Figure 1: Design of isotropic nonlinear materials: The soft-body motion of the wrestler was computed using FEM, constrained to a motion capture skeletal dancing animation. Using our method, we designed a nonlinear isotropic material that performs well both during impulsive and gentle animation phases. Top row: the wrestler is performing high jumps. The soft Neo-Hookean material exhibits artifacts (belly, thighs) when the character moves abruptly. Our material and the stiff Neo-Hookean material produce good deformations. Bottom row: deformations during a gentle phase (walking while dancing) of the same motion sequence. The soft Neo-Hookean material and our method produce rich small-deformation dynamics, whereas the stiff Neo-Hookean material inhibits it. The Young's modulus of material (a) was chosen to produce good dynamics during gentle motion. We then edited it to address impulsive motion, producing (c). The stiff material in (b) is the best matching material to (c) among Neo-Hookean materials, minimizing the L 2 material curve difference to (c). AbstractThe Finite Element Method is widely used for solid deformable object simulation in film, computer games, virtual reality and medicine. Previous applications of nonlinear solid elasticity employed materials from a few standard families such as linear corotational, nonlinear St.Venant-Kirchhoff, Neo-Hookean, Ogden or Mooney-Rivlin materials. However, the spaces of all nonlinear isotropic and anisotropic materials are infinite-dimensional and much broader than these standard materials. In this paper, we demonstrate how to intuitively explore the space of isotropic and anisotropic nonlinear materials, for design of animations in computer graphics and related fields. In order to do so, we first formulate the internal elastic forces and tangent stiffness matrices in the space of the principal stretches of the material. We then demonstrate how to design new isotropic materials by editing a single stress-strain curve, using a spline interface. Similarly, anisotropic (orthotropic) materials can be designed by editing three curves, one for each material direction. We demonstrate that modifying these curves using our proposed interface has an intuitive, visual, effect on the simulation. Our materials accelerate simulation design and enable visual effects that are difficult or impossible to achieve with standard nonlinear materials.

This practice and experience paper describes a robust C++ implementation of several non‐linear solid three‐dimensional deformable object strategies commonly employed in computer graphics, named the Vega finite element method (FEM) simulation library. Deformable models supported include co‐rotational linear FEM elasticity, Saint–Venant Kirchhoff FEM model, mass–spring system and invertible FEM models: neo‐Hookean, Saint–Venant Kirchhoff and Mooney–Rivlin. We provide several timestepping schemes, including implicit Newmark and backward Euler integrators, and explicit central differences. The implementation of material models is separated from integration, which makes it possible to employ our code not only for simulation, but also for deformable object control and shape modelling. We extensively compare the different material models and timestepping schemes. We provide practical experience and insight gained while using our code in several computer animation and simulation research projects.

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