TOWARDS ADJOINT-BASED INVERSION OF THE LAME PARAMETER FIELD FOR SLENDER STRUCTURES WITH CANTILEVER LOADING

Continuum models of slender structures are effective in simulating the mechanics of nano-scale filaments. However, the accuracy of these simulations strictly depends on the knowledge of the constitutive laws that may in general be non-homogeneous. It necessitates an inverse problem framework that can leverage the data provided by physical experiments and molecular dynamics simulations to estimate the unknown parameters in the constitutive law. In this paper, we formulate a simple but representative inverse problem as a nonlinear least-squares optimization problem whose cost functional is the misfit between synthetic observations of a cantilever displacement field and model predictions. A Tikhonov regularization term is added to the cost functional to render the problem well-posed and account for observational error. We solve this optimization problem with an adjoint-based inexact Newton-conjugate gradient method. We show that the reconstruction of the Lame parameter field converges to the exact coefficient as the observation error decreases.