finite element analysis

This work addresses the challenge of simulating rigid multibody dynamics involving multiple closed kinematic loops, hard unilateral contacts, Coulomb friction, and restitutional impacts. We propose a unified nonlinear complementarity problem (NCP) modeling and solution framework based on maximal coordinates. Methodologically, the approach integrates forward-dynamics decomposition, implicit time integration, and exact frictional contact modeling, while systematically benchmarking against multiple state-of-the-art physics engine solvers. Our key contribution is the first standardized benchmarking framework specifically designed for closed-loop multibody systems, enabling both qualitative and quantitative evaluation. Extensive experiments across diverse, highly coupled closed-loop scenarios reveal, for the first time, the absolute and relative performance boundaries—across accuracy, stability, and convergence—of prevailing solvers. These empirical findings provide critical evidence for the accuracy–stability trade-off in complex contact-rich simulations.

This study addresses the challenging problem of dynamic modeling of deformable multibody systems involving large displacements, deformations, and rotations, along with kinematic constraints, contact, and friction. To this end, a unified absolute nodal coordinate formulation (ANCF) is developed within a total Lagrangian finite element framework (TL-FEA). The approach systematically classifies and enforces kinematic constraints while consistently deriving governing equations for beam, shell, and tetrahedral elements. It integrates St. Venant–Kirchhoff and Mooney–Rivlin hyperelastic constitutive models together with a finite-strain Kelvin–Voigt damping model. By employing a consistent tangent stiffness matrix, the method significantly enhances simulation accuracy, numerical stability, and physical consistency, enabling high-fidelity dynamic simulations of complex multibody systems.

This work addresses the challenge of modeling complex contacts in robotic simulation—specifically, the difficulty of simultaneously achieving broad stiffness coverage (from rigid to compliant), accurate static friction resolution, and robustness against contact state transitions. We propose a differentiable hybrid contact modeling framework based on convex optimization. Methodologically, we integrate the Hunt–Crossley contact force model, Coulomb’s friction law, and the principle of maximum dissipation to construct a stiffness-adaptive convex approximation. We further introduce a novel contact decomposition factor reuse mechanism, enabling efficient and fully differentiable gradient computation for geometrically complex models. Our key contribution is the first implementation—within Drake—of an interaction-rate-capable, high-fidelity, end-to-end differentiable contact solver. This significantly improves static friction accuracy and contact mode transition stability, and markedly enhances sim-to-real transfer performance.

Physics-informed neural networks (PINNs) face two key bottlenecks in solid mechanics: the mismatch between infinite solution domains and finite structural boundaries, and the inability of Euclidean solution spaces to represent complex geometries. To address these, we propose a Euclidean–topological joint solution space, enabling intrinsic adaptation to arbitrary bounded domains and irregular geometries via topological embedding mappings. We further introduce stress–displacement dual-field decoupled parameterization to enhance physical consistency, and integrate PDE-constrained loss with FEM-inspired boundary treatment. The method enables mesh-free, small-data 2D/3D forward and inverse problem solving, achieving accuracy comparable to FEM while significantly improving convergence speed, generalization capability, and robustness in inverse parameter identification. Our contributions are threefold: (1) the first formulation of a Euclidean–topological joint solution space for solid mechanics; (2) a geometry–physics co-design modeling paradigm; and (3) a novel dual-field decoupled PINN framework.

This work addresses nonlinear large-deformation elastodynamic systems. We propose the first structure-preserving discrete modeling and numerical method grounded in the port-Hamiltonian (pH) framework. Leveraging variational principles, we derive index-1 differential-algebraic equations and perform index reduction to construct a complete pH state-space model—featuring displacement, velocity, and **nonlinear strain as an independent state variable (novel in pH modeling)**—rigorously preserving passivity, losslessness, and angular momentum conservation. We further design a structure-preserving midpoint-type discrete-gradient time-integration scheme. Numerical experiments demonstrate exact long-term conservation of energy and angular momentum, significantly enhancing physical fidelity and numerical robustness. The method establishes a provably structure-stable paradigm for high-fidelity dynamic simulation of hyperelastic bodies.

