A Second Order Cone Programming Approach for Simulating Biphasic Materials
| dc.contributor.author | Tang, Pengbin | en_US |
| dc.contributor.author | Coros, Stelian | en_US |
| dc.contributor.author | Thomaszewski, Bernhard | en_US |
| dc.contributor.editor | Dominik L. Michels | en_US |
| dc.contributor.editor | Soeren Pirk | en_US |
| dc.date.accessioned | 2022-08-10T15:19:12Z | |
| dc.date.available | 2022-08-10T15:19:12Z | |
| dc.date.issued | 2022 | |
| dc.description.abstract | Strain limiting is a widely used approach for simulating biphasic materials such as woven textiles and biological tissue that exhibit a soft elastic regime followed by a hard deformation limit. However, existing methods are either based on slowly converging local iterations, or offer no guarantees on convergence. In this work, we propose a new approach to strain limiting based on second order cone programming (SOCP). Our work is based on the key insight that upper bounds on per-triangle deformations lead to convex quadratic inequality constraints. Though nonlinear, these constraints can be reformulated as inclusion conditions on convex sets, leading to a second order cone programming problem-a convex optimization problem that a) is guaranteed to have a unique solution and b) allows us to leverage efficient conic programming solvers. We first cast strain limiting with anisotropic bounds on stretching as a quadratically constrained quadratic program (QCQP), then show how this QCQP can be mapped to a second order cone programming problem. We further propose a constraint reflection scheme and empirically show that it exhibits superior energy-preservation properties compared to conventional end-of-step projection methods. Finally, we demonstrate our prototype implementation on a set of examples and illustrate how different deformation limits can be used to model a wide range of material behaviors. | en_US |
| dc.description.number | 8 | |
| dc.description.sectionheaders | Animation and Simulation Techniques II | |
| dc.description.seriesinformation | Computer Graphics Forum | |
| dc.description.volume | 41 | |
| dc.identifier.doi | 10.1111/cgf.14626 | |
| dc.identifier.issn | 1467-8659 | |
| dc.identifier.pages | 87-93 | |
| dc.identifier.pages | 7 pages | |
| dc.identifier.uri | https://doi.org/10.1111/cgf.14626 | |
| dc.identifier.uri | https://diglib.eg.org:443/handle/10.1111/cgf14626 | |
| dc.publisher | The Eurographics Association and John Wiley & Sons Ltd. | en_US |
| dc.title | A Second Order Cone Programming Approach for Simulating Biphasic Materials | en_US |