Modelling of thin viscoelastic shell structures under Reissner–Mindlin kinematic assumption

Hernández, Erwin; Naranjo, César A.; Vellojin, Jesus

doi:10.1016/j.apm.2019.10.031

Cited by 11 publications

(5 citation statements)

References 26 publications

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“…Liu et al (2017) consider surface viscoelasticity coupled with three-dimensional viscoelastic bulks to model cells and cell aggregates. Hernandez et al (2020) study viscoelastic behavior of Reissner-Mindlin shells. Dadgar-Rad and Firouzi (2021) consider incompressible membranes and quasi-linear viscoelasticity.…”

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.

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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

“…69 Liu et al 70 consider surface viscoelasticity coupled with three-dimensional viscoelastic bulks to model cells and cell aggregates. Hernandez et al 71 study viscoelastic behavior of Reissner-Mindlin shells. Dadgar-Rad and Firouzi 72 consider incompressible membranes and quasi-linear viscoelasticity.…”

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.

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“…Also, Song et al 21 conducted vibration and damping studies for viscoelastic shells subjected to elastic boundaries. By assuming Reissner–Mindlin kinematics, Hernandez et al 22 modelled thin viscoelastic shells efficiently. The nonlinear analysis of viscoelastic sandwich shells was performed by Kordkheili and Khorasani 23 under the framework of the FE method.…”

Section: Introductionmentioning

confidence: 99%

Effect of carbon nanotube-reinforced magneto-electro-elastic facings on the pyrocoupled nonlinear deflection of viscoelastic sandwich skew plates in thermal environment

Mahesh

2021

Proceedings of the Institution of Mechanical Engineers, Part L:

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This work presents a finite-element-based numerical formulation to evaluate the nonlinear deflections of magneto-electro-elastic sandwich skew plates with a viscoelastic core and functionally graded carbon nanotube-reinforced magneto-electro-elastic face sheets. Meanwhile, the proposed formulation accommodates the geometrical skewness as well. The magneto-electro-elastic sandwich skew plate is operated in the thermal environment and subjected to various multiphysics loads, including electric and magnetic loads. The viscoelastic core is modelled via the complex modulus approach. Two different forms of viscoelastic cores, such as Dyad 606 and EC 2216, are considered in this study. Also, different thickness configurations of core and facing arrangements are taken into account. The plate kinematics is presumed through higher-order shear deformation theory, and von Karman's nonlinear strain displacement relations are incorporated. The global equations of motion are arrived at through the total potential energy principle and solved via the direct iterative method. Special attention is paid to assessing the influence of pyroeffects, coupling fields and electromagnetic boundary conditions on the nonlinear deflections of magneto-electro-elastic sandwich plates working in the thermal environment and subjected to electromagnetic loads, which is the first of its kind. Also, parametric studies dealing with the skew angles, carbon nanotube distributions and volume fractions, thickness ratio, and aspect ratio have been discussed. The results of this work are believed to be unique and serve as a guide for the design engineers towards developing sophisticated smart structures for various engineering applications.

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Modelling of thin viscoelastic shell structures under Reissner–Mindlin kinematic assumption

Cited by 11 publications

References 26 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

Effect of carbon nanotube-reinforced magneto-electro-elastic facings on the pyrocoupled nonlinear deflection of viscoelastic sandwich skew plates in thermal environment

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