Multi-resolution isotropic strain limiting
Abstract
In this paper we describe a fast strain-limiting method that allows stiff, incompliant materials to be simulated efficiently. Unlike prior approaches, which act on springs or individual strain components, this method acts on the strain tensors in a coordinate-invariant fashion allowing isotropic behavior. Our method applies to both two-and three-dimensional strains, and only requires computing the singular value decomposition of the deformation gradient, either a small 2x2 or 3x3 matrix, for each element. We demonstrate its use with triangular and tetrahedral linear-basis elements. For triangulated surfaces in three-dimensional space, we also describe a complementary edge-angle-limiting method to limit out-of-plane bending. All of the limits are enforced through an iterative, non-linear, Gauss-Seidel-like constraint procedure. To accelerate convergence, we propose a novel multi-resolution algorithm that enforces fitted limits at each level of a non-conforming hierarchy. Compared with other constraint-based techniques, our isotropic multi-resolution strain-limiting method is straightforward to implement, efficient to use, and applicable to a wide range of shell and solid materials.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Dec 01, 2010
- Source ID
- 10.1145/1882261.1866182
Entities
People
- Huamin Wang
- James O'brien
- Ravi Ramamoorthi
Organizations
- Division of Information and Intelligent Systems
- Office of Naval Research
- University of California
- University of California, Berkeley