Higher order continuum models for cellular materials including damage

Abstract

An extended continuum-mechanical model for the description of the deformation behavior of foam-like structures including damage ist presented. While it is very difficult to formulate constitutive equations on the macroscale for these materials, the constitutive equations, material parameters and evolution equations including damage are assumed to be known for the beamlike microstructure. Within a finite element computation the strains and, according to the macroscopic extended continuum model, the curvatures are mapped to the integration point. Attaching a microstructure to each integration point allows for the construction of a boundary value problem for the local microstructure. After evaluation of the microscopic constitutive equations, the forces and moments are mapped back to the macroscale by a homogenization procedure yielding the stress and couple stress response. This approach is known from literature as FE² model. The capability of the model is demonstrated in a numerical example. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)