The quasistatic deformation problem for shape memory solids is studied based on the
measurements of displacements arising from force actions and temperature
variations. The phenomenological approach relies on generalization curves for
uniaxial tension and compression of specimens at different temperatures.
Under proportional loading and at low temperature the alloy behaves as an
ideal elastoplastic material; the residual strain is observed after unloading. If
the deformed sample is heated to a certain temperature for each alloy, the
initial shape is restored. The first curve of deformation can be described
with the variational principle. Thus, it becomes clear how to explain “the
reverse deformation” within the slightly modified theory of plasticity. It
is necessary to replace the simply connected surface of loading with the
doubly connected one, use the principle of orthogonality for thermodynamic
forces and streams, and update the variational principle with two laws of
thermodynamics.
Keywords
continuum mechanics, solids, variational principle, shape
memory materials, thermal plasticity, space of bounded
deformation, generalized solutions
