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Article available under the terms of the CC-BY-NC-ND licence (https://creativecommons.org/licenses/by-nc-nd/4.0/) eprints@whiterose.ac.uk https://eprints.whiterose.ac.uk/ Reuse Unless indicated otherwise, fulltext items are protected by copyright with all rights reserved. The copyright exception in section 29 of the Copyright, Designs and Patents Act 1988 allows the making of a single copy solely for the purpose of non-commercial research or private study within the limits of fair dealing. The publisher or other rights-holder may allow further reproduction and re-use of this version -refer to the White Rose Research Online record for this item. Where records identify the publisher as the copyright holder, users can verify any specific terms of use on the publisher's website. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Takedown M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT• A numerical demonstration that in phase-field models for brittle fracture the smeared crack length does not necessarily converge to the discrete crack length upon mesh refinement.• A demonstration that the numerical results of boundary value problems that use the phase-field model for brittle fracture are very sensitive to how the boundary conditions are applied.• A proof that the phase-field model for cohesive fracture does not satisfy a two-dimensional patch test, even when the interpolation orders of the displacement field, the phase field and the crack-opening field are balanced. *Highlights (for review)M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPTA numerical assessment of phase-field models for brittle and cohesive fracture: Γ-convergence and stress oscillations AbstractRecently, phase-field approaches have gained popularity as a versatile tool for simulating fracture in a smeared manner. In this paper we give a numerical assessment of two types of phase-field models. For the case of brittle fracture we focus on the question whether the functional that describes the smeared crack surface approaches the functional for the discrete crack in the limiting case that the internal length scale parameter vanishes. By a one-dimensional example we will show that Γ-convergence is not necessarily attained numerically. Next, we turn attention to cohesive fracture. The necessity to have the crack opening explicitly available as input for the cohesive traction-relative displacement relation requires the independent interpolation of this quantity. The resulting three-field problem can be solved accurately on structured meshes when using a balanced interpolation of the field variables: displacements, phase field, and crac...

A new arc-length control method based on the rates of the internal and the dissipated energy AbstractPurpose:The purpose of this paper is to introduce a new arc-length control method for physically non-linear problems based on the rates of the internal and the dissipated energy. Design/methodology/approach: In this paper, the authors derive from the second law of thermodynamics the arc-length method based on the rate of the dissipated energy and from the time derivative of the energy density the arc-length method based on the rate of the internal energy. Findings:The method requires only two parameters and can automatically trace equilibrium paths which display multiple snap-back phenomena. Originality/value: A fully energy-based control procedure is developed, which facilitates switching between dissipative and non-dissipative arc-length control equations in a natural way.The method is applied to a plate with an eccentric hole using the phase field model for brittle fracture and to a perforated beam using interface elements with decohesion.

SUMMARYAn isogeometric model is developed for the analysis of fluid transport in pre-existing faults or cracks that are embedded in a fluid-saturated deformable porous medium. Flow of the interstitial fluid in the porous medium and fluid transport in the discontinuities are accounted for and are coupled. The modelling of a fluid-saturated porous medium in general requires the interpolation of the displacements of the solid to be one order higher than that of the pressure of the interstitial fluid. Using order elevation and Bézier projection, a consistent procedure has been developed to accomplish this in an isogeometric framework. Particular attention has also been given to the spatial integration along the isogeometric interface element in order to suppress traction oscillations that can arise for certain integration rules when a relatively high dummy stiffness is used in a poromechanical model.

This is the peer reviewed version of the following article: May, S., Vignollet, J., and Borst, R. (2015) Powell-Sabin B-splines and unstructured standard T-splines for the solution of the Kirchhoff-Love plate theory exploiting Bézier extraction. Int. J. Numer. Meth. Engng, which has been published in final form at http://dx.doi.org/10.1002/nme.5163. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving (http://olabout.wiley.com/WileyCDA/Section/id-828039.html) eprints@whiterose.ac.uk https://eprints.whiterose.ac.uk/ Reuse Unless indicated otherwise, fulltext items are protected by copyright with all rights reserved. The copyright exception in section 29 of the Copyright, Designs and Patents Act 1988 allows the making of a single copy solely for the purpose of non-commercial research or private study within the limits of fair dealing. The publisher or other rights-holder may allow further reproduction and re-use of this version -refer to the White Rose Research Online record for this item. Where records identify the publisher as the copyright holder, users can verify any specific terms of use on the publisher's website. TakedownIf you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing eprints@whiterose.ac.uk including the URL of the record and the reason for the withdrawal request. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERINGInt. J. Numer. Meth. Engng 0000; 00:1-26 Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002 SUMMARYThe equations that govern Kirchhoff-Love plate theory are solved using quadratic Powell-Sabin B-splines and unstructured standard T-splines. Bézier extraction is exploited to make the formulation computationally efficient. Since quadratic Powell-Sabin B-splines result in C 1 A -continuous shape functions, they are of sufficiently high continuity to capture Kirchoff-Love plate theory when cast in a weak form. Unlike NonUniform Rational B-Splines (NURBS) which are commonly used in isogeometric analysis, Powell-Sabin Bsplines do not necessarily capture the geometry exactly. However, the fact that they are defined on triangles instead of on quadrilaterals increases their flexibility in meshing, and can make them competitive with respect to NURBS, as no bending strip method for joined NURBS patches is needed. This paper further illustrates how unstructured T-splines can be modified such that they are C 1 A -continuous around extraordinary points, and that the blending functions fulfil the partition of unity property. The performance of quadratic NURBS, unstructured T-splines, Powell-Sabin B-splines and NURBS-to-NURPS (Non-Uniform Rational Powell-Sabin B-splines which are obtained by a transformation from a NURBS patch) is compared in a study of a circular plate.