Anholonomic Configuration Spaces and Metric Tensors in Finite Elastoplasticity

摘要: Abstract Deformation mappings are considered that correspond to the motions of lattice defects, elastic stretch and rotation lattice, initial defect distributions. Intermediate (i.e., relaxed) configuration spaces associated with these deformation maps identified then classified from differential-geometric point view. A fundamental issue is proper selection coordinate systems metric tensors in configurations when such as anholonomic. The particular choice a global, external Cartesian system corresponding covariant identity tensor on an intermediate space shown be constitutive assumption often made regardless existence geometrically necessary crystal defects anholonomicity non-Euclidean nature) space. Since anholonomic emerges necessarily definitions scalar products, certain transpose maps, tensorial symmetry operations, Jacobian invariants, its should not trivialized. Several alternative non-Euclidean) representations proposed literature for critically examined.