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In this work, we present an application of two versions of the natural element method (NEM) to the Cahn-Hilliard equation. The Cahn-Hilliard equation is a nonlinear fourth order partial differential equation, describing phase separation of binary mixtures. Numerical solutions requires either a two field formulation with C0 continuous shape functions or a higher order C1 continuous...
The behavior of heterogeneous materials is studied. The dependence of the effective elastic properties of micro-heterogeneous materials on the loading conditions are analyzed and corresponding mathematical methods for the description of the observed effects are proposed. The constitutive relations of the theory of elasticity for isotropic solids with stress state dependent deformation properties are...
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