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Mathematics and Mechanics of Solids
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Continuum Limits of Discrete Systems without Convexity Hypotheses

Andrea Braides

Dipartimento di Matematica, Università di Roma ‘Tor Vergata’ Via della Ricerca Scientifica, 00133, Roma, Italy

Maria Stella Gelli

Dipartimento di Matematica, Università di Pisa Via Buonarroti 2, 56127 Pisa, Italy

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 a bulk and a interfacial energy density, which can be explicitly computed from the discrete energies through operations of limit, scaling and regularization that highlight possible bulk oscillations and multiple cracking.

Key Words: Lattice systems • continuum limits • nearest-neighbour interactions • Gamma-convergence • fracture • microcracking

Mathematics and Mechanics of Solids, Vol. 7, No. 1, 41-66 (2002)
DOI: 10.1177/1081286502007001229
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