Abstract:
An elastoplastic multiscale analysis approach based on the Direct FE
2 is developed for the numerical simulation of elastoplastic mechanical behavior of three-dimensional composite laminates. In this method, the macroscale model and microscale representative volume element (RVE) are combined into a single finite element analysis problem, and the degrees of freedom (DOF) of the two-scale models are directly coupled by linear multi-point constrains (MPCs) to define the scale transition relations. The mechanical response of macroscale homogeneous structures can be obtained directly by numerical analysis using the constitutive relations of microscale heterogeneous material components. The heterogeneous RVE containing elastic fiber and plastic matrix is built, and the nonlinear elastoplastic mechanical behavior of matrix is described by an elastoplastic constitutive model. Based on the radial return algorithm, the numerical algorithm and the corresponding numerical consistency tangent stiffness matrix of elastoplastic model are derived to ensure the computational efficiency of Newton-Raphson method in the finite element analysis. A user-defined subroutine UMAT is developed and embedded in the finite element procedure ABAQUS v6.14 to implement the numerical integration algorithm of the matrix constitutive model. The effectiveness of the proposed Direct FE
2 method is demonstrated through the numerical simulations of T300/7901 composites under different loading conditions using three different models: the single macroscale element model, the multidirectional laminated RVE model and the whole unidirectional laminate model. It is shown that the macroscale stress-strain curves predicted by the present Direct FE
2-elastoplastic multiscale analysis approach agree well with the experimental results, and it is able to capture the evolution of the solution-dependent variables of the microscale RVE. The proposed approach provides an effective analysis method for designing and manufacturing of the microstructures of composite laminates.