bar setup

This paper presents a modeling and simulation study of dynamic compression behavior of Bulk Metallic Glasses (BMGs) at room and elevated temperatures using the split Hopkinson pressure bar (SHPB) setup. The primary objective of this study is to develop and validate a constitutive model and simulation methodology capable of predicting the high strain rate response of BMGs at different temperatures. We propose a constitutive model for BMGs that accounts for the effects of high strain rates and elevated temperatures. We numerically implemented this model in ABAQUS/Explicit Finite Element Analysis software by writing a Vectorized User Material (VUMAT) subroutine. The methodology for modeling and simulation of dynamic compression of BMG specimens using the SHPB setup is developed. The present simulations are able to correctly predict the rate-independent response of Zr41.2Ti13.8Cu12.5Ni10Be22.5 (Vitreloy-1) BMG under dynamic compression at room and elevated temperatures. Furthermore, the present simulations are also able to correctly predict the negative strain rate sensitivity (SRS) of Zr52.5Cu17.9Ni14.6Al10Ti5 (Vitreloy-105) BMG at room temperature. Finally, the present simulations correctly predict that the failure stress of Zr64.13Cu15.75Ni10.12Al10 BMG decreases with increasing temperature and exhibits a minimal positive SRS. The present study is the first successful attempt to model the mechanical response of various BMGs under dynamic compression and at room and elevated temperatures. In particular, the experimentally observed negative SRS in some BMGs has been successfully simulated. The present work has important implications for the design of next generation spacecraft shields that are based on BMGs for mitigating the effects of hypervelocity impacts from debris in space.

A Constitutive Model for Asymmetric Cyclic Hysteresis of Wrought Magnesium Alloys under Variable Amplitude Loading

A cyclic plasticity constitutive model was developed for materials with asymmetric cyclic behavior to explain the stabilized stress–strain response under variable amplitude loading. The proposed constitutive model incorporated the von Mises yield function with an adjustment to accommodate asymmetric yielding under tension and compression. A combined isotropic–kinematic hardening model was proposed to describe the evolution of the yield surface in the reference uniaxial frame and the actual frame. The history of plastic deformation is memorized by introducing internal variables, accumulated slip, and residual twins, which govern the cyclic flow behavior in the subsequent reversal. The additional conditions required to predict the stabilized hysteresis response of a material under variable amplitude loading were set out and incorporated into the constitutive model. The model was numerically implemented and programmed into a user material (UMAT) subroutine to run with the commercial finite element program, Abaqus/Standard 2019. The model was calibrated using the stabilized hysteresis response of ZEK100 and AZ31B sheets under constant amplitude strain-controlled cyclic loading for different strain amplitudes. To verify the model, constant amplitude and four different variable amplitude load spectra tests were performed and the stabilized stress–strain hysteresis response predicted by the model was compared with test results. It was demonstrated that the results are in very good agreement.

Mathematical Formulation and Numerical Simulation of the Mechanical Behavior of Ceramic/Metal (TiB/Ti) FG Sheets Subjected to Spherical Indenter

The main motivation for the present work is to provide an improved description of the response of Functionally Graded (FG) structures under a spherical indenter, considering material nonlinearities. This is achieved through the implementation of elastoplastic material behavior using integration points to avoid the division of the structure into multiple layers. The current paper proposes a numerical investigation into the mechanical response of functionally graded materials (FGMs) in contact with a rigid hemispherical head indenter. The numerical model considers both the Mori–Tanaka model and self-consistent formulas of Suquet to accurately model the smooth variation of material properties through the thickness of the elastoplastic FG material. The model execution involves a UMAT user material subroutine to implement the material behavior into ABAQUS/Standard. The user material UMAT subroutine is employed to introduce material properties based on the integration points, allowing for an accurate representation and analysis of the material’s behavior within the simulation. The developed numerical model is validated through a comparison with experimental results from the literature, showing a good correlation that proves the efficiency of the proposed model. Then, a parametric study is conducted to analyze the effect of the indenter dimension, the indentation depth and the gradient index on the indentation force, the contact pressure evolution, von Mises equivalent stress and equivalent plastic strain distributions located on the vicinity of the contact zone. The results showed that the elastoplastic response of TiB/Ti FG plates is significantly influenced by the gradient index, which determines the properties of the FG composite through the thickness. These results may help development engineers choose the optimal gradation for each industrial application in order to avoid contact damage.

