INVESTIGATION OF STRESS-FREE CONDITIONS IN THE SYSTEMS WITH INTRINSIC DEFORMATION 

Lokhov Valeriy Aleksandrovich, Candidate of physical and mathematical sciences, associate professor, sub-department of theoretical mechanics, Perm National Research Polytechnic University ( Perm, 29a Komsomolsky avenue), valeriy.lokhov@yandex.ru
Tuktamyshev Vadim Saitzyanovich, Candidate of physical and mathematical sciences, associate professor, sub-department of theoretical mechanics, Perm National Research Polytechnic University (Perm, 29a Komsomolsky avenue), helpinvader@list.ru 

539.37 

The authors investigate the conditions for the intrinsic (inelastic strain) deformation without causing mechanical stress. In the framework of elasticity theory problem, zero stress occurs when intrinsic deformation is compatible and appropriate displacement vanishes at the immovable supports. Obtained conditions are adapted for determination of the stress-strain state in the plane isotropic disk made of shape memory alloy. In this problem phase transition strain is considered as intrinsic deformation. It is shown that usage of conditions for stress-free intrinsic deformation allows to find stress and strain distributions in the disk without total solution of appropriate boundary value problem. This result can be successfully used for solution of more complicated problems for the systems with inelastic deformation. 

intrinsic deformation, compatibility conditions, shape memory effect, Lame problem. 

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