A refined thermo-mechanical fully coupled peridynamics with application to concrete cracking

The accurate numerical prediction of concrete cracking under thermal or thermo-mechanical loads is essential and urgent due to the requirement of structure reliability and durability. In the present paper, a refined bond-based peridynamic approach for thermo-mechanical coupling problems is developed and applied to the thermal diffusion, thermal-induced deformation, and fracture of mesoscale concrete structures. Specifically, the classical differential thermo-mechanical equations are reformulated by applying the peridynamic differential operator on and thus converted to a novel nonlocal integral formulation, which is called a refined thermo-mechanical fully coupled peridynamics. It gets rid of the micro-conductivity and does not require any calibration procedure, and the temperature-deformation term is expressed in terms of the integral of displacement difference directly. Besides, A multi-rate explicit time integration scheme is applied to overcome different time-scale problems in multi-physical systems as well. Meanwhile, a new micro-conduction model is developed for the broken bonds, and the cracks are not assumed to be adiabatical herein. And, the fracture energy release rate is considered to be temperature-dependent. Moreover, three benchmark examples for thermal diffusion and fully coupled thermo-mechanical problems are analyzed to illustrate the correctness and accuracy of the proposed peridynamic approach. At last, the simulations of a thick-walled heterogeneous concrete cylinder geometrically modeled in two- and three-dimension suffering heating load are performed, whose cracking results agree well with corresponding experimental results.