Abstract: Systems, methods and articles of manufacture for rendering images depicting materials are disclosed. A stable Neo-Hookean energy model is disclosed which does not include terms that can produce singularities, or require the use of arbitrarily selected clamping parameters. The stable Neo-Hookean energy may include a length-preserving term and volume-preserving term(s), and the volume-preserving terms themselves may include term(s) from a Taylor expansion of a logarithm of a measurement of volume. The stable Neo-Hookean energy may further include an origin barrier term that increases the difficulty of reaching the origin and expands a mesh in response to a perturbation when the mesh is at the origin. Closed-form expressions of eigenvalues and eigenvectors of a Hessian of the stable Neo-Hookean energy are disclosed, which may be used in a simulation of a material to, e.g., project the Hessian to semi-positive-definiteness in Newton iterations used to determine a substantially minimal energy configuration.