On Mathematical Aspects of Dual Variables in Continuum Mechanics. Part 2: Applications in Nonlinear Solid Mechanics

摘要

Continuing the approach of Part 1 of this paper we apply our results to dual variables appearing in continuum mechanics. We investigate the kinematics and dynamics of continuous bodies. As a consequence, this leads to a mixed variant formulation of kinematics and Cauchy's law for the stress tensor. The mixed variant formulation of kinematics is advantageous, for instance, in finite deformation plasticity. Finally, we give some examples of constitutive equations which demonstrate in an exemplaric manner the additional mathematical structure gained through our approach.