Micropolar Crystal Plasticity
This chapter considers advances over the past 15 years achieved by the authors and coworkers on generalized crystal plasticity to address size and configuration effects in dislocation plasticity at the micron scale. The specific approaches addressed here focus on micropolar and micromorphic theories rather than adopting strain gradient theory as the starting point, as motivated by the pioneering ideas of Eringen (Eringen and Suhubi 1964; Eringen and Claus Jr 1969; Eringen 1999). It is demonstrated with examples that for isotropic elasticity and specific sets of slip systems, a dislocation-based formulation of micropolar or micromorphic type provides results comparable to discrete dislocation dynamics and has much in common with the structure of Gurtin’s slip gradient theory (Gurtin 2002; Gurtin et al. 2007).
KeywordsMicropolar Strain gradient GNDs Crystal plasticity Finite elements
JRM acknowledges the support of Los Alamos National Laboratory, operated by Los Alamos National Security LLC under DOE Contract DE-AC52-06NA25936. This work benefited from the support of the Laboratory Directed Research and Development Early Career award 20150696ECR. DLM would like to acknowledge the support of the Carter N. Paden, Jr. Distinguished Chair in Metals Processing.
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