Equivariant graph convolutional neural networks for the representation of homogenized anisotropic microstructural mechanical response
arxiv(2024)
摘要
Composite materials with different microstructural material symmetries are
common in engineering applications where grain structure, alloying and
particle/fiber packing are optimized via controlled manufacturing. In fact
these microstructural tunings can be done throughout a part to achieve
functional gradation and optimization at a structural level. To predict the
performance of particular microstructural configuration and thereby overall
performance, constitutive models of materials with microstructure are needed.
In this work we provide neural network architectures that provide effective
homogenization models of materials with anisotropic components. These models
satisfy equivariance and material symmetry principles inherently through a
combination of equivariant and tensor basis operations. We demonstrate them on
datasets of stochastic volume elements with different textures and phases where
the material undergoes elastic and plastic deformation, and show that the these
network architectures provide significant performance improvements.
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