Fractal patterns are observed in computer simulations of elastic-plastic transitions
in linear, locally isotropic thermoelastic-hardening plastic heterogeneous
materials. The models involve 2D aggregates of homogeneous grains with
weak random fluctuations in thermal expansion coefficients, equivalent to
modeling the effects of random residual strains. The spatial assignment of
material randomness is a nonfractal, strict-white-noise random field on a
square lattice. The flow rule of each grain follows associated plasticity with loading
applied through either one of three macroscopically uniform boundary conditions
admitted by the Hill–Mandel condition. Upon following the evolution of a set of
grains that become plastic (plastic set), we find that it has a fractal dimension
increasing smoothly from 0 towards 2. Transitions under various types of model
randomness and combinations of material constants are examined. While the grains
possess sharp elastic-plastic stress-strain curves, the overall stress-strain responses are
smoothly curved and asymptote toward plastic flows of reference homogeneous
media. As the randomness decreases to zero, they turn into conventional curves
with sharp kinks of homogeneous materials. Overall, the fractal dimension
of the
plastic set is a readily accessible parameter to investigate transition patterns in many
materials.
Keywords
random heterogeneous materials, thermoelastoplasticity,
elastic-plastic transition, fractal pattern
Department of Mechanical Science and
Engineering, Institute for Condensed Matter Theory, and Beckman
Institute
University of Illinois at Urbana–Champaign
Urbana, IL 61801
United States
