Analytic Eigensystems for Isotropic Membrane Energies

08/15/2020

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by   Julian Panetta, et al.

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We extend the approach of [Smith et al. 2019] to derive analytical expressions for the eigenvalues and eigenmatrices of an isotropic membrane energy density function ψ : ℝ^3x2→ℝ. Clamping the eigenvalue expressions to be positive for each quadrature point of a finite element membrane simulation guarantees a positive semi-definite Hessian for the full discrete membrane energy, enabling an efficient Newton-type simulation.