标题： 非线性弹性材料在小变形和大变形下的调校 显示英文标题

标题： Tuning Nonlinear Elastic Materials under Small and Large Deformations

摘要： 在计算机图形学和工程领域，三维体积固体的非线性弹性材料特性通常通过选择一个材料族来调整，例如圣维南-基尔霍夫（St. Venant Kirchhoff）、线性各向同性旋转（Linear Corotational）、（稳定）新胡克（Neo-Hookean）、奥格登（Ogden）等，然后为该族选择特定参数的值，例如拉梅参数、奥格登指数，或者特定族的任何参数化方式。 然而，这些参数值与直观的材料特性（如物体的“刚度”、体积保持或“非线性程度”）之间的关系并不明确，且调整起来可能很繁琐。 对于一个任意各向同性的超弹性能量密度函数 psi，如果它不是以拉梅参数为参数化的形式给出，甚至不清楚拉梅参数、杨氏模量和泊松比是什么。 从 psi 出发，我们首先给出拉梅参数的简明定义，从而得出杨氏模量和泊松比。 其次，我们提供一种方法来调整物体的三个显著特性，即两个小变形特性（整体“刚度”和体积保持量，由物体的杨氏模量和泊松比规定），以及一个大变形特性（材料非线性）。 我们以一种方式实现这一点，使得这三个特性相互解耦，因此可以独立设置。 这使得一种新的能力成为可能，即“材料归一化”：从两种不同的材料出发，我们可以“归一化”它们，使它们具有相同的微小变形特性，或相同的大型变形非线性行为，或者两者都有。 此外，我们的分析产生了一个有用的理论结果，即它确立了以下结论： 线性各向同性旋转材料（可以说是计算机图形学中最广泛使用的材料）是可能的最简单的非线性材料。 显示英文摘要

摘要： In computer graphics and engineering, nonlinear elastic material properties of 3D volumetric solids are typically adjusted by selecting a material family, such as St. Venant Kirchhoff, Linear Corotational, (Stable) Neo-Hookean, Ogden, etc., and then selecting the values of the specific parameters for that family, such as the Lame parameters, Ogden exponents, or whatever the parameterization of a particular family may be. However, the relationships between those parameter values, and visually intuitive material properties such as object's "stiffness", volume preservation, or the "amount of nonlinearity", are less clear and can be tedious to tune. For an arbitrary isotropic hyperelastic energy density function psi that is not parameterized in terms of the Lame parameters, it is not even clear what the Lame parameters and Young's modulus and Poisson's ratio are. Starting from psi, we first give a concise definition of Lame parameters, and therefore Young's modulus and Poisson's ratio. Second, we give a method to adjust the object's three salient properties, namely two small-deformation properties (overall "stiffness", and amount of volume preservation, prescribed by object's Young's modulus and Poisson's ratio), and one large-deformation property (material nonlinearity). We do this in a manner whereby each of these three properties is decoupled from the other two properties, and can therefore be set independently. This permits a new ability, namely "normalization" of materials: starting from two distinct materials, we can "normalize" them so that they have the same small deformation properties, or the same large-deformation nonlinearity behavior, or both. Furthermore, our analysis produced a useful theoretical result, namely it establishes that Linear Corotational materials (arguably the most widely used materials in computer graphics) are the simplest possible nonlinear materials.