Tuning Nonlinear Elastic Materials under Small and Large Deformations

Abstract

In computer graphics and engineering, nonlinear elastic material properties of 3D volumetric solids are typically adjusted by selecting a material family, such as St. Venant Kirchhoff, Linear Corotational, (Stable) Neo-Hookean, Ogden, etc., and then selecting the values of the specific parameters for that family, such as the Lame parameters, Ogden exponents, or whatever the parameterization of a particular family may be. However, the relationships between those parameter values, and visually intuitive material properties such as object's "stiffness", volume preservation, or the "amount of nonlinearity", are less clear and can be tedious to tune. For an arbitrary isotropic hyperelastic energy density function psi that is not parameterized in terms of the Lame parameters, it is not even clear what the Lame parameters and Young's modulus and Poisson's ratio are. Starting from psi, we first give a concise definition of Lame parameters, and therefore Young's modulus and Poisson's ratio. Second, we give a method to adjust the object's three salient properties, namely two small-deformation properties (overall "stiffness", and amount of volume preservation, prescribed by object's Young's modulus and Poisson's ratio), and one large-deformation property (material nonlinearity). We do this in a manner whereby each of these three properties is decoupled from the other two properties, and can therefore be set independently. This permits a new ability, namely "normalization" of materials: starting from two distinct materials, we can "normalize" them so that they have the same small deformation properties, or the same large-deformation nonlinearity behavior, or both. Furthermore, our analysis produced a useful theoretical result, namely it establishes that Linear Corotational materials (arguably the most widely used materials in computer graphics) are the simplest possible nonlinear materials.