High‐Order Elasticity Interpolants for Microstructure Simulation

Geometric Elasticity for Graphics , Simulation , and Computation

We develop new algorithms which combine the rigorous theory of mathematical elasticity with the geometric underpinnings and computational attractiveness of modern tools in geometry processing. We develop a simple elastic energy based on the Biot strain measure, which improves on state-of-the-art methods in geometry processing. We use this energy within a constrained optimization problem to, for...

DRUPing for Interpolants

We present a method for interpolation based on DRUP proofs. Interpolants are widely used in model checking, synthesis and other applications. Most interpolation algorithms rely on a resolution proof produced by a SAT-solver for unsatisfaible formulas. The proof is traversed and translated into an interpolant by replacing resolution steps with AND and OR gates. This process is efficient (once th...

Fracture simulation for zirconia toughened alumina microstructure

Saint-Venant's principle in linear elasticity with microstructure

Toupin's version of the Saint-Venant principle in linear elasticity is generalized to the case of linear elasticity with mierostructure. That is, it is shown that, for a straight prismatic bar made of an isotropic linear elastic material with rnicrostructure and loaded by a self-equilibrated force system at one end only, the strain energy stored in the portion of the bar which is beyond a dista...

Existence of Minimizers and Microstructure in Nonlinear Elasticity

In this paper, the existence of a solution in the form of a minimizer or microstructure is established for the boundary value problems of nonlinear elasticity with certain nonconvex stored energy functions such as those of St. Venant-Kirchhoff type materials. Necessary and sufficient conditions for minimizing sequences of the potential energy to converge to a minimizer or to microstructure are ...