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A method is described for embedding a deformable, elastic, membrane within a lattice Boltzmann fluid. The membrane is represented by a set of massless points which advect with the fluid and which impose forces on the fluid which are derived…

Soft Condensed Matter · Physics 2007-05-23 S V Lishchuk , C M Care

Presented is description of kinematics and dynamics of material points with internal degrees of freedom moving in a Riemannian manifold. The models of internal degrees of freedom we concentrate on are based on the orthogonal and affine…

Mathematical Physics · Physics 2010-03-17 J. J. Sławianowski , V. Kovalchuk , B. Gołubowska , A. Martens , E. E. Rożko

A continuum mixture theory is formulated for large deformations, thermal effects, phase interactions, and degradation of soft biologic tissues. Such tissues consist of one or more solid and fluid phases and can demonstrate nonlinear…

Soft Condensed Matter · Physics 2024-09-10 John D. Clayton

This work presents a finite element method for simulating dynamic processes that involve the coupled evolution of dislocation motion and crack propagation. The method numerically solves the Concurrent Atomistic-Continuum (CAC) formulation…

Materials Science · Physics 2025-12-01 Boyang Gu , Adrian Diaz , Yang Li , Youping Chen

The two-scale computational homogenization method is proposed for modelling of locally periodic fluid-saturated media subjected a to large deformation induced by quasistatic loading. The periodic heterogeneities are relevant to the…

Numerical Analysis · Mathematics 2022-02-11 Vladimír Lukeš , Eduard Rohan

There is an ever-growing need for predictive models for the elasto-viscoplastic deformation of solids. Our goal in this paper is to incorporate recently developed out-of-equilibrium statistical concepts into a thermodynamically consistent,…

Materials Science · Physics 2015-06-18 Ken Kamrin , Eran Bouchbinder

In this paper we present a novel approach to the geometric formulation of solid and fluid mechanics within the port-Hamiltonian framework, which extends the standard Hamiltonian formulation to non-conservative and open dynamical systems.…

Mathematical Physics · Physics 2024-04-19 Ramy Rashad , Stefano Stramigioli

The development of a nonlinear structural theory (model) for isotropic linear-elastic finite continua is the main objective of the study. To derive the theory, we used Taylor's multivariable expansion and Bubnov-Galerkin's weak formulation.…

Classical Physics · Physics 2012-07-31 E Hanukah , Bella Goldshtein

This paper is a summary of the theory of discrete embeddings introduced in [5]. A discrete embedding is an algebraic procedure associating a numerical scheme to a given ordinary differential equation. Lagrangian systems possess a…

Numerical Analysis · Mathematics 2016-01-20 Loïc Bourdin , Jacky Cresson , Isabelle Greff , Pierre Inizan

In this work, we illustrate the underlying mathematical structure of mixed-dimensional models arising from the composition of graphs and continuous domains. Such models are becoming popular in applications, in particular, to model the human…

Numerical Analysis · Mathematics 2020-08-27 Erlend Hodneland , Xiaozhe Hu , Jan Martin Nordbotten

We investigate the finite bending and the associated bending instability of an incompressible dielectric slab subject to a combination of applied voltage and axial compression, using nonlinear electro-elasticity theory and its incremental…

Soft Condensed Matter · Physics 2018-10-04 Yipin Su , Bin Wu , Weiqiu Chen , Michel Destrade

Continuum soft robots are mechanical systems entirely made of continuously deformable elements. This design solution aims to bring robots closer to invertebrate animals and soft appendices of vertebrate animals (e.g., an elephant's trunk, a…

Systems and Control · Electrical Eng. & Systems 2023-09-06 Cosimo Della Santina , Christian Duriez , Daniela Rus

By the simple finite element method, we study the symplectic, multisymplectic structures and relevant preserving properties in some semi-linear elliptic boundary value problem in one-dimensional and two-dimensional spaces respectively. We…

High Energy Physics - Theory · Physics 2007-05-23 Han-Ying Guo , Xiao-mei Ji , Yu-Qi Li , Ke Wu

We derive a mixture theory-based mathematical model of the degradation of a poroelastic solid immersed in a fluid bath. The evolution of the solid's mechanical and transport properties are also modeled. The inspiration for the model is the…

Biological Physics · Physics 2019-12-16 Priyanka Patki , Francesco Costanzo

The finite cell method (FCM) belongs to the class of immersed boundary methods, and combines the fictitious domain approach with high-order approximation, adaptive integration and weak imposition of unfitted Dirichlet boundary conditions.…

Numerical Analysis · Mathematics 2018-07-04 Dominik Schillinger , Quanji Cai , Ralf-Peter Mundani , Ernst Rank

In this work we present a novel computational method for embedding arbitrary curved one-dimensional (1D) fibers into three-dimensional (3D) solid volumes, as e.g. in fiber-reinforced materials. The fibers are explicitly modeled with highly…

Computational Engineering, Finance, and Science · Computer Science 2023-08-25 Ivo Steinbrecher , Matthias Mayr , Maximilian J. Grill , Johannes Kremheller , Christoph Meier , Alexander Popp

Finite element plate and shell formulations are ubiquitous in structural analysis for modeling all kinds of slender structures, both for static and dynamic analyses. The latter are particularly challenging as the high order nature of the…

Numerical Analysis · Mathematics 2025-09-03 Giuliano Guarino , Yannis Voet , Pablo Antolin , Annalisa Buffa

In continuum mechanics, the equations of motion for mixtures are derived through the use of Hamilton's extended principle which regards the mixture as a collection of distinct continua. The internal energy is assumed to be a function of…

Classical Physics · Physics 2008-07-29 Henri Gouin

This paper develops and benchmarks an immersed peridynamics method to simulate the deformation, damage, and failure of hyperelastic materials within a fluid-structure interaction framework. The immersed peridynamics method describes an…

Numerical Analysis · Mathematics 2023-10-19 Keon Ho Kim , Amneet P. S. Bhalla , Boyce E. Griffith

We investigate a specific finite element model to study the thermoelastic behavior of an elastic body within the context of nonlinear strain-limiting constitutive relation. As a special subclass of implicit relations, the thermoelastic…

Numerical Analysis · Mathematics 2022-03-02 Hyun C. Yoon , Karthik K. Vasudeva , S. M. Mallikarjunaiah