Nanoscratching of polycrystalline copper examined through strain gradient crystal plasticity

Nanoscratch testing is a method pivotal for evaluating the mechanical and tribological characteristics of materials which involves the controlled scratching of specimens with a nano-scale indenter. This research delves into the analysis of effect of grain size on the deformation mechanisms and material responses during nanoscratch tests on polycrystalline copper. By utilizing finite element method and adopting a lower-order strain gradient crystal plasticity framework, this study investigates results such as reaction forces on the indenter, apparent friction coefficients, and alterations in pile-up topography. These factors are examined with the aforementioned strain gradient theory, employing calculations of the density of geometrically necessary dislocations to obtain size-dependent material response. The crystal plasticity framework is implemented into ABAQUS as a user material subroutine (UMAT), and the model's accuracy is affirmed through comparisons with experimental data from single crystal copper studies available in the literature. 3D geometries are generated to model a single crystal and three polycrystal materials with average grain diameters of 5 µm, 15 µm, and 50 µm. These specimens are subjected to deformation by a rigid Berkovich indenter to simulate nanoscratching tests in the numerical examples, where the key point is to examine the grain size effects while keeping fixed any other variables that may influence the results.

Characterization and Simulation of Shear-Induced Damage in Selective-Laser-Sintered Polyamide 12.

This paper presents the characterisation of selective-laser-sintered (SLS) samples of polyamide 12 (PA12) under shear loading. PA12 is a semi-crystalline thermoplastic and is used in various industries. Its behaviour under shear stress, which is particularly important for product reliability, has not yet been sufficiently investigated. This research focuses on understanding the material and damage behaviour of PA12 under shear-induced stress conditions. The study included quasi-static experiments and numerical simulations. Samples were prepared via SLS and tested according to ASTM standards. Digital image correlation (DIC) was used for precise deformation measurements. The Chaboche material model was used for the viscoplastic behaviour in the numerical simulations. Due to existing material discontinuities in the form of voids, the material model was coupled with the Gurson-Tvergaard-Needleman (GTN) damage model. A modified approach of the GTN model was used to account for low stress triaxiality under shear loading. These models were implemented in MATLAB and integrated into Abaqus via a User Material (UMAT) subroutine. The results of the experiments and simulations showed a high degree of accuracy. An important finding was the significant influence of the shear factor kw on the damage behaviour, especially during failure. This factor proved to be essential for the accurate prediction of material behaviour under shear-induced stress conditions. The integration of the modified GTN model with the Chaboche material model in UMAT enables an accurate prediction of the material and damage behaviour and thus makes an important contribution to the understanding of the mechanical material behaviour of SLS PA12 specimens.

Finite Element Analysis of the Effect for Different Thicknesses and Stitching Densities under the Low-Velocity Impact of Stitched Composite Laminates.

In this study, a progressive damage model was developed for the mechanical response and damage evolution of carbon fiber stitched composite laminates under low-velocity impact (LVI). The three-dimensional Hashin and Hou failure criteria were used to identify fiber and matrix damage. The cohesive zone model was adopted to simulate the delamination damage, combined with the linear degradation discounting of the equivalent displacement method to characterize the stiffness degradation of the material, and the corresponding user material subroutine VUMAT was coded. The finite element analysis of the LVI of stitched composite laminates under different energies was finished in Abaqus/Explicit. Furthermore, the simulation predictions matched well with the results of the experimental tests. Based on this, composite laminates' mechanical response and damage forms with different thicknesses and stitch densities were analyzed. The findings show that the main damages of composite laminates were matrix tensile damage and delamination. The stitching process could improve the impact tolerance of composite laminates, inhibiting delamination and reducing the area of the delamination damage. The higher the density of the stitching, the more noticeable its inhibition would be. The thickness of the laminate also had a more significant effect on the damage to the laminate. Thin plates were more prone to matrix tensile damage due to their lower flexural rigidity, whereas thick plates were more susceptible to delamination because of their higher flexural rigidity.

