A time-integration method for stable simulation of extremely deformable hyperelastic objects

• Published in: The Visual computer Vol. 33; no. 10; pp. 1335 - 1346
• Main Author: Kikuuwe, Ryo
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2017; Springer Nature B.V
• Subjects: Algorithms; Approximation; Artificial Intelligence; Computer Graphics; Computer Science; Deformation; Equations of motion; Formability; Haptics; Image Processing and Computer Vision; Iterative methods; Linear equations; Mathematical analysis; Original Article; Simulation; Stiffness matrix; Taylor series; Time integration; Finite elements; Interactive simulation; QMR; Hyperelasticity
• ISSN: 0178-2789; 1432-2315
• DOI: 10.1007/s00371-016-1225-0

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.