Inverse statics of plates and shells

Participants : Florence Bertails-Descoubes, Romain Casati, Gilles Daviet.

We have started to investigate the problem of interpreting an arbitrary 3D mesh as an equilibrium configuration of an elastic plate/shell, subject to gravity and frictional contact forces. We have first considered a simple nodal shell model accounting for stretch, shear and bending. For such a model, inverse statics formulates as an ill-posed minimization problem with a nonlinear objective and nonsmooth constraints. Our objective is to examine this problem in the case where the rest pose of the system is left as unknown, while material parameters (mass, stiffness) are assumed to be known (inverse design problem). In some specific cases (cloth modeling), we use a priori information such as locally low Gaussian curvature so as to help the retrieval of most natural solutions. We plan to submit our results to Siggraph 2015. Targeted applications include virtual garment modeling and parameter retrieval from 3D image-based capture.