Quasistatic Deformation of Shape Memory Rigid-Plastic Bodies under Variable External Loads and Temperatures

Plastic deformation plays a decisive role in inelastic deformation of solids. Therefore, it is appropriate to analyze mechanical behaviour within an ideal rigid plastic model with two loading surfaces. In the first section the problem of deformation of rigid plastic bodies is defined at the constant temperature in two equivalent forms: as a principle of virtual velocities and as a requirement of the minimum dissipative functional. In the second section the rigid plastic model of the solid is studied at the changing temperature with two loading surfaces. Two optimal principles are stated: for the force loading and for shape restoration. The existence of the generalized velocities is proved for 3D domains. The first and second laws of thermodynamics introduced in the design model enable the application of the variational principle at changing temperatures. In the third section shape memory materials are defined as solids with two loading surfaces. In conclusion problems for further studies are stated.