1,433 research outputs found
Embedded symmetric positive semi-definite machine-learned elements for reduced-order modeling in finite-element simulations with application to threaded fasteners
We present a machine-learning strategy for finite element analysis of solid
mechanics wherein we replace complex portions of a computational domain with a
data-driven surrogate. In the proposed strategy, we decompose a computational
domain into an "outer" coarse-scale domain that we resolve using a finite
element method (FEM) and an "inner" fine-scale domain. We then develop a
machine-learned (ML) model for the impact of the inner domain on the outer
domain. In essence, for solid mechanics, our machine-learned surrogate performs
static condensation of the inner domain degrees of freedom. This is achieved by
learning the map from (virtual) displacements on the inner-outer domain
interface boundary to forces contributed by the inner domain to the outer
domain on the same interface boundary. We consider two such mappings, one that
directly maps from displacements to forces without constraints, and one that
maps from displacements to forces by virtue of learning a symmetric positive
semi-definite (SPSD) stiffness matrix. We demonstrate, in a simplified setting,
that learning an SPSD stiffness matrix results in a coarse-scale problem that
is well-posed with a unique solution. We present numerical experiments on
several exemplars, ranging from finite deformations of a cube to finite
deformations with contact of a fastener-bushing geometry. We demonstrate that
enforcing an SPSD stiffness matrix is critical for accurate FEM-ML coupled
simulations, and that the resulting methods can accurately characterize
out-of-sample loading configurations with significant speedups over the
standard FEM simulations
Polyconvex anisotropic hyperelasticity with neural networks
In the present work, two machine learning based constitutive models for
finite deformations are proposed. Using input convex neural networks, the
models are hyperelastic, anisotropic and fulfill the polyconvexity condition,
which implies ellipticity and thus ensures material stability. The first
constitutive model is based on a set of polyconvex, anisotropic and objective
invariants. The second approach is formulated in terms of the deformation
gradient, its cofactor and determinant, uses group symmetrization to fulfill
the material symmetry condition, and data augmentation to fulfill objectivity
approximately. The extension of the dataset for the data augmentation approach
is based on mechanical considerations and does not require additional
experimental or simulation data. The models are calibrated with highly
challenging simulation data of cubic lattice metamaterials, including finite
deformations and lattice instabilities. A moderate amount of calibration data
is used, based on deformations which are commonly applied in experimental
investigations. While the invariant-based model shows drawbacks for several
deformation modes, the model based on the deformation gradient alone is able to
reproduce and predict the effective material behavior very well and exhibits
excellent generalization capabilities. In addition, the models are calibrated
with transversely isotropic data, generated with an analytical polyconvex
potential. For this case, both models show excellent results, demonstrating the
straightforward applicability of the polyconvex neural network constitutive
models to other symmetry groups
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