Continuum Limits of Discrete Systems Without Convexity Hypotheses  

Oleh:

Braides, Andrea ; Gelli, Maria Stella

Jenis: Article from Journal - ilmiah internasional
Dalam koleksi: Mathematics and Mechanics of Solids vol. 7 no. 1 (Feb. 2002), page 41-66.
Topik: Lattice systems; continuum limits; nearest-neighbour interactions; Gamma-convergence; fracture; microcracking
Fulltext: 41MMS71.pdf (263.05KB)

Isi artikel

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.

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