A time-integration method for stable simulation of extremely deformable hyperelastic objects
A time-integration method for stable simulation of extremely deformable hyperelastic objects
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DOI：
10.1007/s00371-016-1225-0
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发表时间：
2017-10
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影响因子：
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通讯作者：
Ryo Kikuuwe-
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文献类型：
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作者：
Ryo Kikuuwe-
本文提出了一种实时模拟几何非线性超弹性大变形物体的时间积分方法。在所提出的方法中，系统的运动方程离散的向后欧拉方法，并通过一阶泰勒展开线性近似。使用准最小残值法（QMR）求解近似线性方程，准最小残值法是一种非对称或不定矩阵的迭代线性方程求解器。然后，考虑在泰勒展开中省略的非线性项来校正解。该方法不要求本构关系保证刚度矩阵的正定性。实验结果表明，该方法实现了模拟模型在四面体单元几乎变扁变形下的稳定性。它还表明，QMR优于双共轭梯度稳定的方法（BiCGStab）在此应用中。
This paper presents a time integration method for realtime simulation of extremely deformable objects subject to geometrically nonlinear hyperelasticity. In the presented method, the equation of motion of the system is discretized by the backward Euler method, and linearly approximated through the first-order Taylor expansion. The approximate linear equation is solved with the quasi-minimal residual method (QMR), which is an iterative linear equation solver for non-symmetric or indefinite matrices. The solution is then corrected considering the nonlinear term that is omitted at the Taylor expansion. The method does not demand the constitutive law to guarantee the positive definiteness of the stiffness matrix. Experimental results show that the presented method realizes stable behavior of the simulated model under such deformation that the tetrahedral elements are almost flattened. It is also shown that QMR outperforms the biconjugate gradient stabilized method (BiCGStab) in this application.