Abstract: A model for effects related to hystersis in continuum mechanics is introduced. Its key idea is to consider locally minimizing Young measures describing the deformation gradient of a body. These Young measures are defined as limit of a quasi-static evolution by means of gradient flow with respect to a special ``regularized'' Wasserstein metric. The model is described for the space-homogeneous case, and some one-dimensional examples illustrate possible applications in problems like fracture and plasticity.
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