Direct FE2 multiscale method for modeling the three-dimensional elastoplastic behavior of composite laminates

Abstract

In this work, the nonlinear elastoplastic mechanical behavior of three-dimensional unidirectional fiber-reinforced composites is simulated using a multiscale method - Direct ${\mathrm{FE}}^2$. In this method, the macroscopic and microscopic degrees of freedom (DOFs) are directly coupled through kinematic constraints to define the scale transition relations in a single finite element analysis. Its numerical implementation avoids intricate coding, thus, exhibiting higher computational efficiency. Furthermore, numerical simulations using this method only require the constitutive relationships of the microscopic components of the Representative Volume Element (RVE). In this study, the heterogeneous RVE containing elastic fiber and plastic matrix is built to obtain the macroscale homogeneous constitutive behavior of composite laminates, and capture the evolution of solution-dependent state variables of microscale components. The nonlinear response of matrix is described using a 3D elastoplastic model with its numerical integration algorithm based on radial return method and implemented using a user-defined subroutine UMAT in the finite element procedure ABAQUS. The effectiveness of the proposed Direct ${\mathrm{FE}}^2$ multiscale method is demonstrated through two different size models including a single macroscale element model and a whole unidirectional laminate model. It is shown that the macroscale stress–strain curves predicted by Direct ${\mathrm{FE}}^2$ agree well with the experimental results.