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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 197632, 5 pages
Research Article

Qualitative Behaviour of Elastic-Plastic Solutions for a Class of Damage Mechanics Models Near Bimaterial Interfaces: A Simple Analytical Example

1A.Yu. Ishlinskii Institute for Problems in Mechanics, Russian Academy of Sciences, 101-1 Prospect Vernadskogo, Moscow 119526, Russia
2Faculty of Mechanical Engineering, Universiti Teknologi Malaysia, 81310 Skudai, Johor, Malaysia

Received 8 August 2013; Revised 22 November 2013; Accepted 24 November 2013

Academic Editor: Yuri Petryna

Copyright © 2013 Sergei Alexandrov and Yusof Mustafa. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The paper presents an exact analytic solution for a class of elastic-plastic models with damage evolution. The boundary value problem consists of a planar deformation comprising the simultaneous shearing and expansion of a hollow cylindrical specimen of material and involves a bimaterial interface at which the materials stick to each other. With no loss of generality for understanding the qualitative behaviour of the solution near the bimaterial interface, an extreme case when the hard material is rigid is considered. The solution is reduced to a transcendental equation for the value of the equivalent plastic strain at the bimaterial interface. This equation predicts that the equivalent plastic strain attains a maximum under certain conditions. The existence of the solution of the boundary value problem depends on the value of the damage parameter at fracture, which is a material constant. In particular, if this value is larger than the value of the damage parameter at the bimaterial interface corresponding to the maximum possible value of the equivalent strain at this interface, then no solution exists. Experimental data available in the literature are used to assess whether Lemaitre’s model is applicable.