Thermomechanics of damage in brittle solids: A peridynamics model. (April 2021) - Pathrikar, Anil; Tiwari, Shashi Bhushan; Arayil, Prashanthan; Roy, Debasish
Highlights: A fully coupled NOSB PD model for brittle damage under thermomechanical loads. A scalar entropy and heat flux is introduced in proposed peridynamics(PD) model. PD correspondence relations are derived using energy and entropy equivalences. Model considers: heat transfer via conduction, radiation; local crack-tip heating. Numerical simulations for a silica tile experiment and Kalthoff's experiment. Abstract: We propose a fully coupled model for damage in brittle solids undergoing thermomechanical deformation. The model is fully coupled in the sense that, just as the thermal field appears in the evolutions of mechanical deformation and damage, the deformation and damage fields also occur in the evolutions of the other two complementing state variables. Damage is presently described by a continuous field variable, an order parameter, that undergoes a smooth transition from the undamaged to a fully fractured state. The governing equations describing the evolutions of deformation, damage and temperature are in the form of coupled partial differential equations (PDEs). The constitutive relations and temperature evolution equation are derived consistent with the two laws of thermodynamics. Other than accounting for the thermal loads, the temperature evolution also incorporates the effects of local heat generation (entropy production due to evolving damage) at a crack tip and thermomechanical coupling (in the form of a dilatation term). In addition to heat transfer through conduction, the heat equation also incorporates heat flow through the radiation mode. The model is computationally implemented through non-ordinary state-based (NOSB) peridynamics (PD) considering the evolving discontinuities (e.g. the cracked surfaces) and the higher order derivatives appearing in the governing PDEs. In the PD implementation, a scalar entropy flux and hence a scalar heat flux, is introduced and a notion of entropy equivalence is exploited. The entropy equivalence furnishes a constitutive correspondence for the entropy and heat fluxes. In the PD formulation, the governing PDEs are converted to the integro-differential type. Validation exercises on the model's performance against transient heat transfer in a silica tile experiment and Kalthoff's experiment are carried out to demonstrate the predictive ability. By way of a more comprehensive assessment of the model, numerical simulation of a silica tile under fully coupled thermomechanical loading is also performed.