4.7 Article

A structure-preserving integrator for incompressible finite elastodynamics based on a grad-div stabilized mixed formulation with particular emphasis on stretch-based material models

相关参考文献

注意:仅列出部分参考文献,下载原文获取全部文献信息。
Article Engineering, Multidisciplinary

A thermodynamically consistent time integration scheme for non-linear thermo-electro-mechanics

M. Franke et al.

Summary: This paper aims to design a new Energy-Momentum (EM) preserving time integration scheme for thermo-electro-elastic processes undergoing large deformations. By utilizing polyconvexity and a new tensor cross product algebra, the scheme is able to derive comparatively simple formulas for discrete derivatives, overcoming the complex derivatives in classical EM schemes. The newly proposed scheme inherits the advantages of previous EM schemes while extending to the more generic case of nonlinear thermo-electro-mechanics, with a focus on robustness and numerical stability properties.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2022)

Article Mechanics

A conserving formulation of a simple shear- and torsion-free beam for multibody applications

Juan C. Garcia Orden

Summary: This paper proposes an energy-conserving and symmetry-preserving extension of a beam model, the configuration of which is described by a rotation-free parameterization. The resulting time-integration scheme produces an approximated solution where total mechanical discrete energy and symmetries are exactly preserved.

MULTIBODY SYSTEM DYNAMICS (2021)

Article Engineering, Multidisciplinary

A continuum and computational framework for viscoelastodynamics: I. Finite deformation linear models

Ju Liu et al.

Summary: This work presents a new viscohyperelastic modeling framework based on fundamental thermomechanical principles, discussing the evolution equations of internal state variables and a finite deformation linear model. By revisiting the classical polymer chain model and proposing a modified version, the importance of vanishing non-equilibrium stress in the equilibrium limit is emphasized.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2021)

Review Computer Science, Interdisciplinary Applications

Hybrid-Mixed Low-Order Finite Elements for Geometrically Exact Shell Models: Overview and Comparison

Marko Lavrencic et al.

Summary: In this study, fifteen mixed and mixed-hybrid nonlinear shell finite element formulations with 4 nodes were critically reviewed and compared. Through extensive numerical experiments, it was found that combining different concepts can generate formulations with excellent performance.

ARCHIVES OF COMPUTATIONAL METHODS IN ENGINEERING (2021)

Article Engineering, Multidisciplinary

Energy-decaying and momentum-conserving schemes for transient simulations with mixed finite elements

Marko Lavrencic et al.

Summary: The paper presents mixed variational formulations for structural dynamics, which can be used to derive energy-decaying and momentum-conserving time-stepping schemes for transient simulations. These schemes are applied to recently proposed mixed-hybrid shell finite elements, extending their superior properties for long-term transient simulations. Numerical examples show that the underlying structure of shell motion is preserved even for very large time steps.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2021)

Article Engineering, Multidisciplinary

Multipatch Isogeometric Analysis for electrophysiology: Simulation in a human heart

Michele Bucelli et al.

Summary: In this study, multipatch NURBS-based Isogeometric Analysis was applied for the space discretization of the Monodomain model in cardiac electrophysiology. IGA, a technique for solving PDEs, was utilized to accurately represent the computational geometry using high-order basis functions. The use of multiple patches allowed for increased flexibility in the design of the computational domain, particularly in complex bioengineering applications.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2021)

Article Engineering, Multidisciplinary

A new energy-momentum time integration scheme for non-linear thermo-mechanics

R. Ortigosa et al.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2020)

Article Engineering, Multidisciplinary

Weak Cn coupling for multipatch isogeometric analysis in solid mechanics

M. Dittmann et al.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING (2019)

Article Computer Science, Interdisciplinary Applications

A robust and efficient iterative method for hyper-elastodynamics with nested block preconditioning

Ju Liu et al.

