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Summary: The concept of energy‐sampling stabilization is used to develop a mean‐strain quadratic 10‐node tetrahedral element for the solution of geometrically nonlinear solid mechanics problems. The development parallels recent developments of a “composite” uniform‐strain 10‐node tetrahedron for applications to linear elasticity and nonlinear deformation. The technique relies on stabilization by energy sampling with a mean‐strain quadrature and proposes to choose the stabilization parameters as a quasi‐optimal solution to a set of linear elastic benchmark problems. The accuracy and convergence characteristics of the present formulation are tested on linear and nonlinear benchmarks and compare favorably with the capabilities of other mean‐strain and high‐performance tetrahedral and hexahedral elements for solids, thin‐walled structures (shells), and nearly incompressible structures. [ABSTRACT FROM AUTHOR]

The paper presents a concept to compress and synthesize complex material morphologies that is based on Wang tilings. Specifically, a microstructure is stored in a set of Wang tiles and its reconstruction is performed by means of a stochastic tiling algorithm. A substantial part of the study is devoted to the setup of optimal parameters of the automatic tile design by means of parametric studies with statistical descriptors at heart. The performance of the method is demonstrated on four two-dimensional two-phase target systems, monodisperse media with hard and soft disks, sandstone, and high porosity metallic foam.