Volume Preserving Simulation of Soft Tissue with Skin

Simulation of human soft tissues in contact with their environment is essential in many fields, including visual effects and apparel design. Biological tissues are nearly incompressible. However, standard methods employ compressible elasticity models and achieve incompressibility indirectly by setting Poisson's ratio to be close to 0.5. This approach can produce results that are plausible qualitatively but inaccurate quantatively. This approach also causes numerical instabilities and locking in coarse discretizations or otherwise poses a prohibitive restriction on the size of the time step. We propose a novel approach to alleviate these issues by replacing indirect volume preservation using Poisson's ratios with direct enforcement of zonal volume constraints, while controlling fine-scale volumetric deformation through a cell-wise compression penalty. To increase realism, we propose an epidermis model to mimic the dramatically higher surface stiffness on real skinned bodies. We demonstrate that our method produces stable realistic deformations with precise volume preservation but without locking artifacts. Due to the volume preservation not being tied to mesh discretization, our method also allows a resolution consistent simulation of incompressible materials. Our method improves the stability of the standard neo-Hookean model and the general compression recovery in the Stable neo-Hookean model.

The Measurement of Compressible Elasticity Modulus and Poisson Ratio of Ziziphus Montana Wood

Timber is a typical orthotropic material, of which the accurate measurement of elasticity modulus and Poisson ratio is important. In this article, the test samples are manufactured according to GB 1943-1991 and 1935-1991. An electronic testing machine is employed to add longitudinal load on samples and the longitudinal and transverse strains are measured via Wheatstone bridge. Then, the compressible elasticity modulus and Poisson ratio of Ziziphus montana wood in three directions is obtained. The results show that the elasticity modulus measured is of similar magnitude to those with similar dry density and of great importance to finite element calculation.

Numerical convergence and stability of mixed formulation with X-FEM cut-off

In this paper, we are concerned with the mathematical and numerical analysis of convergence and stability of the mixed formulation for incompressible elasticity in cracked domains. The objective is to extend the extended finite element method (X-FEM) cut-off analysis done in the case of compressible elasticity to the incompressible one. A mathematical proof of the inf-sup condition of the discrete mixed formulation with X-FEM is established for some enriched fields. We also give a mathematical result of quasi-optimal error estimate. Finally, we validate these results with numerical tests.