Damage evolution and fracture of aluminum alloy based on a modified Lemaitre model

Ensuring that metal materials do not fail during the forming process is a concern; forming is a complex process with development of a large amount of macroscopic and mesoscopic damage inside the metal. In this study, the damage evolution of 5052 aluminum alloy during the plastic forming process was studied using a modified Lemaitre damage model. First, a combination of theoretical derivation, experimental analysis, and fracture scanning was used to study the material damage evolution law at different strain rates. Subsequently, a more accurate nonlinear relationship between plastic strain and damage value was proposed, and an assumption regarding the Lemaitre damage model was revised. A VUMAT user material subroutine based on the Lemaitre damage model was developed; the reliability of the modified Lemaitre damage model was verified by numerically simulating the tensile process of 5052 aluminum alloy at different strain rates. The relative error between the fracture failure location of the specimen obtained from the numerical simulation of the modified Lemaitre model and that in the experiment was 3%.

Large deformation analysis of functionally graded revolutionary shallow thin shells with bi-modular effect: Snap-through buckling under different boundary constraints

Functionally graded materials (FGMs) enable structures to achieve a smooth transition between different material properties, providing an optimized combination of functions to meet the diversity of engineering needs. However, the presence of bi-modular effect in FGMs is often neglected due to the complexity in the analysis. In this paper, the curvature correction equivalent method based on the von Kármán theory will be applied to the theoretical study for the large deformation problem and the resulting snap-through buckling of functionally graded revolutionary shallow thin shells with bi-modular effect under different boundary constraints. Furthermore, a bi-modular FGMs user material subroutine (UMAT) is developed for the first time to simulate the real material model, thus validating the theoretical solution. The results show that except for the bi-modular effect of materials, boundary constraints of shells also have important influences on the relationship of load vs. central deflection and snap-through buckling. The research of boundary constraints brings new conclusions to snap-through buckling: the rotation constraint and radial constraint at the shell edge have opposite effects on snap-through buckling. This work will contribute to the analysis of the snap-through buckling of functionally graded revolutionary shallow thin shells with an obvious bi-modular effect and under various boundary constraints.

Parameter determination and verification of ZWT viscoelastic dynamic constitutive model of Al/Ep/W material considering strain rate effect

As a new type of energetic structural material, Al/Ep/W(Aluminum/epoxy/tungsten), whether as a fragment or projectile material, should comprehensively consider the impact energy release and structural strength, especially the structural strength is the premise to ensure the material integrity. The dynamic constitutive model of materials is the theoretical basis for describing the strength and dynamic behavior of materials. Therefore, it is great significance to determine the dynamic constitutive model parameters of Al/Ep/W materials considering strain rate effect, and to verify the reliability of the model. In this paper, Al/Ep/W material is prepared, and the stress/strain relationship curve of the material under high strain rate is obtained through Split Hopkinson Pressure Bar (SHPB) test. The ZWT viscoelastic constitutive model is selected based on the composition of the material and the distribution of the internal components, and the simplified ZWT constitutive model with damage under constant strain rate is derived, and the parameters of the constitutive model are fitted by the least square method. By using Kirchhoff stress and Green strain tensor theory, the incremental form of the constitutive model is derived, and the Abaqus user material subroutine is written and embedded in the finite element software. The accuracy of material VUMAT subroutine is verified by comparing the results of SHPB test and numerical simulation under high strain rate. Combined with the verified material model subroutine, the experiment and numerical simulation of Al/Ep/W cylindrical projectile impacting aluminum plate are conducted. The results show that the experimental and numerical simulation results are in good agreement. The proposed model can be used to evaluate the dynamic response characteristics of the new energetic material projectile to the lightweight aluminum armor protective structure.

