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In this paper, employing the Hencky strain, viscoelastic-viscoplastic response of self-healing materials is investigated. Considering the irreversible thermodynamics and using the effective configuration in the Continuum Damage-Healing Mechanics (CDHM), a phenomenological finite strain viscoelastic-viscoplastic constitutive model is presented. Considering finite viscoelastic and viscoplastic deformations, total deformation gradient is multiplicatively decomposed into viscoelastic and viscoplastic parts. Due to mathematical advantages and physical meaning of Hencky strain, this measure of strain is employed in the constitutive model development. In this regard, defining the damage and healing... 

This paper models the kinetics of dynamic recovery and recrystallization under hot working conditions. For doing so, the first-order kinetics equation is coupled with a thermo-viscoplastic finite element analysis to determine the kinetics of dynamic softening processes at different points of deforming metal. The proposed model can consider the effects of macro parameters, such as temperature and strain rate variations as well as the influences of microparameters as initial grain size on the rate of dynamic softening processes. © 2005 Elsevier B.V. All rights reserved  

This paper is concerned with objective stress update algorithm for elasto-plastic and elasto-viscoplastic endochronic theory within the framework of additive plasticity. The elastic response is stated in terms of hypoelastic model and endochronic constitutive equations are stated in unrotated frame of reference. A trivially incrementally objective integration scheme for rate constitutive equations is established. Algorithmic modulus consistent with numerical integration algorithm of constitutive equations is extracted. The implementation is validated by means of a set of simple deformation paths (simple shear, extension and rotation), two benchmark test in nonlinear mechanics (the necking of... 

In this paper, employing the definition of an effective configuration in the continuum damage mechanics, mechanical response of a compressible viscoelastic-viscoplastic material is investigated. We present a phenomenological viscoelastic-viscoplastic-viscodamage constitutive model, developed within the framework of irreversible thermodynamics. The formulation is based on the additive decomposition of the total strain into elastic, viscoelastic, and viscoplastic parts in the effective configuration. Thus, the Helmholtz energy is partitioned into elastic, elastic-viscoelastic, and viscoplastic parts. Then, each one is divided into deviatoric and volumetric energies. Considering the... 

The present experimental study investigated the behavior of hot-mix asphalt (HMA) under repetitive creep and recovery loading. Cylindrical samples of HMA were subjected to trapezoidal and haversine loading followed by unloading. Different amounts of unloading (stress reduction) and relaxation periods (rest periods in complete unloading) were tested. The measured vertical deformation was decomposed into viscoelastic and viscoplastic components. It was observed for cyclic loading that an increase in unloading and/or relaxation period increased the recovery of viscoelastic strain, which in turn increased the accumulated viscoplastic strain in subsequent loading cycles. It appears that... 

Asphalt concrete is a complex mixture, the behavior of which is dependent on its components while showing different nonlinear behaviors under various conditions. Application of rest time between compressive loading cycles causes hardening-relaxation (H-R) behavior in the sample and increases the deformation potential of the sample. This process might induce changes in the microstructure and the pattern of the placement and rotation of the aggregates. These changes cause a relaxation in the hardening of the material, pose a higher potential of reception of viscoplastic strain in the following cycles, and increase the rate of accumulation of the permanent deformation in contrast with creep... 

In this paper, the dynamic large deformation X-FEM method is presented for modeling the full process of dynamic ductile fracture based on a nonlocal damage visco-plasticity model. The effect of inertia is modeled using an explicit central difference scheme which is enhanced through the use of mass lumping, reduced integration with hourglass control, and numerical damping. The material nonlinearity and the flow stress dependency on strain rate, hardening and temperature are modeled with the Johnson-Cook visco-plastic model. The micro-void nucleation, growth and coalescence are modeled macroscopically with an isotropic damage model. The localization phenomenon due to the damage and thermal... 

In the first part of this paper series, a complete formulation for fully coupled ALE analysis of large deformation solid mechanic problems was developed. The formulation incorporated inertial, rate and thermal effects, and the treatment of rate and temperature dependent constitutive equations were presented. In this part, the ALE equations are discretized to form finite element equations. An algorithm for the treatment of mesh motion is described and example problems are presented to demonstrate the capability of the proposed formulation  

Arbitrary Lagrangian Eulerian (ALE) finite element method is extensively used for numerical simulation of solid mechanics problem. The versatility of the mesh in ALE approach makes it particularly effective and efficient in solving large deformation problems. In this work, a complete treatment of fully coupled ALE formulation is presented incorporating inertial, rate and thermal effects. The formulation may be used in conjunction with thermo-elasto-viscoplactic material models. A consistent and efficient tangent operator is developed in closed form to handle stress integration. The applications of this formulation are given in the second part of this paper  

This paper numerically studies the interaction of a flowing granular material with an entrainable granular bed, while materials are mixed at the interface of two materials. The rheological behavior of this granular mixture is characterized by a generalized viscoplastic model that includes local volume fraction of materials as well as their physical properties, i.e. size, density, and friction angle. Additionally, the effect of the dynamics of entrained bed-type particles on the rheology of the granular mixture is considered. The governing equations of the flow are discretized using the Incompressible Smoothed Particle Hydrodynamics (SPH) method in which mixing of particles can be... 

