A model reduction method for nonlinear analysis of materials and structures with tension–compression asymmetric properties

Abstract

A non-smooth tension–compression asymmetric constitutive law has important applications in modelling of bio-composite structures with a unilateral contact behavior and no-tension/compression structures. Quadratic programming algorithms based on Parametric Variational Principle (PVP) have good numerical robustness on this kind of issue. However, the challenge of computational cost prevents its application into some practical engineering structures with a large-scale degree of freedoms (DOFs). The paper proposes an efficient model reduction method based on the Extended Multiscale FEM (EMsFEM) for mechanical analysis of composite structures with tension–compression asymmetric properties. At the macro-scale, a reduced-order model is constructed and solved to get the displacement field, while a complementarity finite element formulation is proposed to get the stress field at the micro-scale. A two-scale iterative scheme bridging upscale and downscale computations is developed to deal with material nonlinearity. Numerical simulations show satisfactory computational accuracy of the proposed model reduction method, which can find applications in nacre-like composites and membrane antennae. Compared with the previous FEM-PVP, the proposed EMsFEM-PVP method saves computer’s memory and CPU time greatly. The study provides a generalized numerical way to handle large-scale non-smooth mechanics.