Set Of Internal State Variables Research Articles

Dynamic resistive switching devices for neuromorphic computing

Neuromorphic systems that can emulate the structure and the operations of biological neural circuits have long been viewed as a promising hardware solution to meet the ever-growing demands of big-data analysis and AI tasks. Recent studies on resistive switching or memristive devices have suggested such devices may form the building blocks of biorealistic neuromorphic systems. In a memristive device, the conductance is determined by a set of internal state variables, allowing the device to exhibit rich dynamics arising from the interplay between different physical processes. Not only can these devices be used for compute-in-memory architectures to tackle the von Neumann bottleneck, the switching dynamics of the devices can also be used to directly process temporal data in a biofaithful fashion. In this review, we analyze the physical mechanisms that govern the dynamic switching behaviors and highlight how these properties can be utilized to efficiently implement synaptic and neuronal functions. Prototype systems that have been used in machine learning and brain-inspired network implementations will be covered, followed with discussions on the challenges for large scale implementations and opportunities for building bio-inspired, highly complex computing systems.

Investigation on a full coupling between damage and other thermomechanical behaviours in the standard thermodynamic framework including environmental effects

In the present paper, constitutive equations accounting for coupled damage-thermo-elasto-(visco)plastic and diffusion at small deformation are proposed in the standard thermodynamics of irreversible processes framework. One main objective is to include the diffusion phenomenon in the models with ductile damage. The model is developed in the framework of thermodynamics of irreversible processes with a set of internal state variables. For illustration, we consider hydrogen diffusion in both normal interstitial lattice sites and trapping sites. The damage modelling of microvoids or microcracks is introduced by the use of Continuum Damage Mechanics framework leading to the definition of effective state variables on fictive undamaged configuration based on the total energy equivalence assumption. Consequently, the full coupling concerns not only the elastic and inelastic behaviour with hardening (isotopic and kinematic), but also the thermal and diffusion phenomena. The concept of the total energy equivalence is thus extended to define effective temperature, entropy, and effective state variables associated with diffusion. It enables to obtain different couplings between thermal phenomena, diffusion phenomena, and the mechanical behaviour, especially isotropic ductile damage. Such a full coupled model is then applied to a representative volume element subject to some typical simple loading paths for illustration and test of such couplings.

A Unified Elastoplastic Model of Unsaturated Soils Considering Capillary Hysteresis

Unlike its saturated counterparts, the mechanical behavior of an unsaturated soil depends not only upon its stress history but also upon its hydraulic history. In this paper, a soil-water characteristic relationship which is capable of describing the effect of capillary hysteresis is introduced to characterize the influence of hydraulic history on the skeletal deformation. The capillary hysteresis is viewed as a phenomenon associated with the internal structural rearrangements in unsaturated soils, which can be characterized by using a set of internal state variables. It is shown that both capillary hysteresis and plastic deformation can be consistently addressed in a unified theoretical framework. Within this context, a constitutive model of unsaturated soils is developed by generalizing the modified Cam-Clay model. A hardening function is introduced, in which both the matric suction and the degree of saturation are explicitly included as hardening variables, so that the effect of hydraulic history on the mechanical response can be properly addressed. The proposed model is capable of capturing the main features of the unsaturated soil behavior. The new model has a hierarchical structure, and, depending upon application, it can describe the stress-strain relation and the soil-water characteristics in a coupled or uncoupled manner.

Implicit integration scheme for porous viscoplastic potential-based constitutive equations

This paper deals with a viscoplastic potential-based model allowing thermomechanical damage behavior modeling of porous materials. The model describes rate dependent effects, hardening, creep as well as defects coalescence and propagation. Kinematic and isotropic hardening effects are taken into account by a set of internal state variables. The integration and implementation of the model into the FE code using a fully implicit integration scheme is exposed. Finally, it's used to predict mechanical behaviour degradation of solder layers used in power electronic packaging. Stress-strain behaviour and the evolution of volumic fraction of voids for the material under cyclic loading are presented.

