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We extend the theory of exterior differential systems from manifolds and their tangent bundles to Lie algebroids. In particular, we define the concept of an integral manifold of such an exterior differential system. We support our…

Differential Geometry · Mathematics 2026-01-21 Tom Mestdag , Kenzo Yasaka

Previous work introduced a lower-dimensional numerical model for the geometric nonlinear simulation and optimization of compliant pressure actuated cellular structures. This model takes into account hinge eccentricities as well as…

Quantitative Methods · Quantitative Biology 2017-07-31 Markus Pagitz , Remco I. Leine

The paper extends the formulation of a 2D geometrically exact beam element proposed in our previous paper [1] to curved elastic beams. This formulation is based on equilibrium equations in their integrated form, combined with the kinematic…

Computational Engineering, Finance, and Science · Computer Science 2022-10-06 Martin Horák , Emma La Malfa Ribolla , Milan Jirásek

This work presents a novel formulation and numerical strategy for the simulation of geometrically nonlinear structures. First, a non-canonical Hamiltonian (Poisson) formulation is introduced by including the dynamics of the stress tensor.…

Numerical Analysis · Mathematics 2025-10-27 Andrea Brugnoli , Denis Matignon , Joseph Morlier

This paper presents causal block-diagram models to represent the equations of motion of multi-body systems in a very compact and simple closed form. Both the forward dynamics (from the forces and torques imposed at the various…

Systems and Control · Electrical Eng. & Systems 2025-05-07 Daniel Alazard , Francesco Sanfedino , Ervan Kassarian

Modelling two-dimensional chiral materials is a challenging problem in continuum mechanics because three-dimensional theories reduced to isotropic two-dimensional problems become non-chiral. Various approaches have been suggested to…

Mathematical Physics · Physics 2018-05-01 Sebastian Bahamonde , Christian G. Boehmer , Patrizio Neff

The discrete modeling of a large class of mechanical structures can be based on a stick-and-spring concept. We here present a stick-and-spring theory with potential application to the statics and the dynamics of such nanostructures as…

Materials Science · Physics 2013-07-16 Antonino Favata , Andrea Micheletti , Paolo Podio-Guidugli

Discussed is mechanics of objects with internal degrees of freedom in generally non-Euclidean spaces. Geometric peculiarities of the model are investigated detailly. Discussed are also possible mechanical applications, e.g., in dynamics of…

Mathematical Physics · Physics 2009-12-24 J. J. Sławianowski , B. Gołubowska

We present a model for the dynamics of elastic or poroelastic bodies with monopolar repulsive long-range (electrostatic) interactions at large strains. Our model respects (only) locally the non-self-interpenetration condition but can cope…

Analysis of PDEs · Mathematics 2019-08-07 Tomas Roubicek , Giuseppe Tomassetti

The large deflections of cantilevered beams and plates are modeled and discussed. Traditional nonlinear elastic models (e.g., that of von Karman) employ elastic restoring forces based on the effect of stretching on bending, and these are…

Analysis of PDEs · Mathematics 2022-05-25 Maria Deliyianni , Kevin McHugh , Justin T. Webster , Earl Dowell

Cutting-edge smart materials are transforming the domains of soft robotics, actuators, and sensors by harnessing diverse non-mechanical stimuli, such as electric and magnetic fields. Accurately modelling their physical behaviour…

Classical Physics · Physics 2024-07-09 Abhishek Ghosh , Andrew McBride , Zhaowei Liu , Luca Heltai , Paul Steinmann , Prashant Saxena

From the principle that there is no absolute description of a physical state, we advance the approach according to which one should be able to describe the physics from the perspective of a quantum particle. The kinematics seen from this…

Quantum Physics · Physics 2012-11-02 R. M. Angelo , A. D. Ribeiro

We are concerned with underlying connections between fluids, elasticity, isometric embedding of Riemannian manifolds, and the existence of wrinkled solutions of the associated nonlinear partial differential equations. In this paper, we…

Analysis of PDEs · Mathematics 2017-08-29 Amit Acharya , Gui-Qiang Chen , Siran Li , Marshall Slemrod , Dehua Wang

We employ a port-Hamiltonian approach to model nonlinear rigid multibody systems subject to both position and velocity constraints. Our formulation accommodates Cartesian and redundant coordinates, respectively, and captures kinematic as…

Dynamical Systems · Mathematics 2025-04-25 Thomas Berger , René Hochdahl , Timo Reis , Robert Seifried

We propose a variational formulation for the nonequilibrium thermodynamics of discrete open systems, i.e., discrete systems which can exchange mass and heat with the exterior. Our approach is based on a general variational formulation for…

Mathematical Physics · Physics 2018-12-05 François Gay-Balmaz , Hiroaki Yoshimura

Recently there has been interest in studying a new class of elastic materials, which is described by implicit constitutive relations. Under some basic assumption for elasticity constants, the system of governing equations of motion for this…

Analysis of PDEs · Mathematics 2017-04-05 Shou-Jun Huang , K. R. Rajagopal , Hui-Hui Dai

This paper proposes a low order geometrically exact flexible beam formulation based on the utilisation of generic beam shape functions to approximate distributed kinematic properties of the deformed structure. The proposed nonlinear beam…

Classical Physics · Physics 2018-09-05 C. Howcroft , R. G. Cook , S. A. Neild , M. H. Lowenberg , J. E. Cooper , E. B. Coetzee

Budiansky's nonlinear shell theory is particularized to a 2D setting, and thereupon generalized to a fully nonlinear, statically and kinematically exact, theory of strain-gradient elasticity of beams. The governing equations are displayed…

Classical Physics · Physics 2022-09-27 Marcelo Epstein , Mohammadjavad Javad

Global existence for the nonisentropic compressible Euler equations with vacuum boundary for all adiabatic constants $\gamma > 1$ is shown through perturbations around a rich class of background nonisentropic affine motions. The notable…

Analysis of PDEs · Mathematics 2021-06-03 Calum Rickard , Mahir Hadzic , Juhi Jang

This work presents a general unified theory for coupled nonlinear elastic and inelastic deformations of curved thin shells. The coupling is based on a multiplicative decomposition of the surface deformation gradient. The kinematics of this…

Classical Physics · Physics 2019-09-12 Roger A. Sauer , Reza Ghaffari , Anurag Gupta