dc.contributor.author Molari, L en dc.contributor.author Garikipati, K en dc.contributor.author Wells, Garth en dc.contributor.editor Carpinteri, A en dc.date.accessioned 2011-04-04T13:30:41Z dc.date.available 2011-04-04T13:30:41Z dc.date.issued 2006 en dc.identifier.issn 1567-2069 dc.identifier.uri http://www.dspace.cam.ac.uk/handle/1810/236593 dc.description.abstract Continuum damage models are widely used to represent the development of microscopic defects that coalesce into a macroscopic crack. The microscopic defects cause a progressive weakening or softening of the material (damage). Strain gradient-dependent terms have been included in some damage theories to regularize them, and thereby avoid a pathological mesh-dependence in the solution. A strain gradient-dependent damage model is considered here for the simulation of this feature in quasi-brittle materials. In the model considered, the damage parameter depends upon a regularized equivalent strain. The regularization is introduced through a dependency on the Laplacian of an equivalent strain measure. The introduction of the Laplacian of the strain leads to numerical difficulties as the governing differential equations are fourth-order, and additional boundary conditions must be specified. The application of such a model in a standard finite element framework requires $C^1$ continuity of the shape functions. Here, a continuous/discontinuous mixed Galerkin method is presented which avoids the need for high-order continuity. The formulation allows the use of $C^0$ or $C^{-1}$ interpolations for the regularized strain field and a $C^0$ interpolation of the displacement field. Numerical examples are presented to validate the formulation in one and two dimensions. Several interpolations are tested extensively in one dimension in order to provide guidance for the most appropriate formulations in two dimensions. The formulation is applied to crack propagation in a three-point bending test, with the computed result being independent of the discretization. dc.format.medium paper en dc.language.iso en en_GB dc.title Formulation of continuous/discontinuous Galerkin methods for strain gradient-dependent damage en dc.type Conference Object prism.edition 1 en prism.issueIdentifier 1 en prism.number 1 en prism.publicationDate 2006 en prism.publicationName Strength Fracture and Complexity en prism.publicationName Strength Fracture and Complexity en prism.volume 4 en rioxxterms.licenseref.uri http://www.rioxx.net/licenses/all-rights-reserved en rioxxterms.licenseref.startdate 2006 en dc.contributor.orcid Wells, Garth [0000-0001-5291-7951] rioxxterms.type Conference Paper/Proceeding/Abstract en pubs.conference-name 11th International Conference on Fracture en pubs.conference-start-date 2005-03-20 en
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