Coupling effects in dynamic calorimetry: Frequency-dependent relations for specific heat and thermomechanical responses — A one-dimensional approach based on thermodynamics with internal state variables

As shown by Christensen et al. [2], temperature-induced stresses or strains can have a strong influence on the frequency-dependent specific heat, especially of thin layers of viscoelastic materials near the glass transition. Thus, both the mathematical representation and the physical understanding of these couplings are essential for the interpretation of temperature-modulated DSC data. The approach provided in this paper is based on thermodynamics with internal state variables. It thus differs from the transfer-matrix method which has been applied in Refs. [2,29] and constitutes a thermodynamic basis from a different point of view for the interpretation of the results obtained in Refs. [2,29,32]. Furthermore, although not the object of this paper, time-domain simulations can also be done with the model presented thus allowing for the calculation of temperature-ramping experiments and effects observed therein [42]. The approach in this paper is restricted to one-dimensional states of stress and strain to focus on the main idea and keep the mathematical formalism to a minimum. The Gibbs free energy is chosen as thermodynamic potential and the primary variables – the stress and the temperature – are supplemented by a set of internal state variables which is introduced to include history-dependent and hence viscoelastic effects. The Gibbs free energy is approximated up to second order terms in the vicinity of a reference state. Employing the Legendre transform, a corresponding expression for the Helmhotz free energy is obtained. Evaluating the laws of thermodynamics, explicit frequency-dependent expressions for the specific heat under constant stress or strain, the thermal expansion behaviour as well as the mechanical response functions are obtained. Recently published formulations of the Prigogine–Defay ratio can also be derived from the proposed constitutive model.

On the frequency-dependent specific heat and TMDSC: Constitutive modelling based on thermodynamics with internal state variables

To develop constitutive models to represent the thermomechanically chemically coupled behaviour of curing resins, vulcanizing elastomers or melting and crystallizing polymers the technique of DSC is extremely helpful. In the present study, the method of TMDSC is interpreted and evaluated in the context of thermodynamics with internal state variables. The balance equation of energy and the dissipation principle in the form of the Clausius–Duhem inequality form the theoretical basis of our study. Since the pressure and the temperature are the external variables in DSC, the specific Gibbs free energy is used as thermodynamic potential. It depends on temperature, stress and a set of internal state variables to represent the microstructure of the material on a phenomenological basis. The temperature- and internal variable-induced changes in the Gibbs free energy are approximated by a Taylor series up to second order terms. As a substantial result of this work, closed-form expressions for the dynamic calorimetric response due to harmonic temperature perturbations and the frequency-dependent complex heat capacity are derived. The theory allows a physical interpretation of the complex heat capacity and its underlying phenomena and is in accordance with experimental observations from literature.

Modeling the Coupled Strain and Magnetization Response of Magnetic Shape Memory Alloys under Magnetomechanical Loading

This article is concerned with the modeling of the magnetic shape memory alloy (MSMA) constitutive response caused by the reorientation of martensitic variants under mechanical and magnetic fields. The presented model is able to better capture the complexity of the magnetomechanical MSMA behavior by accounting not only for the mechanism of field-induced variant reorientation, but also the magnetization rotation away from magnetic easy axes and the magnetic domain wall motion at low stress and magnetic field levels. Following the general formulation of the model, reduced versions of the constitutive equations are derived for three specific loading cases: (1) magnetic-field-induced variant reorientation at constant stress; (2) stress-induced variant reorientation at constant magnetic field; (3) variant reorientation under collinear magnetic field and stress with perpendicular bias field. For each of these cases the nonlinear and hysteretic strain and magnetization response of MSMAs are predicted and compared to experimental data where available. The relation of critical stresses and magnetic fields for the activation of the reorientation process are visualized in a variant reorientation diagram. The captured loading-history-dependent macroscopic material response is explained in detail by connecting it to the evolution of the crystallographic and magnetic microstructure as represented by a set of internal state variables.

Numerical Analysis of Triaxial Residual Stresses in Quenched 316H Stainless Steel

Residual stress fields can cause creep damage in thermally aged components, even in the absence of working loads. In order to study this issue, the authors present a numerical study on the development of triaxial residual stresses in stainless steel specimens. A mechanical model dedicated to the analysis of heat treatment problems is described. The presented formulations are implemented incrementally with a non-linear constitutive model, adequate to the simulation of a wide range of thermal processes. The flow rule is a function of the equivalent stress and the deviatoric stress tensor, of the temperature field and of a set of internal state variables. The thermomechanical coupled problem is solved with a staggered approach. Spray water quenching was used to generate residual stress fields in solid cylinders and spheres made from 316H stainless steel. Finite element simulations were performed to find out how process conditions and specimen geometry influence the resulting residual stress distributions. The results show that compressive residual stresses are developed near the surfaces of the cylinders and spheres while tensile residual stresses occur near the centre. The level of residual stresses was found to be dependent on the heat transfer coefficient.

