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.