Generalized FVDAM Theory for Periodic Materials Undergoing Finite Deformations—Part II: Results

Abstract

In Part I, a generalized finitevolume direct averaging micromechanics (FVDAM) theory was constructed for periodic materials with complex microstructures undergoing finite deformations. The generalization involves the use of a higherorder displacement field representation within individual subvolumes of a discretized analysis domain whose coefficients were expressed in terms of surfaceaveraged kinematic variables required to be continuous across adjacent subvolume faces. In Part II of this contribution we demonstrate that the higherorder displacement representation leads to a substantial improvement in subvolume interfacial conformability and smoother stress distributions relative to the original theory based on a quadratic displacement field representation, herein called the 0th order theory. This improvement is particularly important in the finitedeformation domain wherein large differences in adjacent subvolume face rotations may lead to the loss of mesh integrity. The advantages of the generalized theory are illustrated through examples based on a known analytical solution and finiteelement results generated with a computer code that mimics the generalized theory's framework. An application of the generalized FVDAM theory involving the response of wavy multilayers confirms previously generated results with the 0th order theory that revealed microstructural effects in this class of materials which are important in bioinspired material architectures that mimic certain biological tissues.