Numerical investigation of dynamic shear bands in inelastic solids as a problem of mesomechanics

The main objective of the present paper is to discuss very efficient procedure of the numerical investigation of the propagation of shear band in inelastic solids generated by impact-loaded adiabatic processes. This procedure of investigation is based on utilization the finite element method and ABAQUS system for regularized thermo-elasto-viscoplastic constitutive model of damaged material. A general constitutive model of thermo-elasto-viscoplastic polycrystalline solids with a finite set of internal state variables is used. The set of internal state variables is restricted to only one scalar, namely equivalent inelastic deformation. The equivalent inelastic deformation can describe the dissipation effects generated by viscoplastic flow phenomena. As a numerical example we consider dynamic shear band propagation in an asymmetrically impact-loaded prenotched thin plate. The impact loading is simulated by a velocity boundary condition, which are the results of dynamic contact problem. The separation of the projectile from the specimen, resulting from wave reflections within the projectile and the specimen, occurs in the phenomenon. A thin shear band region of finite width which undergoes significant deformation and temperature rise has been determined. Shear band advance, shear band velocity and the development of the temperature field as a function of time have been determined. Qualitative comparison of numerical results with experimental observation data has been presented. The numerical results obtained have proven the usefulness of the thermo-elasto-viscoplastic theory in the investigation of dynamic shear band propagations.

Modelling and numerical analysis of heat treatments on aluminium parts

AbstractA theoretical model suitable for the modelling and analysis of heat treatment problems is described. The presented formulations are implemented incrementally with a non‐linear rate‐dependent constitutive model, adequate to the simulation of a wide range temperature processes. The large deformation model is based on the additive decomposition of the strain rate tensor in elastic, thermal and viscoplastic parts. The flow rule is a function of the equivalent stress and the deviatoric stress tensor of the temperature field and of a set of internal state variables. The thermal problem is solved by a prediction/correction algorithm. The prediction, which uses a semi‐implicit integration, provides a first estimation of the temperature field. The correction stage, performed with a Newton–Raphson implicit scheme, improves the solution until a satisfactory result is found. The thermomechanical coupled problem is solved with a staggered approach. The finite element formulations for coupled analysis of deformation and heat transfer given in this article are validated and applied to the process of quenching of aluminium parts into boiling water. Copyright © 2006 John Wiley & Sons, Ltd.

Formulation of capillary hysteresis with internal state variables

A thermodynamically consistent framework is proposed for modeling the hysteresis of capillarity in partially saturated porous media. Capillary hysteresis is viewed as an intrinsic dissipation mechanism, which can be characterized by a set of internal state variables. The volume fractions of pore fluids are assumed to be additively decomposed into a reversible part and an irreversible part. The irreversible part of the volumetric moisture content is introduced as one of the internal variables. It is shown that the pumping effect occurring in a porous medium experiencing a wetting/drying cycle is thermodynamically admissible. A generic evolution equation for internal variables is developed. By virtue of the notion of the bounding surface plasticity, a model of capillary hysteresis is developed, which is capable of predicting all types of (primary, secondary, and higher‐order) scanning curves within the boundary loop. Provided that the main wetting curve and the main drying curve have been experimentally determined, the proposed model requires only one additional parameter to describe all the scanning curves. The model predictions are compared with experimental measurements found in the literature, showing that the new model is capable of describing the capillary hysteretic phenomena in a variety of partially saturated porous materials.

Numerical analysis of large deformation processes at elevated temperatures

The authors describe a theoretical model and kinematic approach suitable for the numerical analysis of problems at large deformation finite strains and rotations. The presented formulations are implemented incrementally with a non-linear and rate-dependent constitutive model, adequate to the simulation of high temperature processes. The large deformation kinematic model is based on the additive decomposition of the transformation gradient and the strain rate tensor in thermoelastic and viscoplastic parts. Stress–strain relations leading to the constitutive equations governing finite deformations are formulated on an unrotated frame of reference. These relations are obtained either by polar decomposition of the transformation gradient or by the rotation increment method. Both approaches and algorithms are thoroughly compared and discussed. The flow rule is a function of the equivalent stress and the deviatoric stress tensor, of the temperature field and of a set of internal state variables. The increments of the state variables are calculated with a forward gradient time integration procedure, based on a numerical estimation of the integral of the strain rate tensor. The model was implemented in a three-dimensional finite element code and tested with a set of tensile and shear tests on aluminium alloy specimens. In order to evaluate the performance of the numerical algorithms with elevated temperature processes, tests were done at temperatures ranging from room temperature to 580K. Numerical simulation results are compared with experimental results and shown to be in good agreement. Real material behaviour is fairly well predicted and matches the experimental results obtained with different loading conditions at different temperatures.

