Download this article
 Download this article For screen
For printing
Recent Issues

Volume 19
Issue 3, 303–540
Issue 2, 157–302
Issue 1, 1–156

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 5 issues

Volume 15, 5 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 8 issues

Volume 7, 10 issues

Volume 6, 9 issues

Volume 5, 6 issues

Volume 4, 10 issues

Volume 3, 10 issues

Volume 2, 10 issues

Volume 1, 8 issues

The Journal
About the journal
Ethics and policies
Peer-review process
Submission guidelines
Submission form
Editorial board
ISSN (electronic): 1559-3959
ISSN (print): 1559-3959
Author index
To appear
Other MSP journals
Mixed variational principle for shape memory solids

Vladimir A. Grachev and Yuriy S. Neustadt

Vol. 18 (2023), No. 5, 621–633

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.

continuum mechanics, solids, variational principle, shape memory materials, thermal plasticity, space of bounded deformation, generalized solutions
Received: 28 September 2021
Revised: 21 September 2022
Accepted: 14 June 2023
Published: 25 October 2023
Vladimir A. Grachev
Academy of Architecture and Building
Samara State Technical University
Yuriy S. Neustadt
Academy of Architecture and Building
Samara State Technical University