Progressive pseudograin damage accumulation model for short fiber-reinforced plastics and its application to fatigue life prediction

A progressive pseudograin damage accumulation (PPDA) model is proposed to predict the fatigue life of short fiber-reinforced plastics (SFRPs), combining viscoelastic-viscoplastic (VEVP) two-step homogenization theory with Chaboche fatigue damage model. Each representative volume element (RVE) of SFRPs is decomposed into pseudograins using a two-step homogenization framework. Then, the fatigue life of each pseudograin is predicted using a master S-N curve, which is prepared based on the “normalized fatigue factor” taking into account both the stress ratio and multiaxial stress state. Thereafter, the overall failure of RVE is predicted by a PPDA model, in which each pseudograin fails progressively considering the stress concentration of the living pseudograins, resulting in non-linear fatigue damage evolution. Finally, the PPDA model is successfully implemented into ABAQUS user material subroutine (UMAT), predicting the fatigue lifetime in good agreement with experimental data.

Numerical predictions of low cyclic fatigue and creep-fatigue behavior of P92 steel under non-isothermal-mechanical loading

Low-Cycle Fatigue (LCF) and creep-fatigue-interaction (CFI) behavior of a ferritic-martensitic stainless steel P92 is studied under strain-controlled non-isothermal -mechanical fatigue loading in the temperature range of 300°C∼620°C and 500°C∼620°C, respectively. The strain-controlled tests with and without the tensile and compression holding times are simulated for different mechanical strains amplitudes. An improved Unified Viscoplastic constitutive Model (UVM) is proposed based on the framework of modified Chaboche non-linear kinematic hardening rule. The improved UVM incorporates strain rate sensitivity, temperature rate dependence, static recovery associated with plastic strain, mean stress evolution and cyclic softening of strain range dependence, and so on. Furthermore, the expressions of the implicit stress integration algorithm and the consistent tangential modulus are deduced on the basis of radial return mapping and backward Euler integration methods, respectively, and the improved UVM is implemented into the ABAQUS software using the user material subroutine UMAT. The simulation results of the UVM correlate well with the experimental data.

Geomechanical reservoir modelling with Thermodynamics-based Artificial Neural Networks (TANNs)

Geological subsurface storage is a promising strategy for large-scale, cost-efficient energy storage systems. Stress sensitivity has notably influence on the long-term stability and serviceability of subsurface reservoirs set for energy storage use. The evolution of the field stress of stress-sensitive reservoirs and the associated structural deformation, often a consequence of fluid production and injection, can cause significant changes to the reservoir stress-dependent properties [1]. These properties include pore and void compressibility, and porosity. For fractured and faulted reservoirs, field stress variation may also impact fracture conductivity, alter pre-existing fractures, and reactivate faults [4].
 Current geomechanical reservoir simulators incorporate the evolution of the reservoir mechanical state by means of material constitutive modelling, typically within a Finite Element Modelling (FEM) framework. In efforts to honour the heterogeneity and multi-scale nature of subsurface reservoirs, multi-scale solution methods are commonly adopted. For a reservoir multi-scale simulation, the micro-scale problem must be iteratively solved for different input parameters, render-ing the solution method computationally exhaustive, particularly for two-way coupled problems.
 The combination of machine learning-based solution methods and FEM frameworks can address the computational inefficiency of conventional multi-scale reservoir modelling schemes. In principle, a machine learning algorithm trained to learn the constitutive behaviour of a material can replace in-built material constitutive models in a FEM framework. We resort to Thermodynamics-based Artificial Neural Networks (TANNs), a physics-based data-driven machine learning algorithm introduced in [5] for material constitutive modelling. TANNs have been shown to guarantee the thermodynamic consistency of learnt material constitutive models. The first and second laws of thermodynamics are directly encoded in the architecture of TANNs through the definition of two scalar functions, an energy potential and a dissipation function, and the computation of their differentials [3].
 TANNs can be incorporated in FEM tools, in what is referred to as TANNxFEM in [6]. We present the application of the TANNxFEM framework to geomechanical reservoir modelling. This work aims to introduce a computationally efficient reservoir modelling framework, for which uncertainty quantification is possible. The proposed framework can maximise the use of information inherently contained in high-dimensional data, and significantly reduce computation demands necessary for accurate statistical evaluation, while warranting physical and geological realism.
 TANNs are first trained on analytical material data, computed by numerical integration of an incremental, thermodynamically consistent material model presented in [2]. The trained TANNs are then imported into a user material subroutine for the finite element package Abaqus. Through an input file, the parameters of the trained neural network are read as a set of material properties. The material subroutine then evaluates the incorporated trained neural network to construct the stress and elasticity tensors necessary for large-scale finite element reservoir simulation. The above proposed framework is validated against a large-scale finite element simulation with a user material subroutine implementing the constitutive model used to first generate the training data for TANNs. The free-energy, dissipation, and the stress-strain response of the two finite element simulations are compared for model verification.

