Nonlinear Material Design Using Principal Stretches

摘要

The Finite Element Method is widely used for solid deformablernobject simulation in film, computer games, virtual reality andrnmedicine. Previous applications of nonlinear solid elasticity employedrnmaterials from a few standard families such as linear corotational,rnnonlinear St.Venant-Kirchhoff, Neo-Hookean, Ogden orrnMooney-Rivlin materials. However, the spaces of all nonlinearrnisotropic and anisotropic materials are infinite-dimensional andrnmuch broader than these standard materials. In this paper, werndemonstrate how to intuitively explore the space of isotropic andrnanisotropic nonlinear materials, for design of animations in computerrngraphics and related fields. In order to do so, we first formulaternthe internal elastic forces and tangent stiffness matrices in thernspace of the principal stretches of the material. We then demonstraternhow to design new isotropic materials by editing a singlernstress-strain curve, using a spline interface. Similarly, anisotropicrn(orthotropic) materials can be designed by editing three curves, one for each material direction. We demonstrate that modifying theserncurves using our proposed interface has an intuitive, visual, effectrnon the simulation. Our materials accelerate simulation design andrnenable visual effects that are difficult or impossible to achieve withrnstandard nonlinear materials.