(The Eurographics Association, 2014) Müller, Matthias; Chentanez, Nuttapong; Kim, Tae-Yong; Macklin, Miles; Vladlen Koltun and Eftychios Sifakis
We propose a new set of constraints within the Position Based Dynamics (PBD) framework that allow the control of strain in directions that are independent of the edge directions of the simulation mesh. Instead of constraining distances between points, we constrain the entries of the Green - St Venant strain tensor. Varying the stiffness values corresponding to the individual strain coefficients lets us simulate anisotropic behavior. By working with Green's rotation-independent, non-linear strain tensor directly we do not have to perform a polar decomposition of the deformation gradient as in most strain limiting approaches. In addition, we propose a modification of the constraints corresponding to the diagonal entries of the strain tensor such that they can be solved in a single step and a modification of the constraints corresponding to the off-diagonal entries to decouple stretch from shear resistance. By formulating the constraints within the PBD framework, they can be used not only for strain limiting but to perform the actual simulation of the deformable object whereas traditional strain limiting methods have to be paired with a separate simulation method.