Constitutive Relations From Images

Constitutive relations close the balance laws of continuum mechanics and serve as a surrogate for a material in the design and engineering process. The problem of obtaining the constitutive relations is an indirect inverse problem where both the relation and the quantities that define the relation have to be inferred from experimental observations. The advent of full-field observation techniques promises a new ability to learn constitutive relations under realistic operational conditions. However, this is done in two steps, first by obtaining deformations from the images and then by obtaining the constitutive relation from deformations and forces. This leads to a variety of difficulties. In this article, we propose a novel approach that enables us to obtain constitutive relations directly from the raw data consisting of images and force measurements.