Computational Modeling of Damage Growth in Composite Laminates

A progressive damage growth model is developed for composite laminates under compression. The mechanics of damage initiation and growth in a single lamina is modeled in a two-dimensional plane stress setting, using a system of orthotropic nonlinear elastic relations and a set of internal state variables. The latter are associated with different damage mechanisms that are unique to a e ber-reinforced lamina. A thermodynamically consistent set of equations is developed for the evolution of damage growth. The formulation is numerically implemented using the commercially available e nite element package ABAQUS. The present method is applied to analyze the problem of damage growth in a compressively loaded notched laminate. Predictions of the model compared against available experimental observations are promising. EVELOPMENT of computational methodologies for the prediction of progressive damage growth in continuous e ber composite laminates is presently an active area of research. Available predictive methods are based on dee ning strength-based criteria at the lamina level. Based on critical values for tensile, compressive and shear “ strengths,” these methods compute predee ned damage indices that are expressed in functional form in terms of the current stress state. When any of these indices exceeds a predee ned critical value, the material is said to have failed. 1 Beyond initial failure, a consistent and rigorous methodology to account for progressive material deterioration has not been investigated thoroughly. An exception to this is the work by Schapery and Sicking, 2 who carried out lamina-level tests and validated the test results by developing a thermodynamically based progressive damage formation and growth model. In these studies Schapery and Sicking assumed that the e ber-direction response is essentially linear (slight elastic nonlinearity in the e ber direction was accounted for), but damage (microcracking and transverse cracking) formation affected the response in the transverse direction. Consequently, internal state variables that are related to the damage mechanisms in the transverse direction were identie ed, and evolution laws that specify the growth of damage and hence its ine uence on the transverse direction response were prescribed. In contrast to the transverse direction, in which damage accumulation results in progressively decreasing but smooth variations in instantaneous tangent moduli, damage accumulation in the e ber direction leads to nonsmooth abrupt changes in the corresponding moduli. These changes must be properly captured if progressive damage growth in composite laminates is to be modeled accurately. In the present paper Schapery’ s theory (ST) is extended to account for e ber-direction damage (both, in tension and compression) by identifying an additional internal state variable associated with the e ber-direction response. By doing this, we have shown that it is

Non-local coupling of viscoplasticity and anisotropic viscodamage for impact problems using the gradient theory

A general framework for the analysis of heterogeneous media that assesses a strong coupling between viscoplasticity and anisotropic viscodamage evolution is formulated for-impact related problems within the framework of thermodynamic laws and nonlinear continuum mechanics. The proposed formulations include thermo-elasto-viscoplastici- ty with anisotropic thermo-elasto-viscodamage, a dynamic yield criterion of a von Mises type and a dynamic viscodamage criterion, the associated flow rules, non-linear strain hardening, strain-rate hardening, and temperature softening. The constitutive equations for the damaged material are written according to the principle of strain energy equivalence between the virgin material and the damaged material. That is, the damaged material is modeled using the constitutive laws of the effective undamaged material in which the nominal stresses are replaced by the effective stresses. The evolution laws are impeded in a finite deformation framework based on the multiplicative decomposition of the deformation gradient into elastic, viscoplastic, and viscodamage parts. Since the material macroscopic thermomechanical response under high-impact loading is governed by different physical mechanisms on the macroscale level, the proposed three-dimensional kinematical model is introduced with manifold structure accounting for discontinuous fields of dislocation interactions (plastic hardening), and crack and void interactions (damage hardening). The non-local theory of viscoplasticity and viscodamage that incorporates macroscale interstate variables and their higher-order gradients is used here to describe the change in the internal structure and in order to investigate the size effect of statistical inhomogeneity of the evolution-related viscoplasticity and viscodamage hardening variables. The gradients are introduced here in the hardening internal state variables and are considered to be independent of their local counterparts. It also incorporates the thermomechanical coupling effects as well as the internal dissipative effects through the rate-type covariance constitutive structure with a finite set of internal state variables. The model presented in this paper can be considered as a framework, which enables one to derive various non-local and gradient viscoplasticity and viscodamage theories by introducing simplifying assumptions.

