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Continuum limits of discrete systems without convexity hypotheses. (English) Zbl 1024.74004
Summary: We describe the variational limit of one-dimensional nearest-neighbour systems of interactions, under no structure hypotheses on the discrete energy densities. We show that the continuum limit is characterized by bulk and interfacial energy density, which can be explicitly computed from discrete energies through operations of limit, scaling and regularization that highlight possible bulk oscillations and multiple cracking.

MSC:
74A25 Molecular, statistical, and kinetic theories in solid mechanics
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