Capturing Animation-Ready Isotropic Materials Using Systematic Poking

Huanyu Chen, Danyong Zhao, J. Barbič
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Abstract

Capturing material properties of real-world elastic solids is both challenging and highly relevant to many applications in computer graphics, robotics and related fields. We give a non-intrusive, in-situ and inexpensive approach to measure the nonlinear elastic energy density function of man-made materials and biological tissues. We poke the elastic object with 3d-printed rigid cylinders of known radii, and use a precision force meter to record the contact force as a function of the indentation depth, which we measure using a force meter stand, or a novel unconstrained laser setup. We model the 3D elastic solid using the Finite Element Method (FEM), and elastic energy using a compressible Valanis-Landel material that generalizes Neo-Hookean materials by permitting arbitrary tensile behavior under large deformations. We then use optimization to fit the nonlinear isotropic elastic energy so that the FEM contact forces and indentations match their measured real-world counterparts. Because we use carefully designed cubic splines, our materials are accurate in a large range of stretches and robust to inversions, and are therefore "animation-ready" for computer graphics applications. We demonstrate how to exploit radial symmetry to convert the 3D elastostatic contact problem to the mathematically equivalent 2D problem, which vastly accelerates optimization. We also greatly improve the theory and robustness of stretch-based elastic materials, by giving a simple and elegant formula to compute the tangent stiffness matrix, with rigorous proofs and singularity handling. We also contribute the observation that volume compressibility can be estimated by poking with rigid cylinders of different radii, which avoids optical cameras and greatly simplifies experiments. We validate our method by performing full 3D simulations using the optimized materials and confirming that they match real-world forces, indentations and real deformed 3D shapes. We also validate it using a "Shore 00" durometer, a standard device for measuring material hardness.
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利用系统戳穿技术捕捉动画准备就绪的各向同性材料
捕捉真实世界弹性固体的材料特性既具有挑战性,又与计算机图形学、机器人技术和相关领域的许多应用高度相关。我们提出了一种非侵入式、原位和廉价的方法来测量人造材料和生物组织的非线性弹性能量密度函数。我们用已知半径的3d打印刚性圆柱体戳戳弹性物体,并使用精密力计记录接触力作为压痕深度的函数,我们使用力计支架或新型无约束激光装置进行测量。我们使用有限元方法(FEM)建模三维弹性固体,并使用可压缩Valanis-Landel材料建模弹性能量,该材料通过允许大变形下的任意拉伸行为来推广新胡克材料。然后,我们使用优化来拟合非线性各向同性弹性能,使有限元接触力和压痕与实际测量值相匹配。因为我们使用精心设计的三次样条,所以我们的材料在大范围的拉伸和反转中都是准确的,因此对于计算机图形应用程序来说是“动画就绪”的。我们演示了如何利用径向对称性将三维弹性静力接触问题转换为数学上等效的二维问题,从而大大加速了优化。我们还通过给出一个简单而优雅的公式来计算切线刚度矩阵,并通过严格的证明和奇点处理,大大提高了基于拉伸的弹性材料的理论和鲁棒性。我们还观察到,用不同半径的刚性圆柱体戳戳可以估计体积的可压缩性,这避免了光学相机,大大简化了实验。我们通过使用优化的材料进行全3D模拟来验证我们的方法,并确认它们与现实世界的力、压痕和真实变形的3D形状相匹配。我们还使用测量材料硬度的标准设备“Shore 00”硬度计进行验证。
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