A framework for efficient isogeometric computations of phase-field brittle fracture in multipatch shell structures

Proserpio, Davide; Ambati, Marreddy; Lorenzis, Laura De; Kiendl, Josef

doi:10.1016/j.cma.2020.113363

Cited by 34 publications

(13 citation statements)

References 66 publications

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“…36,37 Taken together, the phase-field approach to fracture applied to shells has been subject of extensive research in the recent years, focusing mainly on the extension to specific problems, namely ductile fracture, 38 finite strains, 39 functionally graded materials, 40 thick shells, 41 dynamic problems 42,43 as well as the isogeometric implementation with adaptive refinement 44 or multipatch coupling techniques. 45 However, the application of the phase-field approach to model cracks along the thickness direction of shells has been given very limited attention up until now. To the author's best knowledge, except two contributions, 46,47 all of the aforementioned models consider the phase-field to be constant along the thickness direction of shells argued for with their slenderness.…”

Section: Introductionmentioning

confidence: 99%

“…Further approaches to deal with the thinness of the structure in the context of phase‐field modeling exist, such as a formulation with a mixed interpolation of tensorial components (MITC)4+ RM degenerated shell 35 and a solid‐shell approach 36,37 . Taken together, the phase‐field approach to fracture applied to shells has been subject of extensive research in the recent years, focusing mainly on the extension to specific problems, namely ductile fracture, 38 finite strains, 39 functionally graded materials, 40 thick shells, 41 dynamic problems 42,43 as well as the isogeometric implementation with adaptive refinement 44 or multipatch coupling techniques 45 …”

Section: Introductionmentioning

confidence: 99%

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Phase‐field modeling of brittle fracture along the thickness direction of plates and shells

Ambati

Heinzmann

Seiler

et al. 2022

Numerical Meth Engineering

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The prediction of fracture in thin-walled structures is decisive for a wide range of applications. Modeling methods such as the phase-field method usually consider cracks to be constant over the thickness which, especially in load cases involving bending, is an imperfect approximation. In this contribution, fracture phenomena along the thickness direction of structural elements (plates or shells) are addressed with a phase-field modeling approach. For this purpose, a new, so called "mixed-dimensional" model is introduced, which combines structural elements representing the displacement field in the two-dimensional shell midsurface with continuum elements describing a crack phase-field in the three-dimensional solid space. The proposed model uses two separate finite element discretizations, where the transfer of variables between the coupled twoand three-dimensional fields is performed at the integration points which in turn need to have corresponding geometric locations. The governing equations of the proposed mixed-dimensional model are deduced in a consistent manner from a total energy functional with them also being compared to existing standard models. The resulting model has the advantage of a reduced computational effort due to the structural elements while still being able to accurately model arbitrary through-thickness crack evolutions as well as partly along the thickness broken shells due to the continuum elements. Amongst others, the higher accuracy as well as the numerical efficiency of the proposed model are tested and validated by comparing simulation results of the new model to those obtained by standard models using numerous representative examples.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Phase‐field modeling of brittle fracture along the thickness direction of plates and shells

Ambati

Heinzmann

Seiler

et al. 2022

Numerical Meth Engineering

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“…Isogeometric analysis has been used within several applications for shell structures, e.g. it has been applied in fracture (Ambati and De Lorenzis, 2016;Kiendl et al, 2016;Paul et al, 2020b;Proserpio et al, 2020):, shape and topology optimization (Nagy et al, 2013;Kiendl et al, 2014;Hirschler et al, 2019), elasto-plasticity (Ambati et al, 2018;Huynh et al, 2020), composite shells (Thai et al, 2012;Deng et al, 2015;Roohbakhshan and Sauer, 2016;Schulte et al, 2020), inverse analysis (Vu-Bac et al, 2018Borzeszkowski et al, 2022), Cahn-Hilliard phase separations (Valizadeh and Rabczuk, 2019;Zimmermann et al, 2019), biological shells (Tepole et al, 2015;Roohbakhshan and Sauer, 2017), and surfactants (Roohbakhshan and Sauer, 2019).…”

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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“…Thus, isogeometric KL shells [39][40][41][42][43][44][45][46][47] have gained popularity in the simulation and analysis community due to their computationally efficient rotation-free formulation and model simplification into the midsurface representation. The formulations have been previously demonstrated as an effective solution for the analysis of complex problems [48][49][50][51][52][53][54][55][56][57][58][59][60][61], including wind turbine blades [62][63][64][65][66][67][68][69][70][71][72] and heart valves [73][74][75][76][77][78][79][80][81]. While computational efficiency is an important factor in numerical analysis, KL shells have limited accuracy in predicting the transverse stress and strain states.…”

Section: Introductionmentioning

confidence: 99%

Blended isogeometric Kirchhoff–Love and continuum shells

Liu

Johnson

Rajanna

et al. 2021

Computer Methods in Applied Mechanics and Engineering

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The computational modeling of thin-walled structures based on isogeometric analysis (IGA), non-uniform rational B-splines (NURBS), and Kirchhoff-Love (KL) shell formulations has attracted significant research attention in recent years. While these methods offer numerous benefits over the traditional finite element approach, including exact representation of the geometry, naturally satisfied high-order continuity within each NURBS patch, and computationally efficient rotation-free formulations, they also present a number of challenges in modeling real-world engineering structures of considerable complexity. Specifically, these NURBS-based engineering models are usually comprised of numerous patches, with discontinuous derivatives, nonconforming discretizations, and non-watertight connections at their interfaces. Moreover, the analysis of such structures often requires the full stress and strain tensors (i.e., including the transverse normal and shear components) for subsequent failure analysis and remaining life prediction. Despite the efficiency provided by the KL shell, the formulation cannot accurately predict the response in the transverse directions due to its kinematic assumptions. In this work, a penalty-based formulation for the blended coupling of KL and continuum shells is presented. The proposed approach embraces both the computational efficiency of KL shells and the availability of the full-scale stress/strain tensors of continuum shells where needed by modeling critical structural components using continuum shells and other components using KL shells. The proposed method enforces the displacement and rotational continuities in a variational manner and is applicable to non-conforming and non-smooth interfaces. The efficacy of the developed method is demonstrated through a number of benchmark studies with a variety of analysis configurations, including linear and nonlinear analyses, matching and non-matching discretizations, and isotropic and composite materials. Finally, an aircraft horizontal stabilizer is considered to demonstrate the applicability of the proposed blended shells to real-world engineering structures of significant complexity. c

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A framework for efficient isogeometric computations of phase-field brittle fracture in multipatch shell structures

Cited by 34 publications

References 66 publications

Phase‐field modeling of brittle fracture along the thickness direction of plates and shells

Phase‐field modeling of brittle fracture along the thickness direction of plates and shells

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

Blended isogeometric Kirchhoff–Love and continuum shells

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