Transition from hyperelastic micromorphic to micropolar and microstrain continua

Micromorphic continua are equipped with additional degrees of freedom in comparison to the classical continuum, representing micro deformations of the material points of a body. They are also 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 micro deformations are allowed for in the micromorphic continuum, while the special cases micropolar continuum and microstrain continuum merely allow for micro rotation and micro strain, respectively. This paper is concerned with the transition from a micromorphic to a micropolar and a microstrain continuum. Three simple constitutive models are shown, which represent the three different continua. Additionally, the role of the micropolar and microstrain part in a micromorphic continuum is illustrated by a numerical example. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)