“Shape Targeting: A Versatile Active Elasticity Constitutive Model” by Klár, Moffat, Museth and Sifakis

  • ©Gergely Klár, Andrew Moffat, Ken Museth, and Eftychios D. Sifakis



Entry Number: 59


    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.


    S. Bouaziz, S. Martin, T. Liu, L. Kavan, and M. Pauly. 2014. Projective dynamics: fusing
    constraint projections for fast simulation. ACM Transactions on Graphics (TOG) 33,
    4 (2014), 1–11.
    S. Coros, S. Martin, B. Thomaszewski, C. Schumacher, R. Sumner, and M. Gross. 2012.
    Deformable Objects Alive! ACM Trans. Graph. 31, 4, Article 69 (July 2012), 9 pages.
    A.-E. Ichim, P. Kadleček, L. Kavan, and M. Pauly. 2017. Phace: Physics-based face
    modeling and animation. ACM Transactions on Graphics (TOG) 36, 4 (2017), 153.

    G. Klár, T. Gast, A. Pradhana, C. Fu, C. Schroeder, C. Jiang, and J. Teran. 2016. Drucker-
    Prager Elastoplasticity for Sand Animation. ACM Trans. Graph. 35, 4, Article 103 (July 2016), 12 pages. https://doi.org/10.1145/2897824.2925906

    A. McAdams, Y. Zhu, A. Selle, M. Empey, R. Tamstorf, J. Teran, and E. Sifakis. 2011. Effi-
    cient elasticity for character skinning with contact and collisions. ACM Transactions

    on Graphics (TOG) 30, 4 (2011), 37.



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