Mechanical and thermal properties of environmentally friendly straw boards

Straw is an environmentally friendly, cost-effective, and abundant raw material for building boards. To assess the feasibility of using straw boards in building envelops, such as being alternative sheathing panels in light-gauge steel-framed members, for instance, walls and floors, both the mechanical and thermal properties of straw boards with high densities were investigated. The straw boards involved in this study include five wheat straw strand boards (WSSB12, WSSB15, WSSB18, WSSB25, and WSSB30) and a paper straw board (PSB58) named with a combination of the respective board type and thickness. Among them, the WSSBs are a type of straw composite, while the PSB is an improved straw bale with sheathing paper, which is mainly for enhancing the board integrality. Moreover, the former is composed of smashed straw fibers and isocyanate resin and has higher densities, while the latter is without using any artificial binders. Mechanical properties, including compression, tension, and bending properties, were investigated by tests and a proposed prediction method of tensile strength. In the experimental studies of compression properties, the failure modes, characteristics of load-deformation curves, and the differences in material directivity were analyzed and discussed. The results show that the WSSBs were considered to be transverse isotropic material with brittle characteristics in the plane. Then, the experimental studies of bending properties were carried out, and the results show that the bending strength is less than the compressive strength for WSSBs, while the bending strength of PSB is greater than its compressive strength. And the bending elastic modulus and the compression elastic modulus are close for either the WSSBs or the PSB. Furthermore, finite element models of the bending test specimens using the user material subroutine UMAT were developed to predict the tensile strength ft, and the constraint checks were conducted. It is verified that the prediction results of ft are believable, and the prediction method proposed is feasible. For the thermal properties of straw boards, tests were performed using the temperature control box - heat flux meter method, and the thermal conductivity λ was mainly focused. It is found that a significant linear correlation exists between the density ρ and λ, and the proposed fitting formula can be used to predict the thermal conductivities of such materials. Finally, brief comparisons of the mechanical and thermal properties between the straw boards and the oriented strand boards (OSBs) were conducted, and the feasibility of applying straw boards in building envelops, such as alternative sheathing panels with load bearing and insulation demands was verified. This study contributes to popularizing the application of straw boards in engineering structures by a compromising consideration of mechanical and thermal properties, which plays a positive role in the development of green buildings.

Damage of CRTS III type ballastless track-32 m simply supported girder structural system under long-term deformation effects

Until now, the CRTS (China’s Railway Track System) III type ballastless track-girder system has been gradually used in high-speed railway engineering. However, the effect of long-term deformation of prestressed box girders on the upper track structure is often overlooked. Given the strict requirements for track smoothness in high-speed railways, an in-depth study of the long-term deformation of the CRTS III type ballastless track-32 m simply supported girder system (girder-track system) is particularly important. In this study, a refined finite element model was established for a three-span CRTS III type ballastless track- simply supported box girder system. Based on the aid of the CEB-FIP 90 creep model and the UMAT (User-Material) subroutine, the long-term deformation calculations were investigated. Furthermore, an in-depth analysis of stress and damage of the CRTS III type ballastless track under the long-term deformation of the box girder was conducted by combining concrete damaged plasticity (CDP) and cohesive zone model (CZM) constitutive models. The numerical simulated results indicated that after four years of operation, the creep camber of the box girder in the girder-track system would reach to 3.41 mm. The maximum tensile and compressive longitudinal stresses of the base plate would reach to 0.537 MPa and 11.983 MPa, respectively. Meanwhile, the maximum tensile and compressive longitudinal stresses of the self-compacting concrete layer would reach to 0.958 MPa and 2.701 MPa, respectively. In the box girder mid-span, significant damage could be observed in the edge of the two base plates near the mid-span, with a maximum compressive damage rate of 0.164 and the maximum tensile damage rate of 0.304. The research of this study has achieved the prediction of long-term deformation in the girder-track system, providing an important basis for the reliability assessment and life prediction of the girder-track system.

