Time-Dependent Response of Incompressible Membranes Based on Quasi-Linear Viscoelasticity Theory

Dadgar‐Rad, Farzam; Firouzi, Nasser

doi:10.1142/s1758825121500368

Cited by 6 publications

(2 citation statements)

References 60 publications

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“…Hernandez et al (2020) study viscoelastic behavior of Reissner-Mindlin shells. Dadgar-Rad and Firouzi (2021) consider incompressible membranes and quasi-linear viscoelasticity. Following the work on surface elasticity by Steinmann (2009, 2010), Dortdivanlioglu and Javili (2021) develop a theory for nonlinear surface viscoelasticity at finite strains by accounting for strain-dependent boundary stresses.…”

Section: Introductionmentioning

confidence: 99%

An isogeometric finite element formulation for surface and shell viscoelasticity based on a multiplicative surface deformation split

Paul,

Sauer

2022

Preprint

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This work presents a numerical formulation to model isotropic viscoelastic material behavior for membranes and thin shells. The surface and the shell theory are formulated within a curvilinear coordinate system, which allows the representation of general surfaces and deformations. The kinematics follow from Kirchhoff-Love theory and the discretization makes use of isogeometric shape functions. A multiplicative split of the surface deformation gradient is employed, such that an intermediate surface configuration is introduced. The surface metric and curvature of this intermediate configuration follow from the solution of nonlinear evolution laws -ordinary differential equations (ODEs) -that stem from a generalized viscoelastic solid model. The evolution laws are integrated numerically with the implicit Euler scheme and linearized within the Newton-Raphson scheme of the nonlinear finite element framework. The implementation of surface and bending viscosity is verified with the help of analytical solutions and shows ideal convergence behavior. The chosen numerical examples capture large deformations and typical viscoelasticity behavior, such as creep, relaxation, and strain rate dependence. It is shown that the proposed formulation can also be straightforwardly applied to model boundary viscoelasticity of 3D bodies.

show abstract

Section: Introductionmentioning

confidence: 99%

An isogeometric finite element formulation for surface and shell viscoelasticity based on a multiplicative surface deformation split

Paul,

Sauer

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Hernandez et al 71 study viscoelastic behavior of Reissner-Mindlin shells. Dadgar-Rad and Firouzi 72 consider incompressible membranes and quasi-linear viscoelasticity. Following the work on surface elasticity, 73,74 Dortdivanlioglu and Javili 75 develop a theory for nonlinear surface viscoelasticity at finite strains by accounting for strain-dependent boundary stresses.…”

Section: Introductionmentioning

confidence: 99%

An isogeometric finite element formulation for boundary and shell viscoelasticity based on a multiplicative surface deformation split

Paul

Sauer

2022

Numerical Meth Engineering

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This work presents a numerical formulation to model isotropic viscoelastic material behavior for membranes and thin shells. The surface and the shell theory are formulated within a curvilinear coordinate system, which allows the representation of general surfaces and deformations. The kinematics follow from Kirchhoff-Love theory and the discretization makes use of isogeometric shape functions. A multiplicative split of the surface deformation gradient is employed, such that an intermediate surface configuration is introduced. The surface metric and curvature of this intermediate configuration follow from the solution of nonlinear evolution laws-ordinary differential equations-that stem from a generalized viscoelastic solid model. The evolution laws are integrated numerically with the implicit Euler scheme and linearized within the Newton-Raphson scheme of the nonlinear finite element framework. The implementation of membrane and bending viscosity is verified with the help of analytical solutions and shows ideal convergence behavior. The chosen numerical examples capture large deformations and typical viscoelasticity behavior, such as creep, relaxation, and strain rate dependence. It is also shown that the proposed formulation can be straightforwardly applied to model boundary viscoelasticity of 3D bodies.

show abstract

Large deformation analysis of two-dimensional visco-hyperelastic beams and frames

Dadgar‐Rad

Firouzi

2021

Arch Appl Mech

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Time-Dependent Response of Incompressible Membranes Based on Quasi-Linear Viscoelasticity Theory

Cited by 6 publications

References 60 publications

An isogeometric finite element formulation for surface and shell viscoelasticity based on a multiplicative surface deformation split

An isogeometric finite element formulation for surface and shell viscoelasticity based on a multiplicative surface deformation split

An isogeometric finite element formulation for boundary and shell viscoelasticity based on a multiplicative surface deformation split

Large deformation analysis of two-dimensional visco-hyperelastic beams and frames

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