A stochastic approach to capture crystal plasticity

• Published in: International journal of plasticity Vol. 27; no. 9; pp. 1432 - 1444
• Main Authors: Zhang, Liangzhe, Dingreville, Rémi, Bartel, Timothy, Lusk, Mark T.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.09.2011; Elsevier
• Subjects: Activated; Algorithms; Computer simulation; Condensed matter: structure, mechanical and thermal properties; Crystal plasticity; Crystals; Deformation and plasticity (including yield, ductility, and superplasticity); Efficiency; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Inelasticity (thermoplasticity, viscoplasticity...); Mechanical and acoustical properties of condensed matter; Mechanical properties of solids; Monte Carlo; Monte Carlo methods; Physics; Plasticity; Rate independent; Single slip; Slip; Solid mechanics; Stochasticity; Structural and continuum mechanics; Crystal plasticity; Single slip; Rate independent; Monte Carlo; Efficiency; Deformation band; Stresses; Constitutive equation; Probabilistic approach; Polycrystals; Material point method; Inelasticity; Monte Carlo methods; Particle method; Elastoplasticity; Slip system; Plasticity; Slip band; Modelling; Deterministic approach; Singular value decomposition
• ISSN: 0749-6419; 1879-2154
• DOI: 10.1016/j.ijplas.2011.04.002

A stochastic crystal plasticity model is proposed and applied within the rate-independent regime. As opposed to conventional deterministic algorithms wherein multiple slip systems are activated and redundant constraints may exist, the new Monte Carlo plasticity (MCP) paradigm is based on a stochastic chain of singly activated slip systems and thus avoids the possible ill-condition associated with multi-slip algorithms. The choice of the activated slip system is made at each Monte Carlo (MC) step based on the Metropolis algorithm. The MCP model is implemented within a Material Point Method (MPM) as a constitutive model to capture the elasto-plastic behavior of polycrystalline materials. A comparison with a commonly used singular value decomposition (SVD) algorithm indicates that MCP offers superior computational efficiency while maintaining comparable accuracy.