  Stochastic multi-scale modeling and simulation for nonlinear
thermo-mechanical problems of composite materials with complicated random
microstructures remains a challenging issue. In this paper, we develop a novel
statistical higher-order multi-scale (SHOMS) method for nonlinear
thermo-mechanical simulation of random composite materials, which is designed
to overcome limitations of prohibitive computation involving the macro-scale
and micro-scale. By virtue of statistical multi-scale asymptotic analysis and
Taylor series method, the SHOMS computational model is rigorously derived for
accurately analyzing nonlinear thermo-mechanical responses of random composite
materials both in the macro-scale and micro-scale. Moreover, the local error
analysis of SHOMS solutions in the point-wise sense clearly illustrates the
crucial indispensability of establishing the higher-order asymptotic corrected
terms in SHOMS computational model for keeping the conservation of local energy
and momentum. Then, the corresponding space-time multi-scale numerical
algorithm with off-line and on-line stages is designed to efficiently simulate
nonlinear thermo-mechanical behaviors of random composite materials. Finally,
extensive numerical experiments are presented to gauge the efficiency and
accuracy of the proposed SHOMS approach.

Numerical Analysis;Numerical Analysis