Two-scale thermomechanical damage model for dynamic shear failure in brittle solids
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O R I G I NA L A RT I C L E
Kokouvi Gbetchi · Cristian Dascalu
Two-scale thermomechanical damage model for dynamic shear failure in brittle solids
Received: 28 February 2020 / Accepted: 11 August 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract A coupled thermomechanical damage approach for dynamic shear failure in brittle solids is proposed in the present contribution. The model is constructed by asymptotic homogenization from microstructures with dynamically evolving microcracks, in mode II, with unilateral contact and friction conditions on their lips. Crack-tip and frictional heating effects assumed at the small scale give rise to distributed heat sources in the macroscopic temperature equation and specific dissipation terms in the upscaled damage law. The analysis of the effective thermomechanical response of the model reveals strain rate and size effects and the influence of friction and growth of microcracks on the macroscopic thermal evolutions. Keywords Microcracks · Mode II dynamic propagation · Frictional and crack-tip heating · Homogenization · Damage law · Macroscopic response simulations 1 Introduction The material response of quasi-brittle solids under compression loadings involving complex features like hardening and softening, stiffness degradation, induced anisotropy, irreversible deformations and thermal changes is the result of microscopic evolutions of microcracks with frictional sliding on their lips. The dynamic behavior of these materials is often associated with important thermal changes originated by small-scale dissipation processes related to microcrack propagation and frictional heating. In order to properly account for such mechanisms and their coupling, a multiscale modeling framework is well suited. The objective of the present contribution is to construct a two-scale thermomechanical damage model based on dynamic evolutions of mode II microcracks with associated heat dissipation effects due to their propagation and frictional sliding. Micromechanical approaches for stationary or evolving frictional microcracks have been developed, among others, in [2,4,24,26,27,29,32–35,51,54,55]. In dynamics, models based on micromechanics have been developed to study the compressive failure response of brittle solids in the case when the main microscopic mechanism is the tensile fracture mode. A study of an array of interacting and dynamically growing wing cracks and the corresponding rate-dependent dynamic damage evolution has been performed in [36]. In [40] the authors developed a micromechanical model for ceramics based on noninteracting, uniformly distributed sliding microcracks subjected to dynamic compressive loading and predicted effects of the rate sensitivity on failure strength. A model that combines damage evolution theory with dynamic crack growth under uniaxial dynamic compression has been proposed in [28]. Also, in [37] a model based on the evolution of tensile wing microcracks in the case of uniaxial compression under constant strain loading is develope
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