We discuss the correspondence between discrete and continuum models of one-dimensional (1D) elastic structures. We propose positive definiteness as a consistency condition for continuum models. As a result, generalized continuum models may be required, as simple (Cauchy-type) continuum models may be insufficient. This theory is illustrated by a few physical examples.
Positive definiteness of deformation energy as a consistency condition of discrete-to-continuum transition
Eremeyev V. A.
Primo
;
2026-01-01
Abstract
We discuss the correspondence between discrete and continuum models of one-dimensional (1D) elastic structures. We propose positive definiteness as a consistency condition for continuum models. As a result, generalized continuum models may be required, as simple (Cauchy-type) continuum models may be insufficient. This theory is illustrated by a few physical examples.
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