Nonlocal Theories in Continuum Mechanics

Abstract

The purpose of this paper is to explain why the standard continuum theory fails to properly describe certain mechanical phenomena and how the description can be improved by enrichments that incorporate the influence of gradients or weighted spatial averages of strain or of an internal variable. Three typical mechanical problems that require such enrichments are presented: (i) dispersion of short elastic waves in heterogeneous or discrete media, (ii) size effects in microscale elastoplasticity, in particular with the size dependence of the apparent hardening modulus, and (iii) localization of strain and damage in quasibrittle structures and with the resulting transitional size effect. Problems covered in the examples encompass static and dynamic phenomena, linear and nonlinear behavior, and three constitutive frameworks, namely elasticity, plasticity and continuum damage mechanics. This shows that enrichments of the standard continuum theory can be useful in a wide range of mechanical problems.

Keywords

• Damage mechanics
• dispersion
• elasticity
• enriched continuum
• gradient models
• nonlocal models
• plasticity
• quasibrittle materials
• size effect
• strain localization
• wave propagation