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Wednesday, September 21, 2022 – 12:00PM to 1:00PM
Oscar Lopez-Pamies ( University of Illinois Urbana-Champaign)
In this talk, I will present a macroscopic (continuum) theory, alongside its numerical implementation, aimed at describing and predicting when and how fracture nucleates and propagates in a body made of rubber that is subjected to arbitrary quasistatic loading conditions.
I will begin by summarizing the slew of existing experimental observations on nucleation and propagation of fracture in rubber that have been generated ever since vulcanized rubber was invented by Charles Goodyear in the 1840s. The observations will reveal that there are three basic ingredients that any attempt at a complete macroscopic theory of fracture ought to account for: i) the elasticity of the rubber, ii) its strength at large, and iii) its fracture energy.
Having pinpointed to the basic ingredients required for a complete theory, I will then present one such theory, regularized, of phase-field type. The theory can be viewed as a natural generalization of the phase-field approximation of the celebrated variational theory of brittle fracture of Francfort and Marigo (1998) - which is nothing more than the mathematical statement of Griffith's competition of bulk and fracture energies - to account for the material strength at large. This is accomplished by the addition of an external driving force - which physically represents the macroscopic manifestation of the presence of inherent microscopic defects in the material - in the equation governing the evolution of the phase field.
In the latter part of the presentation, I will illustrate the descriptive and predictive capabilities of the theory via simulations of several famous experiments, including the poker-chip experiments of Gent and Lindley (1959) on natural rubber, which despite being commonly credited with initiating the so-called field of cavitation in elastomers have remained unexplained until now.
I will close by discussing how exactly the same ideas behind the proposed theory apply directly to the nucleation and propagation of fracture in any nominally brittle material.