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Based on the second law of thermodynamics, a set of constitutive equations for small deformation of heat conducting, hysteretic materials is proposed. It is shown that the model exhibits elastic-viscoplastic-fluid behavior similar to Bingham's materials. Therefore, it may be a suitable candidate for modeling the mechanical behaviors of materials during melting and/or solidification processes. The corresponding bi-axial and uni-axial force-displacement models are also developed and their properties are discussed. It is shown that the resulting force-displacement relations are similar to those given by the Bouc-Wen Model; however, certain modifications are needed to make the earlier model thermodynamically consistent. Several numerical experiments for the uni-axial and bi-axial models are also presented.
- G. Ahmadi, F.-G. Fan, M. Noori