Mechanical and Civil Engineering Seminar

Direct estimation of material properties and their changes is many times infeasible, and even not desirable. For instance, in biomedical applications, it is of interest to estimate the mechanical properties of soft tissue in its natural, functioning state. In aerospace and civil structures, it is desirable to estimate changes in mechanical properties due to the onset of damage while a structure is in service. In geophysics, the common approach for oil exploration is to image the material compressional and shear wave speeds from surface measurements of scattered waves. These and many other applications abound in engineering and science.

Indirect characterization of material properties can be cast as an inverse problem. Inverse problems arise when we observe the response of a system and try to infer the cause of this response from imperfect and partial information. In this talk, I will focus on my current work on Error in Constitutive Equations (ECE) methods for materials identification. The basic premise in the ECE approach is to define a cost functional based on an energy norm that connects a set of kinematically admissible displacements and a set of dynamically admissible stresses. The inverse problem is solved by finding material properties along with admissible displacement and stress fields such that the ECE functional is minimized. The talk will focus on the identification of the spatial variation of elastic and viscoelastic properties in the context of steady-state dynamics. In addition, I will show the advantages and shortcomings of the ECE approach as compared to more conventional approaches that use an L2 cost functional in the inverse problem. Finally, I will briefly illustrate how ECE methods could be generalized to a wide range of problems in mechanics.