Fractals in elastic-plastic transitions of random heterogeneous materials

random heterogeneous materials;elastic-plastic transition;fractals;Markov random field

Li, Jun ; Ostoja-Starzewski, Martin ; Ostoja-Starzewski ; Martin

关键词: random heterogeneous materials;    elastic-plastic transition;    fractals;    Markov random field;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/14674/1_Li_Jun.pdf?sequence=4&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

In this thesis we propose a fractal analysis methodology to study elastic-plastic transitions in random heterogeneous materials. While it is well known that many materials display fractal characteristics, very little work was done on fractals in elasto-plasticity, and so this study is one of the first attempts in that direction. Fractal patterns have been found to form in 2D aggregates of grains of either elastic-perfectly plastic type, or elastic-hardening-plastic type, or thermo-elastic-plastic class (or elastic-plastic type with residual strains). The grains are either isotropic or anisotropic, with random, spatially non-fractal perturbations in properties such as elastic/plastic moduli, yield stresses or thermal expansion coefficients (or residual strains). The flow rule of each grain follows associated plasticity with increasing loads applied through either one of three macroscopically uniform boundary conditions admitted by the Hill-Mandel condition. Following an evolution of a set of grains that have become plastic, we find that it is an evolving fractal with its fractal dimension increasing from 0 towards 2. In essence, any non-zero noise in grains’ properties gives rise to fractal patterns of plastic grains. While the grains possess sharp elastic-plastic stress-strain curves, the overall stress-strain responses are curved and asymptote toward perfectly-plastic flows; all these responses display smooth transitions but, as the randomness in properties decreases to zero, they turn into conventional curves with sharp kinks of homogeneous materials. The influence of plastic hardening and thermal effects on elastic-plastic transitions are further investigated by varying model configurations. It turns out that the fractal dimension provides an optimal parameter for describing the transition patterns in a unified way for a range of different materials.