A comparison of Gurtin type and micropolar theories of generalized single crystal plasticity

• Published in: International journal of plasticity Vol. 57; pp. 29 - 51
• Main Authors: Mayeur, J.R., McDowell, D.L.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.06.2014
• Subjects: A. Geometrically necessary dislocations; A. Gradient plasticity; B. Crystal plasticity; B. Microforce balance; C. Finite elements; Equivalence; Mathematical analysis; Mathematical models; Mechanical properties; Numerical prediction; Plasticity; Single crystals; Thin films; A. Gradient plasticity; B. Microforce balance; C. Finite elements; A. Geometrically necessary dislocations; B. Crystal plasticity
• ISSN: 0749-6419; 1879-2154
• DOI: 10.1016/j.ijplas.2014.01.010

•Gurtin type and micropolar theories of generalized single crystal plasticity are compared.•Several theoretical equivalences are established.•Simulation results of both theories are discussed with respect to predicted size effects. We compare and contrast the governing equations and numerical predictions of two higher-order theories of extended single crystal plasticity, specifically, Gurtin type and micropolar models. The models are presented within a continuum thermodynamic setting, which facilitates identification of equivalent terms and the roles they play in the respective models. Finite element simulations of constrained thin films are used to elucidate the various scale-dependent strengthening mechanisms and their effect of material response. Our analysis shows that the two theories contain many analogous features and qualitatively predict the same trends in mechanical behavior, although they have substantially different points of departure. This is significant since the micropolar theory affords a simpler numerical implementation that is less computationally expensive and potentially more stable.