Session S02 - Diverse Aspects of Elliptic PDEs and Related Problems

Wednesday, July 21, 16:00 ~ 16:30 UTC-3

Uncertainty Quantification and Well-Posedness of Damage Mechanics

Petr Plechac

University of Delaware, USA   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Many important materials, including glasses and ceramics, are of the linearly elastic/brittle variety, obeying a classical Hookean law until an applied load reaches a yield stress, at which point they break into some number of fragments. Predicting the behavior of such materials, through modelling and simulation, is of obvious value to a variety of applications. In this work, we add randomness in material properties into the problem, modelling them via random fields within a damage mechanics framework. By identifying key regularizations we establish the well-posedness of a model derived from PDEs of elastodynamics. We then apply tools from uncertainty quantification to investigate the robustness of predictions in the model under materials properties described by random fields.

Joint work with Gideon Simpson (Drexel University, USA) and Jerome Troy (University of Delaware, USA).

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