Nonlinear Multi-Scale Modeling With Frame Elements for Cellular Materials

Abstract

The development of a nonlinear homogenization for media having lattice-like periodic microstructure is presented. For continuum media, conventional homogenization methods lead to classical continuum boundary value problems at both micro-and micro-scales. However, discretizing latticelike micro-structures, such as cellular solids, by frame elements is a natural step. The main difficulty in applying frame elements to micro-scale problems is inconsistencies between the kinematic field of the frame elements and the micro-scale displacement field. Numerical examples of cellular solids demonstrate the feasibility and strengths of the computational efficiency of the method presented.