Keywords: constitutive equation, composite, anisotropic damage, singular value decomposition, low-rank matrix approximation, dimensionality reduction..

In this paper, different methodologies for reducing the dimensionality of a complex constitutive law for ceramic matrix composites (CMC) using the singular value decomposition (SVD) are presented. An exploration of methods for low-rank matrix approximations begins by proposing a decomposition of the internal state variables (fourth-order tensors) of the reference thermodynamic potential in a certain range of loading conditions. Furthermore, another approach that introduces a modified potential with a reduced set of internal state variables is presented. The performance of the specific low-rank approximations are illustrated by thorough investigations concerning the 'energy' captured by the singular vectors, the relative error in the energy potential, the elastic strain tensor components and the energy dissipation. Levels of the relative error are compared over a wide range of loading conditions for different rank-k approximations. The reduced models are shown to be efficient in representing the reference model, and are well suited for the application and implementation in standard finite element codes.

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