Fully coupled thermomechanical behaviour of viscoelastic solids treated with finite elements

Holzapfel, Gerhard; Reiter, G.

doi:10.1016/0020-7225(94)00072-r

Cited by 22 publications

(7 citation statements)

References 4 publications

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“…In their work, they extended the recurrence formulation to nonlinear problems. Additional general finite element formulations for viscoelastic continua can be found in [7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear quasi‐static finite element formulations for viscoelastic Euler–Bernoulli and Timoshenko beams

Payette

Reddy

2009

Numer Methods Biomed Eng

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SUMMARYWeak form finite element models for the nonlinear quasi-static bending and extension of initially straight viscoelastic Euler-Bernoulli and Timoshenko beams are developed using the principle of virtual work. The mechanical properties of the beams are considered to be linear viscoelastic. However, large transverse displacements, moderate rotations and small strains are allowed by retaining the von Kármán strain components of the Green-Lagrange strain tensor in the formulation. The fully discretized finite element equations are developed using the trapezoidal rule in conjunction with a two-point recurrence relation. The resulting finite element equations, therefore, necessitate data storage from the previous time step only, and not the entire deformation history. Membrane locking is eliminated from the Euler-Bernoulli formulation through the use of selective reduced Gauss-Legendre quadrature. Membrane and shear locking are both circumvented in the Timoshenko beam finite element by employing a family of high-order Lagrange polynomials. A Newton-Raphson iterative scheme is used to solve the nonlinear finite element equations.

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“…In their work, they extended the recurrence formulation to nonlinear problems. Additional general finite element formulations for viscoelastic continua can be found in [7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear quasi‐static finite element formulations for viscoelastic Euler–Bernoulli and Timoshenko beams

Payette

Reddy

2009

Numer Methods Biomed Eng

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“…• In Holzapfel and Reiter (1995); Holzapfel and Simo (1996a,b); Lion (1997), a thermomechanical coupling model was developed, which takes into account the temperature dependence of the mechanical characteristics and describes the temperature changes resulting from the mechanical dissipation.…”

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confidence: 99%

Statistical approach for a hyper-visco-plastic model for filled rubber: Experimental characterization and numerical modeling

Martinez

Boukamel

Méo³

et al. 2011

European Journal of Mechanics - A/Solids

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This paper presents a campaign of experimental tests performed on a silicone elastomer filled with silica particles. These tests were conducted under controlled temperatures (ranging from -55 o C to +70 o C) and under uniaxial tension and in shearing modes. In these two classes of tests, the specimens were subjected to cyclic loading at various deformation rates and amplitudes and relaxation tests at various levels of deformation. A statistical hyper-visco-elasto-plastic model is then presented, which covers a wide loading frequency spectrum and requires indentifying only a few characteristic parameters. The method used to identify these parameters consists in performing several successive partial identifications with a view to reducing the coupling effects between the parameters. Lastly, comparisons between modeling predictions and the experimental data recorded under harmonic loading, confirm the accuracy of the model in a relatively wide frequency range and a large range of deformations.

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“…Further information regarding thermomechanical analysis of linear viscoelastic solids can be found in the work of Taylor et al (1970). In the study of Holzapfel and Reiter (1995), a fully coupled thermomechanical finite element formulation of viscoelastic solids is derived. Further studies related to viscoelastic solids can be found in the work of Kaliske and Rothert (1997), Park and Kim (1999), Lakes (1998), Wineman (2009) and in many others.…”

Section: Introductionmentioning

confidence: 99%

Fatigue fracture characterization by cyclic material forces in viscoelastic solids at small strain

et al. 2022

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The study at hand introduces a new approach to characterize fatigue crack growth in small strain linear viscoelastic solids by configurational mechanics. In this study, Prony series with n-Maxwell elements are used to describe the viscoelastic behavior. As a starting point in this work, the local balance of energy momentum is derived using the free energy density. Moreover, at cyclic loading, the cyclic free energy substitutes the free energy. Using the cyclic free energy, the balance of cyclic energy momentum is obtained. The newly derived balance law at cyclic loading is appropriate for each cycle. In the finite element framework, nodal material forces and cyclic nodal material forces are obtained using the weak and discretized forms of the balance of energy momentum and cyclic energy momentum, respectively. The crack driving force and the cyclic crack driving force are determined by the nodal material forces and the cyclic nodal material forces, respectively. Finally, numerical examples are shown to illustrate path-independence of the domain integrals using material forces and cyclic material forces. The existence of the balance of energy momentum and cyclic energy momentum are also illustrated by numerical examples.

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Fully coupled thermomechanical behaviour of viscoelastic solids treated with finite elements

Cited by 22 publications

References 4 publications

Nonlinear quasi‐static finite element formulations for viscoelastic Euler–Bernoulli and Timoshenko beams

Nonlinear quasi‐static finite element formulations for viscoelastic Euler–Bernoulli and Timoshenko beams

Statistical approach for a hyper-visco-plastic model for filled rubber: Experimental characterization and numerical modeling

Fatigue fracture characterization by cyclic material forces in viscoelastic solids at small strain

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