Isogeometric continuity constraints for multi-patch shells governed by fourth-order deformation and phase field models

Paul, Karsten; Zimmermann, Christopher; Duong, Thang X.; Sauer, Roger A.

doi:10.1016/j.cma.2020.113219

Cited by 20 publications

(12 citation statements)

References 78 publications

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“…13a. A detailed derivation for the enforcement of patch constraints is provided in Paul et al (2020a). Here, the Lagrange multiplier method with element-wise constant interpolation is employed to enforce the constraint…”

Section: Inflated Spherical Shellmentioning

confidence: 99%

“…For complex engineering problems, single patches are often not sufficient to represent shell geometries, such that multi-patch descriptions are required. The continuity of such discretizations is not preserved at patch interfaces and needs to be restored, see Paul et al (2020a) for a recent review on patch enforcement techniques in isogeometric analysis. Isogeometric analysis has been used within several applications for shell structures, e.g.…”

Section: Introductionmentioning

confidence: 99%

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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: Inflated Spherical Shellmentioning

confidence: 99%

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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“…The work of Kiendl et al 23 is the first combining IGA with rotation‐free shells. Since then, rotation‐free IGA shells have been steadily advanced, for example to PHT‐splines, 24 anisotropic materials, 25 damage, 26 biological materials, 27 fracture, 28 liquid shells, 29 elasto‐plasticity, 30 phase separation, 31 thermo‐mechanical coupling, 32 multi‐patch constraints (e.g., see the recent review in Paul et al 33 ), and reduced quadrature 34 . Balobanov et al 35 have presented a general strain gradient theory and its corresponding isogeometric finite element formulation for Kirchhoff‐Love shells.…”

Section: Introductionmentioning

confidence: 99%

A general isogeometric finite element formulation for rotation‐free shells with in‐plane bending of embedded fibers

Duong

Itskov

Sauer

2022

Numerical Meth Engineering

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This article presents a general, nonlinear isogeometric finite element formulation for rotation‐free shells with embedded fibers that captures anisotropy in stretching, shearing, twisting, and bending—both in‐plane and out‐of‐plane. These capabilities allow for the simulation of large sheets of heterogeneous and fibrous materials either with or without matrix, such as textiles, composites, and pantographic structures. The work is a computational extension of our earlier theoretical work that extends existing Kirchhoff‐Love shell theory to incorporate the in‐plane bending resistance of initially straight or curved fibers. The formulation requires only displacement degrees‐of‐freedom to capture all mentioned modes of deformation. To this end, isogeometric shape functions are used in order to satisfy the required C1$$ {C}^1 $$‐continuity for bending across element boundaries. The proposed formulation can admit a wide range of material models, such as surface hyperelasticity that does not require any explicit thickness integration. To deal with possible material instability due to fiber compression, a stabilization scheme is added. Several benchmark examples are used to demonstrate the robustness and accuracy of the proposed computational formulation.

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“…Since then, rotation-free IGA shells have been steadily advanced, for example to PHT-splines (Nguyen-Thanh et al, 2011), anisotropic materials (Nagy et al, 2013), damage (Deng et al, 2015), biological materials (Tepole et al, 2015), fracture (Kiendl et al, 2016), liquid shells , elasto-plasticity (Ambati et al, 2018), phase separation (Zimmermann et al, 2019), thermo-mechanical coupling (Vu-Bac et al, 2019), multi-patch constraints (e.g. see the recent review in Paul et al Paul et al (2020)), and reduced quadrature (Zou et al, 2021). Balobanov et al Balobanov et al (2019) present a general strain gradient theory and its corresponding isogeometric finite element formulation for Kirchhoff-Love shells.…”

Section: Introductionmentioning

confidence: 99%

A general isogeometric finite element formulation for rotation-free shells with embedded fibers and in-plane bending

Duong¹,

Itskov²,

Sauer³

2021

Preprint

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This paper presents a general, nonlinear finite element formulation for rotationfree shells with embedded fibers that captures anisotropy in stretching, shearing, twisting and bending -both in-plane and out-of-plane. These capabilities allow for the simulation of large sheets of heterogeneous and fibrous materials either with or without matrix, such as textiles, composites, and pantographic structures. The work is a computational extension of our earlier theoretical work (Duong et al., 2021) that extends existing Kirchhoff-Love shell theory to incorporate the in-plane bending resistance of initially straight or curved fibers. The formulation requires only displacement degrees-of-freedom to capture all mentioned modes of deformation. To this end, isogeometric shape functions are used in order to satisfy the required C 1 -continuity for bending across element boundaries. The proposed formulation can admit a wide range of material models, such as surface hyperelasticity that does not require any explicit thickness integration. To deal with possible material instability due to fiber compression, a stabilization scheme is added. Several benchmark examples are used to demonstrate the robustness and accuracy of the proposed computational formulation.

show abstract

Isogeometric continuity constraints for multi-patch shells governed by fourth-order deformation and phase field models

Cited by 20 publications

References 78 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

A general isogeometric finite element formulation for rotation‐free shells with in‐plane bending of embedded fibers

A general isogeometric finite element formulation for rotation-free shells with embedded fibers and in-plane bending

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