Finite element analysis of Saint‐Venant end effects in micropolar elastic solids

Abstract

Abstract Distributions of stress and strain in composite and cellular materials can differ significantly from the predictions of classical elasticity. For example, concentration of stress and strain around holes and cracks is consistently less than classical predictions. Generalized continuum theories such as micropolar (Cosserat) elasticity offer improved predictive power. In this article Saint‐Venant end effects for self equilibrated external forces in micropolar solids are investigated in two dimensions. A two dimensional finite element analysis is used which takes into account the extra degrees of freedom, to treat the problem of localized end loads acting upon a strip. The rate of decay of strain energy becomes slower in a two dimensional strip as the micropolar characteristic length l is increased (for l sufficiently less than the strip width). For the strip geometry a Cosserat solid exhibits slower stress decay than a classical solid.