Micromorphic continuum Part I: Strain and stress tensors and their associated rates

摘要: Abstract Micropolar and micromorphic solids are continuum mechanics models, which take into account, in some sense, the microstructure of considered real material. The characteristic property such continua is that state functions depend, besides classical deformation macroscopic material body, also upon microcontinuum modeling microstructure, its gradient with respect to space occupied by body. While micropolar plasticity theories, including non-linear isotropic kinematic hardening, have been formulated, even for geometry, few works known yet about formulation (finite deformation) plasticity. It aim three papers (Parts I, II, III) demonstrate how theories may be formulated a thermodynamically consistent way. In present article we start outlining framework theory. Especially, confine attention theory Mindlin on small deformations. After precising conceptual aspects concerning notion microcontinuum, work out finite version theory, suitable our aims. examined resulting basic field equations same as Eringen, deals different definition microcontinuum. Furthermore, geometrical interpretations strain curvature tensors elaborated. This allows find associated rates natural manner. Dual stress double tensors, well rates, then defined basis powers. way, it possible relate (respectively, tensors) tensors), independently particular constitutive properties.