Premium
On Mathematical Aspects of Dual Variables in Continuum Mechanics. Part 2: Applications in Nonlinear Solid Mechanics
Author(s) -
van der Giessen Erik,
Kollmann F. G.
Publication year - 1996
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19960760903
Subject(s) - continuum mechanics , kinematics , nonlinear system , cauchy stress tensor , classical mechanics , cauchy distribution , constitutive equation , solid mechanics , dual (grammatical number) , analytical dynamics , mathematics , analytical mechanics , mechanics , physics , mathematical analysis , finite element method , thermodynamics , quantum mechanics , art , literature , quantum dynamics , quantum
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 formation 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.