An Explicit D-FE2 Method for Transient Multiscale Analysis

Abstract

Explicit FE (Finite Element) method offers distinct advantages for a variety of simulations, including nonlinear transient dynamics, large deformation due to buckling, and damage evolution in materials or structures. However, conventional computational homogenization techniques, such as the FE2 and direct FE2 (D-FE2) methods, have not yet been integrated with an explicit algorithm because of the implicit framework in their numerical implementation, and thus cannot be widely applied to concurrent multi-level modeling of transient dynamic issues in multiscale materials and structures. In this study, an explicit D-FE2 method was proposed by incorporating explicit integration algorithms into the numerical calculation of microscale RVEs based on the D-FE2 method proposed by Tan [1]. To facilitate this, an extended Hill–Mandel principle which considers the conservation of both kinetic and internal energies between macro- and micro-scales was derived, and the conventional D-FE2 method was modified using the explicit FE method. The proposed explicit D-FE2 method was validated using a series of experiments and numerical examples including drop-hammer impact on multiscale honeycomb, stress wave propagation in porous materials, compressive buckling of multi-stable metamaterials, damage and failure of fiber-reinforced composites, etc. It was validated that the proposed explicit D-FE2 method is feasible and efficient for transient dynamic analysis of multiscale materials and structures, which might be a new avenue of research in the field of impact dynamics.