JOURNAL OF COMPUTATIONAL PHYSICS (2019)

Article Engineering, Multidisciplinary

An energy-stable mixed formulation for isogeometric analysis of incompressible hyperelastodynamics

Ju Liu et al.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING (2019)

Article Engineering, Multidisciplinary

Structure-preserving space-time discretization of a mixed formulation for quasi-incompressible large strain elasticity in principal stretches

Alexander Janz et al.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING (2019)

Article Engineering, Multidisciplinary

Variational-based locking-free energy-momentum schemes of higher-order for thermo-viscoelastic fiber-reinforced continua

Michael Gross et al.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2019)

Article Engineering, Multidisciplinary

A unified continuum and variational multiscale formulation for fluids, solids, and fluid-structure interaction

Ju Liu et al.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2018)

Article Engineering, Multidisciplinary

An energy-momentum time integration scheme based on a convex multi-variable framework for non-linear electro-elastodynamics

R. Ortigosa et al.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2018)

Article Engineering, Multidisciplinary

A mixed variational framework for the design of energy-momentum schemes inspired by the structure of polyconvex stored energy functions

Peter Betsch et al.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2018)

Article Engineering, Multidisciplinary

An energy momentum consistent integration scheme using a polyconvexity-based framework for nonlinear thermo-elastodynamics

M. Franke et al.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING (2018)

Article Mathematics, Interdisciplinary Applications

On the stability analysis of hyperelastic boundary value problems using three- and two-field mixed finite element formulations

Joerg Schroeder et al.

COMPUTATIONAL MECHANICS (2017)

Article Mathematics, Applied

An energy-entropy-consistent time stepping scheme for nonlinear thermo-viscoelastic continua

M. Krueger et al.

ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK (2016)

Article Engineering, Multidisciplinary

Mixed finite element methods with convection stabilization for the large eddy simulation of incompressible turbulent flows

Oriol Colomes et al.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2016)

Article Engineering, Multidisciplinary

An energy-momentum consistent method for transient simulations with mixed finite elements developed in the framework of geometrically exact shells

Peter Betsch et al.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING (2016)

Article Engineering, Multidisciplinary

A computational framework for polyconvex large strain elasticity

Javier Bonet et al.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2015)

Article Engineering, Multidisciplinary

A first order hyperbolic framework for large strain computational solid dynamics. Part I: Total Lagrangian isothermal elasticity

Javier Bonet et al.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2015)

Article Mathematics, Interdisciplinary Applications

Energy-consistent time integration for nonlinear viscoelasticity

Sergio Conde Martin et al.

COMPUTATIONAL MECHANICS (2014)

Article Engineering, Multidisciplinary

Error analysis and iterative solvers for Navier-Stokes projection methods with standard and sparse grad-div stabilization

Abigail L. Bowers et al.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2014)

Article Mathematics, Interdisciplinary Applications

Approximation of incompressible large deformation elastic problems: some unresolved issues

Ferdinando Auricchio et al.

COMPUTATIONAL MECHANICS (2013)

Article Engineering, Multidisciplinary

An implicit thermomechanical theory based on a Gibbs potential formulation for describing the response of thermoviscoelastic solids

K. R. Rajagopal et al.

INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE (2013)

Article Mathematics, Applied

ISOGEOMETRIC DIVERGENCE-CONFORMING B-SPLINES FOR THE DARCY-STOKES-BRINKMAN EQUATIONS

John A. Evans et al.

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES (2013)

Article Mathematics, Interdisciplinary Applications

An analysis of the stress formula for energy-momentum methods in nonlinear elastodynamics

Ignacio Romero

COMPUTATIONAL MECHANICS (2012)

Article Engineering, Multidisciplinary

Subdivision-stabilised immersed b-spline finite elements for moving boundary flows

T. Rueberg et al.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2012)

Article Engineering, Multidisciplinary

A new mixed finite element based on different approximations of the minors of deformation tensors

Joerg Schroeder et al.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2011)

Article Computer Science, Interdisciplinary Applications

IsoGeometric Analysis: Stable elements for the 2D Stokes equation

A. Buffa et al.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS (2011)

Article Mathematics, Applied

A CONNECTION BETWEEN SCOTT-VOGELIUS AND GRAD-DIV STABILIZED TAYLOR-HOOD FE APPROXIMATIONS OF THE NAVIER-STOKES EQUATIONS

Michael A. Case et al.

