Multi-resolution isotropic strain limiting
Multi-resolution isotropic strain limiting
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DOI：
10.1145/1866158.1866182
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发表时间：
2010-12
期刊：
影响因子：
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通讯作者：
Huamin Wang;J. F. O'Brien;R. Ramamoorthi
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文献类型：
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作者：
Huamin Wang;J. F. O'Brien;R. Ramamoorthi
在本文中，我们描述了一种快速的应变限制方法，允许刚性，不符合材料进行有效的模拟。与先前的方法不同，该方法作用于弹簧或单个应变分量，该方法以允许各向同性行为的坐标不变方式作用于应变张量。我们的方法适用于二维和三维应变，只需要计算变形梯度的奇异值分解，对于每个元素，可以是一个小的2x2或3x 3矩阵。我们证明了它的使用与三角形和四面体线性基础元素。对于三维空间中的三角化曲面，我们也描述了一个互补的棱角限制方法来限制面外弯曲。所有的限制都是通过一个迭代的，非线性的，高斯-赛德尔样的约束程序。为了加快收敛速度，我们提出了一种新的多分辨率算法，强制在每个级别的非一致层次的拟合限制。与其他基于约束的技术相比，我们的各向同性多分辨率应变限制方法是简单的实施，有效的使用，并适用于广泛的壳和固体材料。
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.