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Abstract When cylinders are packed and wrapped by the bands around the surface, the effective elastic behavior in the cross section of the assembly, which is of significance to its stability and integrity, can be controlled by the wrapping force in the band. The wrapping force is transferred to the cylinders through the Hertz contact between each pair of neighboring cylinders, which is validated by the experiments. The Singum model is introduced to study the mechanical behaviors of the packed cylinders with two-dimensional (2D) packing lattices, in which an inner cylinder is simulated by a continuum particle of Singum and the inter-cylinder force is governed by the Hertz contact model so as to derive the effective stress-strain relationship. The wrapping force will produce configurational forces given a displacement variation, which significantly changes the effective stiffness of the packed cylinders. The hexagonal packing exhibits isotropic elasticity whereas the square packing is anisotropic. The efficacy of our model is demonstrated by comparing the closed form elasticity against the numerical simulation and the previous models. The explicit form of elasticity can be used for packing design and quality control of cable construction and installation.
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Capturing Animation-Ready Isotropic Materials Using Systematic Poking
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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- Award ID(s):
- 1911224
- PAR ID:
- 10602539
- Publisher / Repository:
- Association for Computing Machinery (ACM)
- Date Published:
- Journal Name:
- ACM Transactions on Graphics
- Volume:
- 42
- Issue:
- 6
- ISSN:
- 0730-0301
- Format(s):
- Medium: X Size: p. 1-27
- Size(s):
- p. 1-27
- Sponsoring Org:
- National Science Foundation
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