Unrestricted micromorphic continuum: Curvature constraints effects

Abstract The properties of two‐phase materials, with the special case of foams, strongly depend on their microstructure. These structures are generally modeled with Hill homogenization methods to reduce the computational effort compared to full‐resolution simulations. For applications where the macroscopic dimensions of the structure under consideration are only a few multiples of its internal length, size effects occur, that is, the effective mechanical properties depend on the structure size. To achieve adequate homogenization, higher‐order continuum theories must then be used to account for strong gradients in mechanical quantities. The present contribution extends the classical approach with the corresponding micromorphic degrees of freedom. In contrast to previous studies in the literature, all components of the micromorphic curvature tensor are incorporated. It has shown how the individual components of the third‐order curvature tensor have to be implemented. Their effects on the structural behavior are investigated in depth.