Theory of strains
Usually in the nonlinear theory of elasticity the theory of
deformations is based only on geometrical reasons, thus a lot of
different strain tensors are considered. It is usually assumed
that all of these tensors can be used with identical success.
However, this is not correct. It is shown (2001), that the
dissipative inequality imposes such restrictions on free energy
[1, 2], which at use of Almansi measure of strain appear
equivalent to the statement, that the considered material is
isotropic. In other words it is shown, that for anisotropic
materials free energy cannot be a function of Almansi measure of
strain. The definition of the strain measure is given on the base
of the equation of balance of energy and the dissipative
inequality. It is shown, that according to the given definition
the strain measure should be an unimodular tensor.
- Zhilin P.A. Basic equations of the theory of non-elastic media // Proc. of the XXVIII Summer School “Actual Problems in Mechanics”. St. Petersburg. 2001. P. 14-58. (In Russian.)
- Zhilin P.A. Phase Transitions and General Theory of Elasto-Plastic Bodies // Proceedings of XXIX Summer School - Conference “Advanced Problems in Mechanics”. St. Petersburg, Russia, 2002. P. 36-48.