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Random Fields: Modeling and Identification

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USMW01 - Introduction to Uncertainty Quantification in Mechanics of Materials

Lecture: Wednesday 12 July 2023, 09:00 – 10:00Title: Random fields, modeling, and identificationPresenter: Christian SOIZE 1. Random fields in the context of mechanics of materials. Example of material with a complex microstructure. Stochastic models for multiscale modeling of materials. Generality on the random fields. Tensor-valued random elasticity field in 3D linear elasticity of random media. Stochastic elliptic operator and BVP in 3D linear elasticity. Stochastic computational model.- Statistical inverse problem for identifying the random elasticity field. 2. Algebraic prior probability model for heterogeneous anisotropic elastic media. Representation with a lower bound and a random germ field. Construction of the random germ field and its generator of realizations.- Definition of the hyperparameter. 3. Algebraic prior stochastic model for heterogeneous elastic media with statistical fluctuations    in a symmetry class and anisotropic statistical fluctuations. Hypotheses on the statistical fluctuations. Notation and properties for positive matrices with symmetry classes.- Advanced prior stochastic model for the random field with material symmetry. 4. Illustrations in stochastic homogenization of heterogeneous materials at microscale and nanoscale- Probabilistic analysis of representative volume element size in stochastic homogenization of a   heterogeneous complex microstructure.- Stochastic continuum modeling of random interphases from atomistic simulations for a polymer   nanocomposite and statistical inverse problem.

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