A numerical study of parameter identification in linear and nonlinear elastic and viscoelastic plates

In the design and fabrication of products, it is typical to require explicit knowledge of the parameters that govern the mechanical properties of the materials used. The parameter identification problem for linear and nonlinear viscoelastic and elastic plates is studied. The material properties of the plate, which appear in the constitutive relations, are recovered by optimizing an objective function constructed from reference strain data. The resulting inverse algorithm consists of an optimization algorithm coupled with a corresponding direct algorithm that computes the strain fields given a set of material properties. A variety of optimization algorithms are tested using several constitutive models to determine the best approach for this class of inverse problem. A general methodology for solving the parameter identification problem is proposed. It is intended that the methodology be used in a laboratory setting where the material can be controlled as much as possible.; Many researchers have studied inverse problems in a variety of contexts (electromagnetics, geophysics and acoustics, for example), both from the analytical and the numerical point of view. Theoretical results discuss the conditions under which the inverse problem can be solved and general statements about the nature of the ill-posedness of particular problems. Numerical results have focused primarily on one dimensional models and often employ ad hoc methods. Other researchers have developed constitutive relations for elastic and viscoelastic materials. What is new here is the focus on numerical inverse problems nonlinear elastic and viscoelastic materials, problems that are two dimensional, the simultaneous recovery of multiple parameters, and the introduction of noise into the reference strain data in order to test the accuracy and robustness of the inverse algorithm.; Future work will focus on finding minimal sets of reference strain data that suffice to recover the material parameters, and to customize the algorithm for use in laboratory experiments that characterize novel materials.