Cohesive fracture analysis using Powell‐Sabin B‐splines

Verhoosel

2018

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Summary Locally refined T‐splines are used to model discrete crack propagation without a predefined interface. The crack is introduced by meshline insertions in the locally refined T‐mesh, which yields discontinuous basis functions. To implement the method in existing finite element programs, Bézier extraction is used. A detailed description is given as to how the crack path is inserted and how the domain is reparameterized after insertion. The versatility and accuracy of the approach to model discrete crack propagation without the crack path being predefined is demonstrated by two examples, namely, an L‐shaped beam and a single‐edge notched beam. When the crack approaches the physical boundaries, limitations to reparameterization arise, as will be discussed at the hand of a double‐edge notched specimen.

Section: Discussionmentioning

confidence: 99%

Discrete fracture analysis using locally refined T‐splines

Verhoosel

2018

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“…In principle, Equation can be minimised without constraining it by Equation . This is the usual way to perform a state vector transfer in crack propagation analysis . In Figure , we compare the results of minimising Equation with and without constraint, ie, Equation .…”

Section: State Vector Update After Crack Insertionmentioning

confidence: 99%

“…The left bottom edge is fixed. To impose the Dirichlet boundary condition for Powell‐Sabin triangles, the algorithm in our other work has been employed. Test results as well as results from a numerical simulation been reported in the work of Ožbolt et al The material parameters for the concrete are Young's modulus E =32.2 GPa, Poissons ratio ν =0.18, density ρ =2210 kg/m 3 , tensile strength t u =3.12 MPa, and fracture energy

{scriptG}_{c} = 58.56 N/m

.…”

Section: Case Studiesmentioning

confidence: 99%

“…This is the usual way to perform a state vector transfer in crack propagation analysis. 30,38 In Figure 4, we compare the results of minimising Equation (25a) with and without constraint, ie, Equation (25b). Qualitatively, the error contours are similar whether the constraint of Equation (25b) is taken into account or not.…”

Section: State Vector Update After Crack Insertionmentioning

confidence: 99%

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Energy conservation during remeshing in the analysis of dynamic fracture

2019

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Summary The analysis of (dynamic) fracture often requires multiple changes to the discretisation during crack propagation. The state vector from the previous time step must then be transferred to provide the initial values of the next time step. A novel methodology based on a least‐squares fit is proposed for this mapping. The energy balance is taken as a constraint in the mapping, which results in a complete energy preservation. Apart from capturing the physics better, this also has advantages for numerical stability. To further improve the accuracy, Powell‐Sabin B‐splines, which are based on triangles, have been used for the discretisation. Since scriptC1 continuity of the displacement field holds at crack tips for Powell‐Sabin B‐splines, the stresses at and around crack tips are captured much more accurately than when using elements with a standard Lagrangian interpolation, or with NURBS and T‐splines. The versatility and accuracy of the approach to simulate dynamic crack propagation are assessed in two case studies, featuring mode‐I and mixed‐mode crack propagation.

“…Since the early simulations in the 1960s two parallel strands have been pursued, namely, discrete and smeared methods 1 . While in the former approach cracks are treated as geometric discontinuities, leading to topological changes, see, for example, recent work which utilizes spline technologies to model the discontinuity, 2‐5 in the latter approach the discontinuity is modeled by distributing it over a small, but finite width 6 . The early attempts appeared to be deficient in the sense that they caused loss of well‐posedness of the boundary value problem at, or close to structural failure.…”

Section: Introductionmentioning

confidence: 99%

Adaptive isogeometric analysis for phase‐field modeling of anisotropic brittle fracture

2020

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Summary The surface energy a phase‐field approach to brittle fracture in anisotropic materials is also anisotropic and gives rise to second‐order gradients in the phase field entering the energy functional. This necessitates C1 continuity of the basis functions which are used to interpolate the phase field. The basis functions which are employed in isogeometric analysis (IGA), such as nonuniform rational B‐splines and T‐splines naturally possess a higher order continuity and are therefore ideally suited for phase‐field models which are equipped with an anisotropic surface energy. Moreover, the high accuracy of spline discretizations, also relative to their computational demand, significantly reduces the fineness of the required discretization. This holds a fortiori if adaptivity is included. Herein, we present two adaptive refinement schemes in IGA, namely, adaptive local refinement and adaptive hierarchical refinement, for phase‐field simulations of anisotropic brittle fracture. The refinement is carried out using a subdivision operator and exploits the Bézier extraction operator. Illustrative examples are included, which show that the method can simulate highly complex crack patterns such as zigzag crack propagation. An excellent agreement is obtained between the solutions from global refinement and adaptive refinement, with a reasonable reduction of the computational effort when using adaptivity.