Multi-temporal scale approach for complex thermo-mechanical loading

Mechanical structures and components, especially in the aviation or automobile sectors are invariably subjected to complex thermo-mechanical loading. The prediction of life-time of such structures can be challenging, especially if complex non-linear material behaviour is coupled with complex load description. The goal of this research is to be able to predict life-time of such complex thermo-mechanical problems efficiently. The obvious choice of quantifying the life-time is to use continuum damage mechanics (CDM), that defines a separate internal variable in a consistent thermodynamic framework to evaluate the loss of load-carrying capacity of structures. Often coupled with (visco)plasticity and hardening, and in this case, also with thermo-elasticity, the generic framework of CDM is extremely expensive when used for fatigue applications involving large number of load cycles. A cycle-by-cycle simulation is extremely expensive as it involves highly non-linear material behaviour coupled with multi-physical phenomena. To circumvent this difficulty, a multi-scale technique has been used, which is based on separating the temporal scal e into a macro-scale corresponding to the slow evolution of quantities of interest, and a micro-scale corresponding to their fast evolution. Based on asymptotic expansion and classical theory of numerical homogenisation, the problem eventually is separated into a macroscopic problem which involves the resolution of the homogenised quantities of interest, and a microscopic problem to evaluate their residual counterparts. Such a framework, avoids cycle by cycle simulation and reduces the numerical expense drastically. Previously used for visco-plasticity and for elastic-damage, the novelty herein lies on the usage of coupled thermo-elastic-plastic-damage behaviour. Although, quite novel and robust, the main drawback is the fact that the method is still in a deterministic framework, and does not take into account the randomness in loading and material parameter. Thereby, the objective hereafter, is to use stochastic analysis in the multi-scale framework, and thereby the real-life engineering problems can be mimicked with precision. To assess the performance of the aforementioned strategy, comparison between reference solution and solution obtained through the multi-scale framework has been performed in a one-dimensional bar problem.