Isogeometric Kirchhoff–Love shell formulations for general hyperelastic materials

Kiendl, Josef; Hsu, Ming‐Chen; Wu, Mike; Reali, Alessandro

doi:10.1016/j.cma.2015.03.010

Cited by 295 publications

(199 citation statements)

References 67 publications

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“…In the past ten years, IGA has gained enormous interest in nearly all fields of computational mechanics and, in particular, it has led to many new developments in shell analysis. The smoothness of the basis functions allows for efficient implementations of rotation-free KirchhoffLove shell models [27][28][29][30][31][32][33], but there are also several developments in the context of ReissnerMindlin shells [34][35][36][37] and solid-shells [38][39][40][41][42], as well as novel approaches such as blended shells [43], hierarchic shells [44], and rotation-free shear deformable shells [45]. Furthermore, IGA was applied successfully to phase-field modeling of fracture.…”

Section: Introductionmentioning

confidence: 99%

Phase-field description of brittle fracture in plates and shells

Kiendl

Ambati

Lorenzis

et al. 2016

Computer Methods in Applied Mechanics and Engineering

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141

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We present an approach for phase-field modeling of fracture in thin structures like plates and shells, where the kinematics is defined by midsurface variables. Accordingly, the phase field is defined as a two-dimensional field on the midsurface of the structure. In this work, we consider brittle fracture and a Kirchhoff-Love shell model for structural analysis. We show that, for a correct description of fracture, the variation of strains through the shell thickness has to be considered and the split into tensile and compressive elastic energy components, needed to prevent cracking in compression, has to be carried out at various points through the thickness, which prohibits the typical separation of the elastic energy into membrane and bending terms. For numerical analysis, we employ isogeometric discretizations and a rotation-free Kirchhoff-Love shell formulation. In several numerical examples we show the applicability of the approach and detailed comparisons with 3D solid simulations confirm its accuracy and efficiency.

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Section: Introductionmentioning

confidence: 99%

Phase-field description of brittle fracture in plates and shells

Kiendl

Ambati

Lorenzis

et al. 2016

Computer Methods in Applied Mechanics and Engineering

Self Cite

141

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“…It has the advantage of not requiring rotational degrees of freedom. Extension to general hyperelastic material can be found in [4]. The formulation has been successfully used in computation of a good number of challenging problems, including wind-turbine fluid-structure interaction (FSI) [3,[5][6][7][8][9], bioinspired flapping-wing aerodynamics [10], bioprosthetic heart valves [11][12][13][14][15], fatigue and damage [16][17][18][19][20][21], and design [22,23].…”

Section: Introductionmentioning

confidence: 99%

“…In this article, we start with the formulation from [4] and derive, based on the Kirchhoff-Love shell theory and isogeometric discretization, a hyperelastic shell formulation that takes into account the out-of-plane deformation mapping. Accounting for that mapping affects the curvature term.…”

Section: Introductionmentioning

confidence: 99%

Isogeometric hyperelastic shell analysis with out-of-plane deformation mapping

2018

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We derive a hyperelastic shell formulation based on the Kirchhoff-Love shell theory and isogeometric discretization, where we take into account the out-of-plane deformation mapping. Accounting for that mapping affects the curvature term. It also affects the accuracy in calculating the deformed-configuration out-of-plane position, and consequently the nonlinear response of the material. In fluid-structure interaction analysis, when the fluid is inside a shell structure, the shell midsurface is what it would know. We also propose, as an alternative, shifting the "midsurface" location in the shell analysis to the inner surface, which is the surface that the fluid should really see. Furthermore, in performing the integrations over the undeformed configuration, we take into account the curvature effects, and consequently integration volume does not change as we shift the "midsurface" location. We present test computations with pressurized cylindrical and spherical shells, with Neo-Hookean and Fung's models, for the compressible-and incompressible-material cases, and for two different locations of the "midsurface." We also present test computation with a pressurized Y-shaped tube, intended to be a simplified artery model and serving as an example of cases with somewhat more complex geometry.Keywords Kirchhoff-Love shell theory · Isogeometric discretization · Hyperelastic material · Out-of-plane deformation mapping · Neo-Hookean material model · Fung's material model · Artery

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“…On the isogeometric side, a variety of advanced formulations for isogeometric shell analysis on spline surfaces have been developed, e.g., based on solid shell theories [14,15], Kirchhoff-Love [16] and ReissnerMindlin theories [17][18][19], and hierarchic combinations thereof [20]. Isogeometric shells have been successfully applied for large-deformation analysis [21], in conjunction with various nonlinear material models [22,23], and in contact and fluid-structure interaction problems [24][25][26][27]. On the embedded domain side, the importance of geometrically faithful quadrature of trimmed elements and corresponding techniques have been discussed in a series of recent papers [28,27,[29][30][31][32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

A parameter-free variational coupling approach for trimmed isogeometric thin shells

2016

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The non-symmetric variant of Nitsche's method was recently applied successfully for variationally enforcing boundary and interface conditions in non-boundary-fitted discretizations. In contrast to its symmetric variant, it does not require stabilization terms and therefore does not depend on the appropriate estimation of stabilization parameters. In this paper, we further consolidate the non-symmetric Nitsche approach by establishing its application in isogeometric thin shell analysis, where variational coupling techniques are of particular interest for enforcing interface conditions along trimming curves. To this end, we extend its variational formulation within Kirchhoff-Love shell theory, combine it with the finite cell method, and apply the resulting framework to a range of representative shell problems based on trimmed NURBS surfaces. We demonstrate that the non-symmetric variant applied in this context is stable and can lead to the same accuracy in terms of displacements and stresses as its symmetric counterpart. Based on our numerical evidence, the non-symmetric Nitsche method is a viable parameter-free alternative to the symmetric variant in elastostatic shell analysis.

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Isogeometric Kirchhoff–Love shell formulations for general hyperelastic materials

Cited by 295 publications

References 67 publications

Phase-field description of brittle fracture in plates and shells

Phase-field description of brittle fracture in plates and shells

Isogeometric hyperelastic shell analysis with out-of-plane deformation mapping

A parameter-free variational coupling approach for trimmed isogeometric thin shells

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