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Shape Targeting: A Versatile Active Elasticity Constitutive Model
Constitutive model for active elasticity that drives simulated flesh and muscle toward target shapes with production-friendly artist controls.
Abstract
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.
How to read this
- Category
- Method: an active-elasticity constitutive model
- Contributions
- Promotes the Phace-style shape-targeting energy into a general, baseline model of active elasticity
- A continuum-mechanics FEM formulation with closed-form strain tensors and exact force derivatives for implicit and quasistatic schemes
- Per-element target shapes act as a multi-dimensional analogue of muscle activation parameters
- Context
- Generalizes the energy potential from Ichim et al.'s Phace facial framework and positions it, against the fibre-based muscle tradition of Teran et al., as an active-elasticity counterpart to corotational isotropic elasticity.Builds on: Creating and Simulating Skeletal Muscle from the Visible Human Data Set
- Correctness
- The argument is that this constitutive law deserves baseline status for active materials; backed by closed-form derivatives and varied active-element examples, it is demonstrated for versatility rather than exhaustively benchmarked, so the practical reach across material regimes is the thing to watch.
- Clarity
- Mathematically dense; the motivation reads on a first pass, the constitutive derivation does not.
- How to read it
- First pass for the analogy to corotational elasticity and what shape targeting buys you; second and likely third pass on the strain tensors and force derivatives if you implement the model.
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