Elasto-viscoplastic Constitutive Relation Research Articles

Gas-Liquid Foam Dynamics: From Structural Elements to Continuum Descriptions

Gas-liquid foams are important in applications ranging from oil recovery and mineral flotation to food science and microfluidics. Beyond their practical use, they represent an intriguing prototype of a soft material with a complex, viscoelastic rheological response. Crucially, foams allow detailed access to fluid-dynamical processes on the mesoscale of bubbles underlying the large-scale material behavior. This review emphasizes the importance of the geometry and interaction of mesoscale structural elements for the description of the dynamics of entire foams. Using examples including bulk flow of foam under steady shear, interfacial instabilities, and foam fracture through bubble rupture, this article highlights the wide variety of available theoretical descriptions, ranging from network modeling approaches coupling structural element equations of motion to full continuum models with elastoviscoplastic constitutive relations. Foams offer the opportunity to develop rigorous links between such disparate descriptions, providing a blueprint for physical modeling of dynamical multiscale systems with complex structure.

Necking instabilities in elastoviscoplastic materials

Necking instabilities, in which tensile (extensional) deformation localizes into a small spatial region, are generic failure modes in elasto-viscoplastic materials. Materials in this very broad class --- including amorphous, crystalline, polycrystalline and other materials --- feature a predominantly elastic response at small stresses, plasticity onset at a rather well-defined yield stress and rate-dependence. Necking instabilities involve a unique coupling between the system's geometry and its constitutive behavior. We consider generic elasto-viscoplastic constitutive relations involving an internal-state field, which represents the structural evolution of the material during plastic deformation, and study necking in the long-wavelength approximation (sometimes termed the lubrication or slender-bar approximation). We derive a general expression for the largest time-dependent eigenvalue in an approximate WKB-like linear stability analysis, highlighting various basic physical effects involved in necking. This expression is then used to propose criteria for the onset of necking and more importantly for the emergence of strong localization. Applications to strain-softening amorphous plasticity, in the framework of the Shear-Transformation-Zone model, and to strain-hardening crystalline/polycrystalline plasticity, in the framework of the Kocks-Mecking model, are presented. These quantitative analyses of widely different material models support the theoretical predictions, most notably for the strong localization during necking.

Correlation between Geometrically Nonlinear Elastoviscoplastic Constitutive Relations Formulated in Terms of the Actual and Unloaded Configurations for Crystallites

A correct description of severe plastic deformation requires the use of nonlinear kinematic and constitutive relations. The relations should meet certain criteria, such as the frame-independence, closed stress cycles and the absence of energy dissipation under elastic cyclic loading. A most complicated issue in formulating these relations is the decomposition of motion into quasi-rigid and strain-induced motions, which is an extremely difficult problem with no unambiguous solution. For the majority of structural metals and alloys, this decomposition can be done in a physically justified way on the level of crystallites. Earlier, using a multilevel approach we introduced a corotational coordinate system for crystallites responsible for quasi-rigid motion. This allowed us to formulate frame-independent mesoscopic constitutive relations in the actual configuration and to perform test calculations to show that the above criteria are satisfied with high accuracy. A new way of motion decomposition was proposed which is a multiplicative representation of the deformation gradient with an explicit extraction of the corotational frame motion. Elastoviscoplastic constitutive relations satisfying the above criteria were formulated in terms of an unloaded "lattice" configuration. However, it is more preferable to formulate nonlinear boundary value problems in terms of the actual configuration in rates. This paper is aimed to study correlation between the earlier derived constitutive relations formulated in terms of the actual configuration and in terms of the unloaded "lattice" configuration. Example problems are solved to demonstrate the closeness of results obtained with these constitutive relations.