Numerical analysis of the impact behaviour of a composite eco-structure

An explicit numerical model is developed for the impact behaviour of a new composite eco-structure made of a plywood core and flax/epoxy composite skin. A constitutive orthotropic material behaviour is imposed to model the elastic response of plies of plywood core and flax skin. A stress-based modified Hashin-3D damage model with four independent failure criteria in tensile and compressive mode is incorporated for predicting the damage initiation. A strain threshold based exponential method is adopted to predict the damage scaling and its evolution. The above proposed model is implemented through user material subroutine (VUMAT) in ABAQUS Explicit. The developed model is validated with experimental low-velocity impact test results and can accurately predict the stiffness degradation, plateau, and post-peak softening of wooden plies. A good agreement with the better accuracy is achieved between the predictions and the test results.

Time-dependent deviation of high-speed railway bridge pier-cap-pile foundations in deep soft soils under surcharge loads: a case study

Permanent surcharges or temporary surcharges along high-speed railway lines occur frequently due to irregularities in construction, resulting in lateral deviations of adjacent pier-cap-pile foundations, especially in soft soil areas. The pier-cap-pile foundation deviation caused by surcharge loads in soft soils shows a significant time-dependent characteristic (TDC) that has been disregarded in most previous studies. In this study, an extended Koppejan model, which considers the TDC of soil movements, was developed, and the corresponding user-material subroutine (UMAT) was programmed in ABAQUS software. Then, the UMAT was embedded into a finite element model that was combined with an actual engineering case. Based on the validated model, the time-dependent deformation development of the pier-cap-pile foundation was investigated, and the subsequent service performance and deformation mechanism characterized by the time-dependent additional load were revealed. In addition, a rectification measure with an unloading + high-pressure rotary jetting pile was proposed, and the pile foundation performance after rectification was evaluated. The evaluation results were successfully applied to field rectified construction. The research findings obtained in this study may provide a valuable reference for similar accidents of pile foundation deviation caused by adjacent surcharge loads.

A 3D Anisotropic Thermomechanical Model for Thermally Induced Woven-Fabric-Reinforced Shape Memory Polymer Composites.

Soft robotic grippers offer great advantages over traditional rigid grippers with respect to grabbing objects with irregular or fragile shapes. Shape memory polymer composites are widely used as actuators and holding elements in soft robotic grippers owing to their finite strain, high specific strength, and high driving force. In this paper, a general 3D anisotropic thermomechanical model for woven fabric-reinforced shape memory polymer composites (SMPCs) is proposed based on Helmholtz free energy decomposition and the second law of thermodynamics. Furthermore, the rule of mixtures is modified to describe the stress distribution in the SMPCs, and stress concentration factors are introduced to account for the shearing interaction between the fabric and matrix and warp yarns and weft yarns. The developed model is implemented with a user material subroutine (UMAT) to simulate the shape memory behaivors of SMPCs. The good consistency between the simulation results and experimental validated the proposed model. Furthermore, a numerical investigation of the effects of yarn orientation on the shape memory behavior of the SMPC soft gripper was also performed.

Finite element implementation of a certain class of elasto-viscoplastic constitutive models

In this paper a selected type of elasto-viscoplastic constitutive equations is considered. The viscoplastic model which was proposed by Marquis is generalized by allowing multiple terms describing the isotropic and the kinematic hardening. Furthermore, the presented model formulation enables one to use an arbitrary equivalent plastic strain function to describe the isotropic hardening behavior. What is more, the backstress evolution equation which was proposed by Marquis was modified so that any equivalent plastic strain function can be used in the recovery term now. The general form of the generalized constitutive model obtained this way was subsequently implemented into the finite element method (FEM). For that purpose, the radial-return mapping algorithm was utilized. The consistent tangent operator was derived for the considered class of models and is presented in the paper. A developed user material subroutine (UMAT) which allows one to use the viscoplastic models under consideration in the FEM program CalculiX is attached in the appendix section. A number of numerical simulations were conducted in order to verify the performance of the developed UMAT code.