Surrogate Modeling, Uncertainty Quantification & Machine Learning

Uncertainty quantification relies on the ability to draw representative samples from complex computational models of interest. In order to avoid a large number of full model evaluations, surrogate models provide an efficient approximation to the relationship between the input parameters and the output response. The Graham-Brady research group uses both adaptive sampling and machine learning to build these surrogate models. More information here

Stochastic Homogenization

Traditional homogenization considers the effective mechanical properties of a representative volume element (RVE), which assumes that the relevant material behavior is averaged over the macro-scale. However, many failure mechanisms are associated with more localized behavior, requiring that homogenization be performed at an intermediate meso-scale, which means that the material properties vary randomly. For 20 years, the Graham-Brady research group has been applying stochastic homogenization as a way to understand stress localizations and failure. More information here

Dynamic Failure of Ceramics

Dynamic failure mechanisms in ceramics are fundamentally different than those in static failure.  While static failure is dictated by a small number of large pre-existing defects, dynamic failure is governed by crack growth from a large number of multi-sized defects. Coalescence of this large number of cracks leads to finer fragmentation of the material, such that the material transforms into a granular medium. The Graham-Brady research group models the mechanisms of brittle dynamic failure in ceramics, including damage growth, fragmentation and granular flow of the fragmented material. More information here

Simulation of Material Microstructure

Digital generation of microstructure provides an efficient means of performing parametric studies on materials with random microstructure, without resorting to extensive characterization of physical specimens. Stochastic simulation and machine learning serve as the basis for these simulations. The Graham-Brady research group has looked at applications in polycrystalline materials, multi-phase composites and functionally graded materials. More information here

Probabilistic Mechanics and Stochastic Finite Elements

All real materials exhibit random variations that affect structural reliability. Probabilistic mechanics tools such as stochastic finite elements provide a means of mapping probabilistic descriptors of materials to probabilistic descriptors of structural behavior. The Graham-Brady research group develops techniques for characterizing the uncertainty in material microstructure, in material properties and in identifying the variability of mechanics models. More information here

Modeling of Cementitious Materials

Because of their inherent random inhomogeneities and brittle failure, models of cementitious materials present a significant modeling challenge. The Graham-Brady group has looked at two primary areas associated with these materials: 1) damage growth and fragmentation at high rates, and 2) localizations of stress and/or damage due to random inhomogeneous microstructure. More information here

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