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Some issues associated with the intermediate space in single-crystal plasticity
Institution:1. Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, USA;2. Department of Mathematics and Applied Mathematics, University of Cape Town, 7701 Rondebosch, South Africa;1. Irstea, Geomechanics Group, ETNA, Grenoble, France;2. SMS-ID, INSA de Lyon, France;3. Laboratoire Sols Solides Structures Risques, UJF-INPG-CNRS, Grenoble, France;1. International Center for Applied Mechanics, State Key Laboratory for Strength and Vibration of Mechanical Structure, School of Aerospace, Xi’an Jiaotong University, Xi’an 710049, China;2. Department of Mechanical and Aerospace Engineering, North Carolina State University, NC 27695, USA;3. Columbia Nanomechanics Research Center, Department of Earth and Environmental Engineering, Columbia University, New York, NY 10027, USA
Abstract:In this study we show that some discussions of finite-deformation single-crystal plasticity are conceptually flawed in their focus on a set referred to as the intermediate configuration. Specifically, we prove that what is usually referred to as the intermediate configuration is not a configuration but instead a vector space that we term the intermediate space. We argue that when applied to single crystals this intermediate space represents the lattice.
Keywords:Finite-deformation single-crystal plasticity  Intermediate space  Lattice  Multiplicative decomposition
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