On motion decomposition and constitutive relations in geometrically nonlinear elastoviscoplasticity of crystallites

The formulation of geometrically nonlinear boundary value problems is a necessary component in modeling real technological processes of thermomechanical material processing, wherein the main issues are the description of nonlinear kinematics and the formulation of constitutive relations. Most of the existing works do not explicitly consider the used method of motion decomposition that implies the extraction of the part responsible for quasi-rigid motion from the motion of a deformed solid. On our opinion, when choosing a method of motion decomposition and the corresponding corotational frame, the latter must be associated with the material to correctly describe the loading history and symmetry properties of the modeled body. Note that crystalline materials (including metals and alloys) at different scale levels are always anisotropic to a certain extent, and their properties can differ significantly in different directions. Even initially isotropic (at the level of the representative macrovolume) polycrystalline materials also become anisotropic under severe plastic deformation due to texturing. A multilevel approach allows the determination of symmetry elements (planes and axes of symmetry) at the crystallite level in metals, and we propose to relate these elements to the axes of the corotational frame that defines quasi-rigid motion. A new way of motion decomposition is proposed, namely, a multiplicative representation of the deformation gradient with an explicit extraction of the corotational frame motion. Elastoviscoplastic constitutive relations are formulated in terms of a stress free configuration. As the used stresses and strains are energetically conjugate, the requirements of no stress hysteresis and no energy dissipation in arbitrary closed elastic strain cycles are automatically satisfied, which is exemplified for anisotropic crystals. ©hus, an approach is proposed for the construction of geometrically nonlinear kinematic and constitutive relations for metal crystallites using a physically justified method of motion decomposition, with taking into account the symmetry properties of materials.

An automatic time increment selection scheme for simulation of elasto-viscoplastic consolidation of clayey soils

An automatic time increment selection scheme for numerical analysis of long-term response of geomaterials is presented. The scheme is simple, rational and stable. Governed by a simple empirical expression, it can adaptively adjust the time increments depending on the strain rate-dependent temporal history of the material response. The proposed expression requires only a few parameters whose selection is a trivial task since they have a small effect on accuracy but have a significant effect on computational efficiency. This generalization has been made possible because of the enforcement of certain predefined control criteria to avoid extreme conditions. If any of the control criteria is satisfied, the computation is restarted by going a few time steps back to ensure the smoothness of the computed responses and time increments are again continuously adjusted through the governing equation provided. Performance of the automatic time increment selection scheme is investigated through finite element analyses of the long-term consolidation response of clay under different geotechnical profiles and loading conditions. Both elastic and elasto-viscoplastic constitutive relations are considered, including the consideration of the destructuration effects of geomaterials. Numerical results show that the performance of the automatic time increment selection scheme is reasonably excellent. While offering reasonable accuracy of the numerical solution, it can ensure temporal stability at optimal computational efficiency. In addition to the Euler implicit method, the automatic time increment selection scheme also performs well even when the explicit fourth-order Runge–Kutta method is employed for the integration of time derivatives.

Elasto-viscoplastic Finite Element Analysis of the Long-term Behavior of Flexible Pavements Application to Rutting

This paper includes analysis of the flexible pavements rutting using an elastoviscoplastic constitutive relation for the asphalt concrete, which takes into account the influence of the temperature. The latter is considered using the time-temperature superposition principle. The loading is modeled as a uniform pressure applied during the vehicle pass. The superposition principle is used for modeling the traffic with a high number of vehicle passes. The numerical model is first calibrated on full scale tests conducted at different values of the temperature. Then, it is used for the analysis of the influence of the temperature and traffic condition on the pavement rutting. Analyses show that the increase in the temperature leads to an import augmentation in pavement rutting. They also show that the tire type and the traffic speed influence significantly the pavement rutting.

NONLINEAR ANALYSIS OF ONE AND TWO DIMENSIONAL CONSOLIDATION PROBLEMS FOR UNBOUNDED SATURATED SOIL MEDIA

Soil in general is not a linear material, in which the relation between stress and strain is more complicated than the simple, linearly elastic relation. To make accurate deformation analysis of clay deposits, the incremental Biot's theory of consolidation is used together with elasto-viscoplastic constitutive relations based on the critical state concept using the modified Cam-clay model. One and two dimensional consolidation problems were analyzed numerically by the infinite-finite elements. Results show that the proposed method can describe the effect of sample thickness on consolidation phenomena. Also the two dimensional behavior of a clay foundation during the construction of embankment was analyzed.

