Shape Targeting: A Versatile Active Elasticity Constitutive Model

The recent “Phace” facial modeling and animation framework [Ichim et al. 2017] introduced a specific formulation of an elastic energy potential that induces mesh elements to approach certain prescribed shapes, modulo rotations. This target shape is defined for each element as an input parameter, and is a multi-dimensional analogue of activation parameters in fiber-based anisotropic muscle models. We argue that the constitutive law suggested by this energy formulation warrants consideration as a highly versatile and practical model of active elastic materials, and could rightfully be regarded as a “baseline” parametric description of active elasticity, in the same fashion that corotational elasticity has largely established itself as the prototypical rotation-invariant model of isotropic elasticity. We present a formulation of this constitutive model in the spirit and style of Finite Element Methods for continuum mechanics, complete with closed form expressions for strain tensors and exact force derivatives for use in implicit and quasistatic schemes. We demonstrate the versatility of the model through various examples in which active elements are employed.