Applied Math And Analysis Seminar
Wednesday, March 1, 2017, 12:00pm, 119 Physics
Johann Guilleminot (Duke University, Civil and Environmental Engineering)
Stochastic Modeling and Simulations of Random Fields in Computational Nonlinear Mechanics

Abstract:

Accounting for system-parameter and model uncertainties in computational models is a highly topical issue at the interface of computational mechanics, materials science and probability theory. In addition to the construction of efficient (e.g. Galerkin-type) stochastic solvers, the construction, calibration and validation of probabilistic representations are now widely recognized as key ingredients for performing accurate and robust simulations. This talk is specifically focused on the modeling and simulation of spatially-dependent properties in both linear and nonlinear frameworks. Information-theoretic models for matrix-valued random fields are first introduced. These representations are typically used, in solid mechanics, to define tensor-valued coefficients in elliptic stochastic partial differential operators. The main concepts and tools are illustrated, throughout this part, by considering the modeling of elasticity tensors fluctuating over nonpolyhedral geometries, as well as the modeling and identification of random interfaces in polymer nanocomposites. The latter application relies, in particular, on a statistical inverse problem coupling large-scale Molecular Dynamics simulations and a homogenization procedure. We then address the probabilistic modeling of strain energy functions in nonlinear elasticity. Here, constraints related to the polyconvexity of the potential are notably taken into account in order to ensure the existence of a stochastic solution. The proposed framework is finally exemplified by considering the modeling of various soft biological tissues, such as human brain and liver tissues. [video]

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