Elasto-viscoplastic Finite Element Analysis of the Long-term Behavior of Flexible Pavements

ABSTRACT This paper includes analysis of the flexible pavements rutting using an elastoviscoplastic constitutive relation for the asphalt concrete, which takes into account the influence of the temperature. The latter is considered using the time-temperature superposition principle. The loading is modeled as a uniform pressure applied during the vehicle pass. The superposition principle is used for modeling the traffic with a high number of vehicle passes. The numerical model is first calibrated on full scale tests conducted at different values of the temperature. Then, it is used for the analysis of the influence of the temperature and traffic condition on the pavement rutting. Analyses show that the increase in the temperature leads to an import augmentation in pavement rutting. They also show that the tire type and the traffic speed influence significantly the pavement rutting.

Explicit incremental-update algorithm for modeling crystal elasto-viscoplastic response in finite element simulation

Computational stability and efficiency are the key problems for numerical modeling of crystal plasticity, which will limit its development and application in finite element (FE) simulation evidently. Since implicit iterative algorithms are inefficient and have difficulty to determine initial values, an explicit incremental-update algorithm for the elasto-viscoplastic constitutive relation was developed in the intermediate frame by using the second Piola-Kirchoff (P-K) stress and Green stain. The increment of stress and slip resistance were solved by a calculation loop of linear equations sets. The reorientation of the crystal as well as the elastic strain can be obtained from a polar decomposition of the elastic deformation gradient. User material subroutine VUMAT was developed to combine crystal elasto-viscoplastic constitutive model with ABAQUS/Explicit. Numerical studies were performed on a cubic upset model with OFHC material (FCC crystal). The comparison of the numerical results with those obtained by implicit iterative algorithm and those from experiments demonstrates that the explicit algorithm is reliable. Furthermore, the effect rules of material anisotropy, rate sensitivity coefficient (RSC) and loading speeds on the deformation were studied. The numerical studies indicate that the explicit algorithm is suitable and efficient for large deformation analyses where anisotropy due to texture is important.

On incremental non-linearity in granular media: phenomenological and multi-scale views (Part I)

On the basis of fundamental constitutive laws such as elasticity, perfect plasticity, and pure viscosity, many elasto-viscoplastic constitutive relations have been developed since the 1970s through phenomenological approaches. In addition, a few more recent micro-mechanical models based on multi-scale approaches are now able to describe the main macroscopic features of the mechanical behaviour of granular media. The purpose of this paper is to compare a phenomenological constitutive relation and a micro-mechanical model with respect to a basic issue regularly raised about granular assemblies: the incrementally non-linear character of their behaviour. It is shown that both phenomenological and micro-mechanical models exhibit an incremental non-linearity. In addition, the multi-scale approach reveals that the macroscopic incremental non-linearity could stem from the change in the regime of local contacts between particles (from plastic regime to elastic regime) in terms of the incremental macroscopic loading direction. Copyright © 2005 John Wiley & Sons, Ltd.

Study on dynamic constitutive relations for concrete with finite deformation

The differences between finite deformation and infinitesimal deformation are discussed. They are exercised on elasto-viscoplastic constitutive relations of concrete. Then, a rate-dependent mechanics model was presented on the basis of Ottosen's four-parameter yield criterion, where different loading surface transferring laws were taken into account, when material was in hardening stage or in softening stage, respectively. The model is well established, so that it can be applied to simulate the response of concrete subject to impact loading. Green-Naghdi stress rate was introduced as objective stress rate. Appropriate hypothesis was postulated in accordance with many experimental results, which could reflect the mechanical behaviour of concrete with large deformation. Available thoughts as well as effective methods are also provided for the research on related engineering problems.