A Second Order Cone Programming Approach for Simulating Biphasic Materials

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Date
2022
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The Eurographics Association and John Wiley & Sons Ltd.
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.
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@article{
10.1111:cgf.14626
, journal = {Computer Graphics Forum}, title = {{
A Second Order Cone Programming Approach for Simulating Biphasic Materials
}}, author = {
Tang, Pengbin
and
Coros, Stelian
and
Thomaszewski, Bernhard
}, year = {
2022
}, publisher = {
The Eurographics Association and John Wiley & Sons Ltd.
}, ISSN = {
1467-8659
}, DOI = {
10.1111/cgf.14626
} }
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