A Second Order Cone Programming Approach for Simulating Biphasic Materials

dc.contributor.authorTang, Pengbinen_US
dc.contributor.authorCoros, Stelianen_US
dc.contributor.authorThomaszewski, Bernharden_US
dc.contributor.editorDominik L. Michelsen_US
dc.contributor.editorSoeren Pirken_US
dc.date.accessioned2022-08-10T15:19:12Z
dc.date.available2022-08-10T15:19:12Z
dc.date.issued2022
dc.description.abstractStrain 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.number8
dc.description.sectionheadersAnimation and Simulation Techniques II
dc.description.seriesinformationComputer Graphics Forum
dc.description.volume41
dc.identifier.doi10.1111/cgf.14626
dc.identifier.issn1467-8659
dc.identifier.pages87-93
dc.identifier.pages7 pages
dc.identifier.urihttps://doi.org/10.1111/cgf.14626
dc.identifier.urihttps://diglib.eg.org:443/handle/10.1111/cgf14626
dc.publisherThe Eurographics Association and John Wiley & Sons Ltd.en_US
dc.titleA Second Order Cone Programming Approach for Simulating Biphasic Materialsen_US
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