This paper studies entrainment phenomenon in debris flows using full flow (non-depth-averaged) equations and an Incompressible Smoothed Particle Hydrodynamics (ISPH) method. A viscoplastic constitutive relationship is adopted for both the overlying fluid and bed material. Collapse of a two-dimensional dry granular column on a horizontal bed consisting of entrainable dry granular material is considered as a benchmark problem. The adopted ISPH method for simulation of collapse over rigid and entrainable beds is validated using available numerical and experimental data. To quantify the effects of entrainment on dynamics of flow, the initial aspect ratio of granular column (a) is varied and the... 

Soda-lime glass material has been widely used for automobile windscreens. Two commercial finite element programs have been evaluated for simulation of the creep forming process using isotropic viscoplastic behavior assumption for soda-lime glass. This was done by selecting one of the programs and using it in connection with an optimization program for controlling the glass surface temperature, to examine the effect of considering thermal stresses and temperature variations along the surface of glass sheet for obtaining desired geometrical shape. The results show that the thermal stress effect must be considered for achieving more accurate simulation of glass creep forming process. Also... 

A mathematical model has been proposed to predict flow behavior of steel under hot deformation conditions with regard to the effects of dynamic recovery and dynamic recrystallization. For this purpose, Kocks-Mecking dislocation model together with a first order rate equation have been utilized. To associate temperature and strain rate variations on flow behavior of deforming metal, a thermo-viscoplastic finite element model has been coupled with the proposed model. To verify the modeling results, hot rolling experiments were performed and roll forces at various temperatures and rolling speeds were recorded. A good agreement was found between the predicted and the experimental data. © 2005... 

In this paper, a hypoelasto-viscoplastic endochronic model is developed to capture the strain localization phenomena. The elastic response is stated in terms of hypoelastic model and endochronic constitutive equations are stated in unrotated frame of reference. The infinitesimal theory of endochronic plasticity is extended to large strain range on the basis of the additive decomposition of the strain rate tensor and hypoelasticity. Constitutive equations are stated in unrotated frame of reference that greatly simplifies endochronic constitutive relations in finite plasticity and yields the efficiency of the presented algorithm by total uncoupling material and geometrical nonlinearities. An... 

This article presents the cyclic behavior of the A356.0 aluminum alloy under low-cycle fatigue (or isothermal) and thermo-mechanical fatigue loadings. Since the thermo-mechanical fatigue (TMF) test is time consuming and has high costs in comparison to low-cycle fatigue (LCF) tests, the purpose of this research is to use LCF test results to predict the TMF behavior of the material. A time-independent model, considering the combined nonlinear isotropic/kinematic hardening law, was used to predict the TMF behavior of the material. Material constants of this model were calibrated based on room-temperature and high-temperature low-cycle fatigue tests. The nonlinear isotropic/kinematic hardening... 

Cyclic loading on asphalt concrete materials with a longer relaxation time and lower remaining stress lead to higher viscoelastic strain recovery. Consequently, more aggregate reorientation occurs and the rate of viscoplastic strain increases in subsequent cycles. The present study proposes a hardening relaxation constitutive relationship (fHR) as a function of accumulated recovered viscoelastic strain εrve based on experimental observation. This model captures the initiation and evolution of hardening-relaxation during the relaxation time and/or stress reduction under cyclic loading. The model was then coupled with viscoelastic, viscoplastic and viscodamage constitutive relationships. The... 

Self-healing materials, as a class of intelligent materials, are capable to recover a part of the weakened mechanical properties induced by damage. In this article, based on the thermodynamics of irreversible processes, employing the effective configuration in the continuum damage-healing mechanics, a viscoelastic–viscoplastic constitutive model is presented. In the constitutive model development, we adopt an additive decomposition of the total strain into elastic, viscoelastic, and viscoplastic parts. In this regard, defining the damage and healing variables and employing the strain energy equivalence hypothesis, stress and strain tensors in the effective configuration are obtained....