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A model for effects related to hysteresis in continuum mechanics is introduced. Its key idea is to consider local minimizers of Young measures describing the deformation gradient of a body. These Young measures are defined as limit of a quasi-static evolution by means of a gradient flow with respect to a special “regularized” Wasserstein metric. The model is described for the space-homogeneous case, and some one-dimensional examples show the occurrence of hysteresis and illustrate possible applications to fracture.

A Model for Hysteresis in Mechanics Using Local Minimizers of Young Measures