Related papers: Discrete Differential Geometry for Simulating Nonl…
Flexible elastic structures, such as beams, rods, ribbons, plates, and shells, exhibit complex nonlinear dynamical behaviors that are central to a wide range of engineering and scientific applications, including soft robotics, deployable…
In this paper, we propose a novel one-dimensional (1D) discrete differential geometry (DDG)-based numerical method for geometrically nonlinear mechanics analysis (e.g., buckling and snapping) of axisymmetric shell structures. Our numerical…
Soft robots have garnered significant attention due to their promising applications across various domains. A hallmark of these systems is their bilayer structure, where strain mismatch caused by differential expansion between layers…
Motivation: Despite its great success in various physical modeling, differential geometry (DG) has rarely been devised as a versatile tool for analyzing large, diverse and complex molecular and biomolecular datasets due to the limited…
High-fidelity simulation has become essential to the design and control of soft robots, where large geometric deformations and complex contact interactions challenge conventional modeling tools. Recent advances in the field demand…
Biomembranes adopt varying morphologies that are vital to cellular functions. Many studies use computational modeling to understand how various mechanochemical factors contribute to membrane shape transformations. Compared to…
Soft robots utilizing inflatable dielectric membranes can realize intricate functionalities through the application of non-mechanical fields. However, given the current limitations in simulations, including low computational efficiency and…
Discrete dislocation dynamics (DDD) is a widely employed computational method to study plasticity at the mesoscale that connects the motion of dislocation lines to the macroscopic response of crystalline materials. However, the…
Capturing both geometry and rigid motion for structured dynamic objects, like multi-part assemblies or jointed mechanisms, remains a key challenge. Existing dynamic methods, such as deformable meshes or 3DGS, rely on unstructured…
Qualifying the discrepancy between 3D geometric models, which could be represented with either point clouds or triangle meshes, is a pivotal issue with board applications. Existing methods mainly focus on directly establishing the…
Accurate and efficient simulation tools are essential in robotics, enabling the visualization of system dynamics and the validation of control laws before committing resources to physical experimentation. Developing physically accurate…
We present a differentiable dynamics solver that is able to handle frictional contact for rigid and deformable objects within a unified framework. Through a principled mollification of normal and tangential contact forces, our method…
Differentiable simulation of soft bodies is a foundation for system identification, trajectory optimization, and Real2Sim transfer. Yet, existing methods such as the differentiable Projective Dynamics (DiffPD) struggle when faced with…
Multiscale models of materials, consisting of upscaling discrete simulations to continuum models, are unique in their capability to simulate complex materials behavior. The fundamental limitation in multiscale models is the presence of…
Direct numerical simulation of microscale fluid--structure interactions in multicomponent and multiphase flows requires methods that can represent moving boundaries together with fields constrained to evolving interfaces. Diffuse-domain…
Designing and fabricating structures with specific mechanical properties requires understanding the intricate relationship between design parameters and performance. Understanding the design-performance relationship becomes increasingly…
Origami inspired architectures offer a powerful route toward lightweight, reconfigurable, and programmable robotic systems. Yet, a unified mechanics framework capable of seamlessly bridging rigid folding, elastic deformation, and stability…
A new field of discrete differential geometry is presently emerging on the border between differential and discrete geometry. Whereas classical differential geometry investigates smooth geometric shapes (such as surfaces), and discrete…
Differentiable physics is a powerful approach to learning and control problems that involve physical objects and environments. While notable progress has been made, the capabilities of differentiable physics solvers remain limited. We…
Differentiable physics is a powerful tool in computer vision and robotics for scene understanding and reasoning about interactions. Existing approaches have frequently been limited to objects with simple shape or shapes that are known in…