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Abstract: Fractal patterns are observed in computational mechanics of elastic-plastictransitions in two models of linear elastic-perfectly-plastic randomheterogeneous materials: 1 a composite made of locally isotropic grains withweak random fluctuations in elastic moduli and-or yield limits; and 2 apolycrystal made of randomly oriented anisotropic grains. In each case, thespatial assignment of material randomness is a non-fractal, strict-white-noisefield on a 256 x 256 square lattice of homogeneous, square-shaped grains; theflow rule in each grain follows associated plasticity. These lattices aresubjected to simple shear loading increasing through either one of threemacroscopically uniform boundary conditions kinematic, mixed-orthogonal ortraction, admitted by the Hill-Mandel condition. Upon following the evolutionof a set of grains that become plastic, we find that it has a fractal dimensionincreasing from 0 towards 2 as the material transitions from elastic toperfectly-plastic. While the grains possess sharp elastic-plastic stress-straincurves, the overall stress-strain responses are smooth and asymptote towardperfectly-plastic flows; these responses and the fractal dimension-straincurves are almost identical for three different loadings. The randomness inelastic moduli alone is sufficient to generate fractal patterns at thetransition, but has a weaker effect than the randomness in yield limits. In themodel with isotropic grains, as the random fluctuations vanish i.e. thecomposite becomes a homogeneous body, a sharp elastic-plastic transition isrecovered.



Autor: J. Li, M. Ostoja-Starzewski

Fuente: https://arxiv.org/



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