Thermomechanical modeling of polycrystalline SMAs under cyclic loading, Part I: theoretical derivations

A generic form of Gibbs free energy for polycrystalline Shape Memory Alloys (SMAs) is first obtained in this work, by forming the increments of both elastic potential energy and Gibbs chemical energy over a Representative Volume Element (RVE) with respect to an infinitesimal increment of martensite. A set of internal state variables, i.e., martensitic volume fraction, macro-transformation strain, and back and drag stresses due to both martensitic phase transformation and its interaction with plastic strains, are introduced. The evolution of these internal state variables during phase transformation is proposed based on the micromechanical analysis over the RVE. Four primary mechanisms governing the transformation induced hardening effect are discussed. It is concluded that the back and drag stresses related to plastic deformation do not remain constant, but they vary during phase transformation, even though the local plastic residual stresses are assumed to be constant. The initial material heterogeneity of SMAs, which is essential for the initiation of the phase transformation, is modeled by an initial residual stress field, which can be described by a probability distribution function. In this Part I of a four-part paper, the theoretical derivations are presented. Specific cases of the thermomechanical response of SMAs predicted by the model will be presented in Part II, together with experimental results for phase transformation at constant plastic strains. Experimental results and model predictions for cyclic loading of SMAs with evolving plastic strains will be considered in Part III, while the modeling of minor hysteresis loops of SMAs will be presented in Part IV of this series of four papers on SMAs.

Continuum Damage Mechanics Theory and Application-Part I: Theory

A systematic formulation for isotropic and anisotropic elasto-plastic analysis of static and dynamic damage mechanics problems based on the principle of thermodynamics is presented in this article. These formulations are developed by the combination of concepts between the internal energy dissipation and the damage elasto-plasticity energy potential in terms of a set of internal state variables for explanation of microstructural changes in damaged materials. The main studies in this article are related to isotropic and anisotropic elasto-plastic damage mechanics problems, as well as dynamics of damaged materials and structures. The theory of damage mechanics has also been extended to study the behaviour of isotropic and anisotropic damaged materials subjected to dynamic loading.

Analysis of anisotropy and plastic spin effects on localization phenomena

The main objective of the paper is the investigation of the influence of the anisotrophy and plastic spin effects on criteria for adiabatic shear band localization of plastic deformation. A theory of thermoplasticity is formulated within a framework of the rate-type covariance material structure with a finite set of internal state variables. The theory takes into consideration such effects as plastic non-normality, plastic-induced anisotropy (kinematic hardening), micro-damage mechanism, thermomechanical coupling and plastic spin. The next objective of the paper is to focus attention on cooperative phenomena in presence of the plastic spin, and the discussion on the influence of synergetic effects on localization criteria. A particular constitutive law for the plastic spin is assumed. The necessary condition for a localized plastic deformation region to be formed is obtained. This condition is accomplished by the assumption that some eigenvalues of the instantaneous adiabatic acoustic tensor vanish. A procedure has been developed which allows us to discuss two separate groups of effects on the localization phenomenon along a shear band. Plastic spin, spatial covariance and kinematic hardening effects are investigated at an isothermal process in an undamaged solid. In the second case, an adiabatic process in a damaged solid is discussed when the spatial covariance terms and the plastic spin are neglected. Here the thermomechanical coupling, micro-damage mechanism and kinematic hardening effects are examined. For both cases, the criteria for adiabatic shear band localization are obtained in an exact analytical form. Particular attention is focused on the analysis of the following effects: (i) plastic non-normality; (ii) plastic spin; (iii) covariant terms; (iv) plastic strain-induced anisotropy; (v) micro-damage mechanism; (vi) thermomechanical couplings. Cooperative phenomena are considered, and synergetic effects are investigated. A discussion of the influence of the plastic spin, kinematic hardening and covariant terms on the shear band localization conditions is presented. A numerical estimation of the effects discussed is given.

Numerical modelling of localized fracture of inelastic solids in dynamic loading processes

