A nested dynamic multi-scale approach for 3D problems accounting for micro-scale multi-physics

In this paper, a first-order multi-scale approach for three-dimensional structural problems is proposed. A nested solution technique enables the mutual transfer of information between global and local scales which are solved simultaneously in a finite element analysis. Therefore, apart from improving the coarse-scale solution by considering fine-scale features, a detailed simulation of the micro-level also enables the determination of local fine-scale quantities of interest. To account for transient effects, a dynamic simulation on the macro-scale is locally coupled to a quasi-static simulation of the discretized micro-level. For time integration, the generalized-α scheme is employed on both scales. The presented algorithm is applicable for large deformations, rotations and arbitrary micro-structural behavior. On the macro-level, no constitutive assumption is required since the stress–strain relationship is directly computed from the micro-scale using established computational homogenization procedures. First simulations validate the novel approach and demonstrate its suitability for lung parenchyma considering complex surfactant film dynamics as an example of fine-scale multi-physics.