A machine learning accelerated FE${}^2$ homogenization algorithm for elastic solids

Abstract

The FE${}^2$ homogenization algorithm for multiscale modeling iterates between the macroscale and the microscale (represented by a representative volume element) till convergence is achieved at every increment of macroscale loading. The information exchange between the two scales occurs at the gauss points of the macroscale finite element discretization. The microscale problem is also solved using finite elements on-the-fly thus rendering the algorithm computationally expensive for complex microstructures. We invoke machine learning to establish the input-output causality of the RVE boundary value problem using a neural network framework. This renders the RVE as a blackbox which gets the information from the macroscale as an input and gives information back to the macroscale as output, thereby eliminating the need for on-the-fly finite element solves at the RVE level. This framework has the potential to significantly accelerate the FE${}^2$ algorithm.

arXiv admin note: substantial text overlap with arXiv:2002.03770

References in corpus (5)

• A machine learning based plasticity model using proper orthogonal decomposition
• Design of convergence criterion for fixed stress split iterative scheme for small strain anisotropic poroelastoplasticity coupled with single phase flow
• System of equations and staggered solution algorithm for immiscible two-phase flow coupled with linear poromechanics
• Two-grid method on unstructured tetrahedra: Applying computational geometry to staggered solution of coupled flow and mechanics problems
• An efficient algorithm for numerical homogenization of fluid filled porous solids: part-I

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