Finite strain self-consistent clustering analysis under multiplicative kinematics

Abstract

In this paper we propose a new finite strain extension of the Self-consistent Clustering Analysis method compatible with multiplicative kinematics. This formulation demands the adoption of the total deformation gradient as the primary unknown and a proper multiplicative decomposition-based strain loading incrementation. A logarithmic-based strain concentration tensor and a highly efficient Fast Fourier Transform-based solution approach are proposed to accelerate the method’s offline-stage. Akin to the infinitesimal strain setting, a new self-consistent scheme is devised to automatically find the reference material properties that play a fundamental role in the solution of the clustered Lippmann–Schwinger integral equilibrium equation. Despite some limitations tied to such a self-consistent scheme, the method is shown to deliver a remarkable balance between accuracy and efficiency in the homogenization of elastoplastic heterogeneous materials under several finite strain loadings. All the essential ingredients required for a successful computational implementation are provided and the method is made available by means of the open-source software CRATE.