RI-IGABEM for 2D viscoelastic problems and its application to solid propellant grains

Sun, Deyong; Dai, Rui; Liu, Xiangyang; Zhan, Yunsheng; Dong, C.Y.

doi:10.1016/j.cma.2021.113737

Cited by 8 publications

(2 citation statements)

References 56 publications

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“…The work of Dortdivanlioglu and Javili (2021) uses IGA, while Shafei et al (2021) make use of isogeometric analysis for the analysis of nonlinear vibration of viscoelastic plates. Further, Sun et al (2021) employ the isogeometric boundary element method to investigate viscoelastic materials.…”

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

“…The work of Dortdivanlioglu and Javili 75 uses IGA, while Shafei et al 76 make use of isogeometric analysis for the analysis of nonlinear vibration of viscoelastic plates. Further, Sun et al 77 employ the isogeometric boundary element method to investigate viscoelastic materials.…”

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

View full text Add to dashboard Cite

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

RI-IGABEM based on generalized-αmethod in 2D and 3D elastodynamic problems

Dai

Dong

et al. 2021

Computer Methods in Applied Mechanics and Engineering

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RI-IGABEM for 2D viscoelastic problems and its application to solid propellant grains

Cited by 8 publications

References 56 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

RI-IGABEM based on generalized-αmethod in 2D and 3D elastodynamic problems

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