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Equivariant graph convolutional neural networks for the representation of homogenized anisotropic microstructural mechanical response

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.

anisotropy↗

Dual graphs realized in the compounds di-{mu}{sub 3}-4-mercaptopyridine catena-di-{mu}{sub 2}-iodo-di-{mu}{sub 3}-iodo-{mu}{sub 4}-iodo penta copper(I) and di-{mu}{sub 3}-4-mercaptopyridine-di-catena-iodo-di-{mu}{sub 3}-iodo tri copper(I)

Two compounds, [Cu5I5](SNC5H4)2 [i] and [Cu3I3](SNC5H4)2 [ii], were synthesized under hydrothermal conditions and the crystal structures were solved. Both compounds crystallized in space group I41/a. The iodide and the sulphur from mercaptopyridine are connected to copper atom, giving the copper atoms tetrahedral coordination geometry. The pyridine end of the organic moiety is non-bonding and fills the empty space around the tetrahedra formed from copper, sulphur and iodide. - Graphical Abstract: A comparison of the central core in both compounds. Display Omitted

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