simulate deformable bodies

Existing position-based dynamics (PBD) methods support only linear constraints, limiting their ability to model arbitrary nonlinear constitutive forces—such as high-resolution data-driven cloth or neo-Hookean hyperelasticity with inversion barriers. This work proposes a generalized PBD framework: by reformulating the implicit time integration equation, nonlinear internal forces are explicitly embedded into the PBD iteration loop while preserving the original constraint-solving structure. Nonlinear systems are solved efficiently via Gauss–Seidel–style iterations. Our method is the first to unify complex nonlinear material models within the PBD paradigm, enabling stable, penetration-free, high-fidelity deformation simulation. It achieves significant speedups over Newton’s method on high-resolution meshes—delivering both real-time performance and physically accurate behavior.

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 proposes an end-to-end automated framework that generates compliant engineering reports directly from a single image of a mechanical component. The approach employs a solver-agnostic multi-agent system operating within a shared contextual space, leveraging a quality-gated conditional iteration mechanism to collaboratively perform geometric reconstruction, material inference, adaptive mesh generation, multi-case finite element analysis, and code compliance assessment. A unified uncertainty quantification framework is innovatively formulated by integrating interval analysis, probability density functions, and fuzzy logic, complemented by task-dependent conservativeness criteria to reconcile conflicting multi-limit-state requirements. Demonstrated on a single photograph of an L-shaped steel bracket, the system autonomously produced a 171,504-node mesh, executed seven analyses, and delivered a complete report—including failure diagnosis and redesign recommendations—without any human intervention.

This work proposes the first autonomous simulation system that integrates an agent-based architecture with domain-finetuned large language models (LLMs) to enable end-to-end modeling and solution of solid mechanics, fluid dynamics, and multiphysics problems. Addressing the limitations of conventional LLMs—which often hallucinate, lack awareness of variational structures, and fail to close the loop from problem description to verified solutions—the system incorporates retrieval-augmented multi-LLM code generation and filtering, finetuned models spanning 3B to 120B parameters, multi-agent collaboration, and runtime feedback mechanisms. A high-quality corpus of over a thousand FEniCS codes was curated to support training and evaluation. On a benchmark suite of 39 nonlinear elasticity, plasticity, and non-Newtonian fluid problems, the GPT OSS 120B model achieved a code generation success rate of 71.79%, substantially outperforming non-agent-based approaches.

This work addresses the challenge of high-fidelity, efficient simulation of dynamic behaviors of real-world elastic objects. Methodologically, we propose a continuum-mechanics-based neural simulation framework that employs Gaussian kernels as fundamental continuous material units and introduces a Center-of-Mass System (CMS) hierarchical architecture—explicitly embedding physical constraints such as mass and momentum conservation to enable interpretable, physics-consistent modeling across coarse-to-fine granularities. Our key contributions are: (i) the first integration of Gaussian kernels into continuum-based elastic modeling, and (ii) the introduction of an explicit physics-constrained CMS hierarchical simulation paradigm. Evaluated on our newly established READY benchmark—a real-world video dataset—the method significantly outperforms existing physics-driven approaches in dynamic simulation accuracy. Both source code and trained models will be made publicly available.

This study addresses the challenge of accurately capturing the highly nonlinear response of hyperelastic materials under large-deformation impact, which traditional constitutive models struggle to represent. The authors integrate physics-augmented neural networks (PANNs) into industrial-scale explicit finite element solvers—Simcenter Radioss and OpenRadioss—by automatically generating Fortran user material subroutines for data-driven constitutive modeling. Key contributions include the first deployment of PANNs within industrial explicit solvers, the introduction of a computationally more efficient SQuarePlus activation function as a replacement for SoftPlus, and an open-source, automated toolchain enabling end-to-end subroutine generation. Experimental results demonstrate that the proposed approach achieves high accuracy while significantly reducing neural network evaluation overhead, offering an efficient and practical machine learning–based constitutive modeling paradigm for impact simulations.

This study addresses the computational inefficiency of simulating large-deformation flexible multibody systems at high resolution by proposing an efficient GPU-accelerated framework within a total Lagrangian finite element setting. The approach integrates implicit backward Euler time integration with the augmented Lagrangian method to enforce constraints. Key contributions include a two-stage GPU parallelization strategy for accelerating internal force and tangent stiffness computations, an asynchronous collision detection algorithm that avoids bounding volume hierarchies, and a fixed sparsity pattern strategy to enhance Newton solver efficiency. The system incorporates T10 tetrahedral elements, ANCF beam and shell formulations, hyperelastic constitutive models, and Kelvin–Voigt viscoelasticity, leveraging cuDSS for sparse Hessian assembly and factorization. Experiments demonstrate nearly an order-of-magnitude real-time speedup over CPU baselines at the highest tested resolution, while frictional contact scenarios confirm model accuracy.

Traditional simulation of deformable objects relies on mesh-based representations or neural fields requiring per-shape optimization, struggling to balance geometric complexity and computational efficiency. This work proposes a mesh-free reduced-order simulation method that, for the first time, integrates Reproducing Kernel Particle Method (RKPM) with reduced-order elastic dynamics. By employing RKPM to construct a continuous elastic body model and solving the generalized eigenvalue problem of the elastic energy Hessian matrix, the method automatically computes skinning weights without mesh generation or per-shape optimization. The approach achieves a 40× speedup in training compared to neural field–based methods, yields simulation errors lower than those of converged finite element solutions, and demonstrates successful application across diverse geometric representations and robotic simulation tasks.

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%.