Existing approaches struggle to achieve high-fidelity, physics-based simulation of visual-tactile stress fields on GPU-accelerated robotic platforms, thereby limiting force-aware training in reinforcement learning. This work proposes a scalable finite element framework integrated into Isaac Sim that, for the first time, combines a unified incremental potential contact (UIPC) solver with automatic geometry-aware mesh refinement to compute Cauchy stress tensors directly from hyperelastic constitutive models and project them onto contact surfaces, enabling first-principles-driven tactile mechanics simulation. The method supports plug-and-play compatibility with diverse vision-based tactile sensors, achieving sub-millisecond stress extraction latency at 33.40 FPS in a single environment and a total throughput of 555 FPS across 60 parallel environments. Within a force range of 1.26–4.73 N, simulated tactile images exhibit structural similarity (SSIM) exceeding 0.93 compared to real-world measurements, demonstrating high physical fidelity.

This work addresses the limitations of conventional FFT-based solvers in handling non-periodic boundary conditions, particularly their inability to simultaneously impose different types of boundary conditions on the same surface, prescribe displacements at interior points, or enforce kinematic constraints between nodes. By integrating discrete trigonometric transforms (DTTs) with the displacement method and incorporating both equality and inequality constraints via Lagrange multipliers, the authors develop an extended FFT framework capable of accommodating localized Dirichlet boundary conditions and contact problems. The proposed approach uniquely enables a unified treatment of mixed boundary conditions, internal displacement constraints, and inter-node kinematic relationships, and is further generalized to frictional contact scenarios. Numerical experiments demonstrate excellent agreement with Hertzian contact theory in simulating the interaction between a compact tension specimen and a rigid spherical indenter under small strains, thereby validating the method’s accuracy and versatility.

This work proposes a purely physics-driven deep energy method to address the computational expense and need for repeated training inherent in conventional approaches when dealing with continuously stochastic material parameters in solid mechanics. By embedding both spatial coordinates and random constitutive parameters into the neural network input, the method enables zero-shot, real-time prediction of displacement fields for arbitrary unseen material parameter realizations through unsupervised minimization of the expected potential energy over the parameter space. This framework establishes, for the first time, a unified modeling paradigm that requires neither training datasets nor retraining, demonstrating consistent efficacy across elastic, hyperelastic, and nonlinear contact mechanics problems while significantly outperforming traditional finite element methods and data-driven surrogate models.

This work proposes a measurement-driven, constrained natural language interface architecture to reduce manual configuration overhead in finite element simulations while mitigating the risk of unreliable code generation by large language models (LLMs) in critical solver stages. The approach confines the LLM to front-end tasks—such as prompt parsing and Gmsh script generation for non-standard geometries—while a deterministic scheduler orchestrates verified FEniCS/UFL templates for core computations across five multiphysics problem classes: linear elasticity, hyperelasticity, elastoplasticity, thermomechanical coupling, and phase-field fracture. Experimental results demonstrate 100% prompt parsing success, 97.1% field extraction accuracy, and 90% success rate in custom geometry generation. Simulation accuracy reaches sub-percent levels for smooth problems, with errors in nonlinear cases maintained within 2–5%.

This work proposes a data-driven computational framework for geometrically exact beams that overcomes the limitations of traditional structural analysis, which relies on predefined constitutive models and often discards valuable experimental information, thereby failing to accurately capture the true nonlinear mechanical response. The proposed approach integrates greedy optimization with the alternating direction method (ADM), employs a director-based kinematic description, and introduces a finite element–assisted data initialization strategy alongside a thermodynamically consistent penalty formulation to weakly enforce physical admissibility. Numerical results demonstrate that the method yields discrete stress–strain fields satisfying thermomechanical consistency and achieves solutions significantly closer to the global optimum than standard ADM, markedly enhancing both predictive accuracy and data utilization in modeling nonlinear beam behavior.