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Kirchhoff-Love shells are commonly used in many branches of engineering, including in computer graphics, but have so far been simulated only under limited nonlinear material options. We derive the Kirchhoff-Love thin-shell mechanical energy for an arbitrary 3D volumetric hyperelastic material, including isotropic materials, anisotropic materials, and materials whereby the energy includes both even and odd powers of the principal stretches. We do this by starting with any 3D hyperelastic material, and then analytically computing the corresponding thin-shell energy limit. This explicitly identifies and separates in-plane stretching and bending terms, and avoids numerical quadrature. Thus, in-plane stretching and bending are shown to originate from one and the same process (volumetric elasticity of thin objects), as opposed to from two separate processes as done traditionally in cloth simulation. Because we can simulate materials that include both even and odd powers of stretches, we can accommodate standard mesh distortion energies previously employed for 3D solid simulations, such as Symmetric ARAP and Co-rotational materials. We relate the terms of our energy to those of prior work on Kirchhoff-Love thin-shells in computer graphics that assumed small in-plane stretches, and demonstrate the visual difference due to the presence of our exact stretching and bending terms. Furthermore, our formulation allows us to categorize all distinct hyperelastic Kirchhoff-Love thin-shell energies. Specifically, we prove that for Kirchhoff-Love thin-shells, the space of all hyperelastic materials collapses to two-dimensional hyperelastic materials. This observation enables us to create an interface for the design of thin-shell Kirchhoff-Love mechanical energies, which in turn enables us to create thin-shell materials that exhibit arbitrary stiffness profiles under large deformations. 

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. 

Precision modeling of the hand internal musculoskeletal anatomy has been largely limited to individual poses, and has not been connected into continuous volumetric motion of the hand anatomy actuating across the hand's entire range of motion. This is for a good reason, as hand anatomy and its motion are extremely complex and cannot be predicted merely from the anatomy in a single pose. We give a method to simulate the volumetric shape of hand's musculoskeletal organs to any pose in the hand's range of motion, producing external hand shapes and internal organ shapes that match ground truth optical scans and medical images (MRI) in multiple scanned poses. We achieve this by combining MRI images in multiple hand poses with FEM multibody nonlinear elastoplastic simulation. Our system models bones, muscles, tendons, joint ligaments and fat as separate volumetric organs that mechanically interact through contact and attachments, and whose shape matches medical images (MRI) in the MRI-scanned hand poses. The match to MRI is achieved by incorporating pose-space deformation and plastic strains into the simulation. We show how to do this in a non-intrusive manner that still retains all the simulation benefits, namely the ability to prescribe realistic material properties, generalize to arbitrary poses, preserve volume and obey contacts and attachments. We use our method to produce volumetric renders of the internal anatomy of the human hand in motion, and to compute and render highly realistic hand surface shapes. We evaluate our method by comparing it to optical scans, and demonstrate that we qualitatively and quantitatively substantially decrease the error compared to previous work. We test our method on five complex hand sequences, generated either using keyframe animation or performance animation using modern hand tracking techniques.