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Thermomechanics of damage in brittle solids: A peridynamics model

Pathrikar, A and Tiwari, SB and Arayil, P and Roy, D (2021) Thermomechanics of damage in brittle solids: A peridynamics model. In: Theoretical and Applied Fracture Mechanics, 112 .

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Official URL: https://dx.doi.org/10.1016/j.tafmec.2020.102880


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. © 2020 Elsevier Ltd

Item Type: Journal Article
Publication: Theoretical and Applied Fracture Mechanics
Publisher: Elsevier B.V.
Additional Information: Copyright to this article belongs to Elsevier B.V.
Keywords: Brittleness; Continuum mechanics; Crack tips; Deformation; Entropy; Heat flux; Partial differential equations; Silica; Temperature, Comprehensive assessment; Coupled partial differential equations; Deformation and damages; Higher order derivatives; Laws of thermodynamics; Thermo-mechanical coupling; Thermomechanical deformations; Transient heat transfer, Heat transfer performance
Department/Centre: Division of Mechanical Sciences > Civil Engineering
Date Deposited: 09 Feb 2021 09:54
Last Modified: 09 Feb 2021 09:54
URI: http://eprints.iisc.ac.in/id/eprint/67855

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