Variational principles and the related bounding theorems for bi-modulus materials

Variational principles for materials with smooth constitutive laws have been well established in literature. For materials with non-smooth constitutive relations, however, the corresponding development has not reached a mature stage. In the present paper, a series of variational principles and the related bounding theorems for bi-modulus materials, which have different elastic properties in tension and compression, are established. Illustrative examples provided demonstrate the application of the presented theoretical results. (C) 2014 Elsevier Ltd. All rights reserved.