Comparison of hyperelastic micromorphic, micropolar and microstrain continua

Abstract

Micromorphic continua are equipped with additional degrees of freedom in comparison to the classical continuum, representing microdeformations of the material points of a body. Secondary they are provided with a higher order gradient. Therefore, they are able to account for material size-effects and to regularize the boundary value problem, when localization phenomena arise. Arbitrary microdeformations are allowed for in the micromorphic continuum, while the special cases micropolar continuum and microstrain continuum merely allow for microrotation and microstrain, respectively. Amongst these cases, the micropolar case has been covered most extensively in the literature. One goal of this paper is to make the transition from a full micromorphic continuum to a micropolar or microstrain continuum, by varying the constitutive equations. To this end two different possibilities are presented for hyperelasticity with large deformations. This leads to four different material models, which are compared and illustrated by numerical examples. Another goal is to present a constitutive model encompassing the micromorphic, micropolar and microstrain continua as special cases and enabling arbitrary mixtures of micropolar and microstrain parts, allowing the representation of versatile material behaviour.