SIAM JOURNAL ON NUMERICAL ANALYSIS (2011)

Article Engineering, Multidisciplinary

Numerical studies of finite element variational multiscale methods for turbulent flow simulations

Volker John et al.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2010)

Article Engineering, Multidisciplinary

The importance of the exact satisfaction of the incompressibility constraint in nonlinear elasticity: mixed FEMs versus NURBS-based approximations

F. Auricchio et al.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2010)

Article Engineering, Multidisciplinary

Robustness of isogeometric structural discretizations under severe mesh distortion

S. Lipton et al.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2010)

Article Engineering, Multidisciplinary

Energy-momentum consistent finite element discretization of dynamic finite viscoelasticity

M. Gross et al.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING (2010)

Article Engineering, Multidisciplinary

Grad-div stabilization and subgrid pressure models for the incompressible Navier-Stokes equations

Maxim Olshanskii et al.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2009)

Article Engineering, Multidisciplinary

Thermodynamically consistent time-stepping algorithms for non-linear thermomechanical systems

Ignacio Romero

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING (2009)

Article Engineering, Multidisciplinary

Galerkin-based mechanical integrators for finite elastodynamics formulated in principal stretches - Pitfalls and remedies

Rouven Mohr et al.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2008)

Article Engineering, Multidisciplinary

A robust algorithm for finding the eigenvalues and eigenvectors of 3 x 3 symmetric matrices

W. M. Scherzinger et al.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2008)

Article Engineering, Multidisciplinary

On the enforcing energy conservation of time finite elements for discrete elasto-dynamics problems

Q. V. Bui

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING (2007)

Article Engineering, Multidisciplinary

Volume-preserving energy-momentum schemes for isochoric multiplicative plasticity

F. Armero et al.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2007)

Article Mechanics

Three-dimensional nonlinear dynamics of slender structures: Cosserat rod element approach

DQ Cao et al.

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES (2006)

Article Engineering, Multidisciplinary

Energy-controlling time integration methods for nonlinear elastodynamics and low-velocity impact

Patrice Hauret et al.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2006)

Article Engineering, Multidisciplinary

Energy-dissipative momentum-conserving time-stepping algorithms for finite strain multiplicative plasticity

F. Armero

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2006)

Article Engineering, Multidisciplinary

Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement

TJR Hughes et al.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2005)

Article Engineering, Multidisciplinary

A stability study of some mixed finite elements for large deformation elasticity problems

F Auricchio et al.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2005)

Article Engineering, Multidisciplinary

Variational time integrators

A Lew et al.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING (2004)

Article Engineering, Multidisciplinary

A low order Galerkin finite element method for the Navier-Stokes equations of steady incompressible flow: a stabilization issue and iterative methods

MA Olshanskii

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2002)

Article Engineering, Multidisciplinary

Energy consistent algorithms for dynamic finite deformation plasticity

XN Meng et al.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2002)

Article Engineering, Multidisciplinary

Conservation properties of a time FE method - part II: Time-stepping schemes for non-linear elastodynamics

P Betsch et al.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING (2001)

Article Engineering, Multidisciplinary

Energy and momentum conserving elastodynamics of a non-linear brick-type mixed finite shell element

C Miehe et al.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING (2001)

Article Engineering, Multidisciplinary

A new solution procedure for application of energy-conserving algorithms to general constitutive models in nonlinear elastodynamics

TA Laursen et al.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2001)

Article Engineering, Multidisciplinary

On the formulation of high-frequency dissipative time-stepping algorithms for nonlinear dynamics. Part II: second-order methods

F Armero et al.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2001)

Article Engineering, Multidisciplinary

An extension of Key's principle to nonlinear elasticity

MHBM Shariff et al.

JOURNAL OF ENGINEERING MATHEMATICS (2000)

Article Engineering, Multidisciplinary

Dynamic analysis of rigid and deformable multibody systems with penalty methods and energy-momentum schemes

JM Goicolea et al.

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2000)

Article Engineering, Multidisciplinary

Exact energy and momentum conserving algorithms for general models in nonlinear elasticity

O Gonzalez

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING (2000)