The main objective of the paper is the investigation of adiabatic shear band localized fracture phenomenon in inelastic solids during dynamic loading processes. This kind of fracture can occur as a result of an adiabatic shear band localization generally attributed to a plastic instability implied by microdamage and thermal softening during dynamic plastic flow processes. By applying ideas of synergetics it can be shown that as a result of instability hierarchies a system is self-organized into a new shear band pattern system. This leads to the conclusion that inelastic solid body considered during the dynamics process becomes a two-phase material system. Particular attention is focussed on attempt to construct a physically and experimentally justified localized fracture theory that relates the kinetics of material failure on the microstructural level to continuum mechanics. The description of the microstructural damage process is based on dynamic experiments with carefully controlled load amplitudes and duration. The microdamage process has been treated as a sequence of nucleation, growth and coalescence of microcracks. The microdamage kinetics interacts with thermal and load changes to make failure of solids a highly rate, temperature and history-dependent, non-linear process. The theory of thermoviscoplasticity is developed within the framework of the rate-type covariance material structure with a finite set of internal state variables. The theory takes into consideration the effects of microdamage mechanism and thermomechanical coupling. The dynamic failure criterion within localized shear band region is proposed. The relaxation time is used as a regularization parameter. Rate dependency (viscosity) allows the spatial differential operator in the governing equations to retain its ellipticity, and the initial-value problem is well-posed. The viscoplastic regularization procedure assures the unconditionally stable integration algorithm by using the finite element method. Particular attention is focused on the well-posedness of the evolution problem (the initial–boundary value problem) as well as on its numerical solutions. Convergence, consistency and stability of the discretized problem are discussed. The Lax equivalence theorem is formulated and conditions under which this theorem is valid are examined. Utilizing the finite element method and ABAQUS system for regularized elasto–viscoplastic model the numerical investigation of the three-dimensional dynamic adiabatic deformation in a particular body at nominal strain rates ranging over 103−104 s−1 is presented. A thin shear band region of finite width which undergoes significant deformation and temperature rise has been determined. Its evolution until occurrence of final fracture has been simulated. Numerical results are compared with available experimental observation data. © 1997 John Wiley & Sons, Ltd.

A Method of Damage Mechanics Analysis for Solder Material

This paper presents as a method of damage mechanics analysis for solder joint material stressed to extensive plastic deformation. The material chosen for the current work is the 60Sn-40Pb eutectic alloy due to its wide use. The analysis is based on the thermodynamic theory of irreversible processes. With the introduction of a set of internal state variables, known as damage variables, and a damage effect tensor, a damage dissipative potential function is proposed to enable the formulation of the constitutive equations of elasticity and plasticity coupled with damage. The equations of damage evolution are also derived to monitor damage initiation and growth. Before a damage analysis can be performed with a finite element analysis, the mechanical properties of the chosen solder joint material and its damage variables must first be determined. A method of experimental analysis was developed and used to successfully measure the highly strain sensitive 60Sn-40Pb solder material. The measured properties are presented and various characteristics of the solder material are examined and discussed. 7 refs., 8 figs.

Localized Fracture in Inelastic Polycrystalline Solids under Dynamic Loading Processes

The main objective of the paper is the investigation of adiabatic shear band localized fracture phenomenon in inelastic solids during dynamic loading processes. This kind of fracture can occur as a result of an adiabatic shear band localization generally attributed to a plastic instability implied by micro-damage and thermal softening during dynamic plastic flow processes. The theory of thermoviscoplasticity is developed within a framework of the rate type covariance material structure with a finite set of internal state variables. The theory takes into consideration the effects of micro-damage mechanism and thermomechanical coupling. The micro-damage mechanism has been treated as a sequence of nucleation, growth, and coalesence of microcracks. The micro-damage kinetics interacts with thermal and load changes to make failure of solids a highly rate, temperature, and history dependent, nonlinear process. The dynamic failure criterion within localized shear band region is proposed. The relaxation time is used as a regularization parameter. By assuming that the relaxation time tends to zero, the rate independent micro-damage mechanism is considered. Rate dependency (viscosity) allows the spatial differential operator in the governing equations to retain its ellipticity, and the initial-value problem is well posed. The viscoplastic regularization procedure assures the stable integration algorithm by using the finite element method. Particular attention is focused on the well-posedness of the evolution problem (the initial-boundary value problem), as well as on its numerical solutions. Convergence, consistency, and stability of the discretised problem are discussed. The Lax equivalence theorem is formulated and conditions under which this theorem is valid are examined. Utilizing the finite element method and ABAQUS system for regularized elastoviscoplastic model, the numerical investigation of the three-dimensional dynamic adiabatic deformation in a particular body at nominal strain rates ranging from 10-1-104 s-1 is presented. Three particular examples have been considered; namely, a dynamic adiabatic process for a thin-walled steel tube and dynamic adiabatic and quasi-static processes for a thin steel plate. In each case, a thin shear band region of finite width which undergoes significant deformations and temperature rise has been determined. Its evolution until occurrence of final fracture has been simulated. Numerical results are compared with available experimental observation data.