Anisotropic Strain Limiting

Many materials exhibit a highly nonlinear elastic behavior, such as textiles or finger flesh. An efficient way of enforcing the nonlinearity of these materials is through strain-limiting constraints, which is often the model of choice in computer graphics. Strain-limiting allows to model highly non-linear stiff materials by eliminating degrees of freedom from the computations and by enforcing a set of constraints. However, many nonlinear elastic materials, such as composites, wood or flesh, exhibit anisotropic behaviors, with different material responses depending on the deformation direction. This anisotropic behavior has not been addressed in the past in the context of strain limiting, and naïve approaches, such as applying a different constraint on each component of the principal axes of deformation, produce unrealistic results. In this paper, we enable anisotropic behaviors when using strain-limiting constraints to model nonlinear elastic materials. We compute the limits for each principal axis of deformation through the rotation and hyperbolic projection of the deformation limits defined in the global reference frame. The limits are used to formulate the strain-limiting constraints, which are then seamlessly combined with frictional contact constraints in a standard constrained dynamics solver.