A Gibbs-potential-based framework for ideal plasticity of crystalline solids treated as a material flow through an adjustable crystal lattice space and its application to three-dimensional micropillar compression

Abstract

We propose an Eulerian thermodynamically compatible model for ideal plasticity of crystalline solids treated as a material flow through an adjustable crystal lattice space. The model is based on the additive splitting of the velocity gradient into the crystal lattice part and the plastic part. The approach extends a Gibbs-potential-based formulation developed in [21] for obtaining the response functions for elasto-visco-plastic crystals. The framework makes constitutive assumptions for two scalar functions: the Gibbs potential and the rate of dissipation. The constitutive equations relating the stress to kinematical quantities is then determined using the condition that the rate of dissipation is maximal providing that the relevant constraints are met. The proposed model is applied to three-dimensional micropillar compression, and its features, both on the level of modelling and computer simulations, are discussed and compared to relevant studies.

Stress-diffusive regularizations of non-dissipative rate-type materials

“…This fully Eulerian Gibbs-potential-based thermodynamic approach has been further extended to describe the response of visco-elastic materials, see Rajagopal and Srinivasa [36], or to model severe plastic deformations of a crystalline solid treated as a material flow through an adjustable crystal lattice space, see Kratochvíl et al [22].…”

A simple thermodynamic framework for heat-conducting flows of mixtures of two interacting fluids

“…and in view of ( 24), (22), and (15), the standard relation between the total entropy and Helmholtz free energy holds…”

“…From the knowledge of these two scalar quantities, one can derive the complete model involving, in particular, the constitutive equation for the Cauchy stress and the energy flux. This thermodynamic approach has been successfully applied, in many areas, to the development of the models that are capable of describing complicated responses of materials whereas the resulting model is automatically consistent with the laws of thermodynamics (we refer to Rajagopal and Srinivasa [11] , Málek and Rajagopal [10] , Rajagopal and Srinivasa [12] , Málek, Rajagopal, Tůma [13,14] , Kratochvíl, Málek and Minakowski [15] , Cichra and Průša [16] , and a survey paper Málek and Průša [17] for further details and references).…”

Multimaterial Eulerian finite element formulation for pressure‐sensitive adhesives

“…In the literature, such methods have been applied to various problems including high-speed impacts and penetration of steel, 19 explosive welding of aluminum, 20 high-speed machining of steel, 21 stationary hyperelastic deformation processes, 22 mechano-chemical fluid-structure interaction, 23 and dynamic crystal plasticity. 24,25 Given this background, we propose a Eulerian FE formulation and a constitutive equation for PSA simulations involving multiple materials and large deformations. This paper is organized as follows.…”

“…In the literature, such methods have been applied to various problems including high‐speed impacts and penetration of steel, explosive welding of aluminum, high‐speed machining of steel, stationary hyperelastic deformation processes, mechano‐chemical fluid‐structure interaction, and dynamic crystal plasticity. ()…”