Inverse Problem Seminar: Two Inverse Problems in Solid Mechanics with Full-Field Data

DisCoMath Seminar
Two Inverse Problems in Solid Mechanics with Full-Field Data

Tom Seidl
Senior Member of Technical Staff
Sandia National Laboratories

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Abstract:
Constitutive or material models provide a mathematical description of how solids respond to mechanical stimuli. For example, an isotropic linear elastic constitutive model describes a relationship between stress and strain that contains parameters known as material constants or properties (e.g. Young’s modulus, Poisson’s ratio). Using metals as an example, aluminum and stainless-steel alloys will generally have different values for these properties. The predictive power of an analytical or computational model for an engineering system depends on the careful selection of appropriate constitutive model forms and their associated properties for the materials it is comprised of. Advances in metrology have provided the means to measure motion on the surface of or within solids with high spatial resolution and accuracy — so-called full-field deformation data. The process of turning mechanical characterization data into estimates of the material properties that appear in a constitutive model is known as calibration, and it is an example of an inverse problem. This problem is often solved using physics-constrained optimization, where the goal is to adjust the material properties in a computational model of the characterization experiment until they match measured quantities of interest (e.g. full-field displacement and load cell force histories). I will discuss two calibration problems that have roughly occupied the first and second halves of my career. First, I will present my work on computational methods for elastography, which involved estimating a spatially varying material property field in a linear elastic constitutive model from quasi-static displacement data. Then I will show how similar concepts and techniques are used to calibrate nonlinear elastic-plastic constitutive models for homogenous metals from digital image correlation data.

Bio:
Tom is a Senior Member of the Technical Staff in the Scientific Machine Learning department at Sandia National Laboratories. He completed a BS in Biomedical Engineering at the University of Rochester (2010) and then shifted gears to earn MS (2012) and PhD (2015) degrees in Mechanical Engineering from Boston University. A series of fortunate events led to a postdoc in Sandia’s Optimization and Uncertainty Quantification department (2016) and promotion to staff (2017). As a computational engineer, Tom develops computational methods for constitutive model calibration of solid materials with a focus on leveraging full-field experimental data.

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