http://www.dspace.cam.ac.uk:80/handle/1810/217881 Thu, 20 Jun 2013 02:53:57 GMT 2013-06-20T02:53:57Z http://www.dspace.cam.ac.uk:80/handle/1810/243981 Title: Supporting material for the paper 'Unified Form Language: A domain-specific language for weak formulations of partial differential equations' Authors: Alnaes, Martin S.; Logg, Anders; Oelgaard, Kristian B.; Rognes, Marie E.; Wells, Garth N. Abstract: Supporting computer code for the paper 'Unified Form Language: A domain-specific language for weak formulations of partial differential equations' Thu, 01 Nov 2012 00:00:00 GMT http://www.dspace.cam.ac.uk:80/handle/1810/243981 2012-11-01T00:00:00Z http://www.dspace.cam.ac.uk:80/handle/1810/241077 Title: Supporting computer code for the paper 'Energy stable and momentum conserving hybrid finite element method for the incompressible Navier--Stokes equations' Authors: Labeur, Robert Jan; Wells, Garth N. Abstract: Supporting computer code for the paper 'Energy stable and momentum conserving hybrid finite element method for the incompressible Navier-Stokes equations' in SIAM Journal on Scientific Computing. Sun, 01 Jan 2012 00:00:00 GMT http://www.dspace.cam.ac.uk:80/handle/1810/241077 2012-01-01T00:00:00Z http://www.dspace.cam.ac.uk:80/handle/1810/240740 Title: Computer code in support of paper 'Optimal control with stochastic PDE constraints and uncertain controls' Authors: Rosseel, Eveline; Wells, Garth N. Abstract: Computer code in support of the paper 'Rosseel, E. and Wells, G. N. Optimal control with stochastic PDE constraints and uncertain controls. Comput. Methods Appl. Mech. Engrg., http://dx.doi.org/10.1016/j.cma.2011.11.026.' Sat, 01 Jan 2011 00:00:00 GMT http://www.dspace.cam.ac.uk:80/handle/1810/240740 2011-01-01T00:00:00Z http://www.dspace.cam.ac.uk:80/handle/1810/236975 Title: Computer code in support of the manuscript "Phase field model for coupled displacive and diffusive microstructural processes under thermal loading" Authors: Wells, G N; Maraldi, Mirko Abstract: Supporting material for the article: Maraldi, M., Wells, G. N., and Molari, L. (2011). Phase field model for coupled displacive and diffusive microstructural processes under thermal loading. Journal of the Mechanics and Physics of Solids. doi:10.1016/j.jmps.2011.04.017 Sat, 01 Jan 2011 00:00:00 GMT http://www.dspace.cam.ac.uk:80/handle/1810/236975 2011-01-01T00:00:00Z http://www.dspace.cam.ac.uk:80/handle/1810/236913 Title: Application of continuum laws in discontinuity analysis based on a regularised displacement discontinuity Authors: Wells, G N; Sluys, L J Abstract: The application of continuum constitutive laws in embedded strong discontinuity analysis is examined. By adopting a regularised discontinuity (approximating the unbounded strain field resulting from a displacement jump with a bounded function), the strain field in a body is always bounded, hence continuum laws can be applied. However, this must be done with some caution since the ‘fictitious’ strain state at the discontinuity can lead to spurious behaviour that does not arise in the conventional application of classical constitutive laws. Particularly addressed is stress locking as a function of the displacement regularisation in some plasticity models. It is also shown that the regularisation function can have a serious impact on convergence behaviour for some types of constitutive models. Description: In Wunderlich, W., editor, Proceedings of the European Conference on Computational Mechanics (CDROM), Munich. Tue, 31 Aug 1999 23:00:00 GMT http://www.dspace.cam.ac.uk:80/handle/1810/236913 1999-08-31T23:00:00Z http://www.dspace.cam.ac.uk:80/handle/1810/236912 Title: Embedded discontinuities for softening solids Authors: Wells, G N; Sluys, L J Abstract: Additional, discontinuous functions are added to the displacement field of standard finite elements in order to capture highly localised zones of intense straining. By embedding discontinuities within an element it is possible to effectively model localisation phenomena (such as fracture in concrete) with a relatively small number of finite elements. The displacement jump is regularised, producing bounded strains and allowing the application of classical strain softening constitutive laws. It is then possible to achieve mesh-objective results with respect to energy dissipation without resorting to higher-order continuum theories. Description: In Wang, C. M., Lee, K. H., and Ang, K. K., editors, Computational Mechanics for the Next Millennium, pages 393–398, Singapore. Elsevier Science Ltd. Fri, 01 Jan 1999 00:00:00 GMT http://www.dspace.cam.ac.uk:80/handle/1810/236912 1999-01-01T00:00:00Z http://www.dspace.cam.ac.uk:80/handle/1810/236911 Title: Discrete analysis of localisation in three-dimensional solids Authors: Wells, G N; Sluys, L J Abstract: A procedure is illustrated for the determination of the normal direction of a discontinuity plane within a solid finite element. Using so-called embedded discontinuities, discrete constitutive models can be applied within a continuum framework. A significant difficulty within this method for three-dimensional problems is the determination of the normal direction for a discontinuity. Bifurcation analysis indicates the development of a discontinuity and multiple solution for the normal. The procedure developed here chooses the appropriate normal by exploiting features of the embedded discontinuity method. Description: In Oñate, E., Bugeda, G., and Suárez, B., editors, European Congress on Computational Methods in Applied Sciences and Engineering (CDROM), Barcelona, Spain. Thu, 31 Aug 2000 23:00:00 GMT http://www.dspace.cam.ac.uk:80/handle/1810/236911 2000-08-31T23:00:00Z http://www.dspace.cam.ac.uk:80/handle/1810/236910 Title: The time scale in concrete fracture: A model based on partitions of unity Authors: van Zijl, G P A G; Wells, G N Abstract: Intense research efforts have been put in the formulation of theories for crack initiation and propagation in concrete. Yet, little attention has been paid to the time-dependence of fracture, despite evidence of its significance. This paper reports a finite element model which captures the time scale in concrete fracture. Visco-elasticity is employed to capture bulk creep. In the fracture process zone a different time scale acts. Therefore, a rate-dependent cracking resistance is modelled. A recently developed finite element method for modelling cohesive cracks is employed. It is based on partitions of unity, by which means displacement jumps are introduced independently of the mesh structure. This avoids the requirement of dense meshes by regularised continuum approaches to model localisation, and a priori knowledge of where cracks occur for standard discrete cracking approaches via interfaces. Description: In de Borst, R., Mazars, J., Pijaudier-Cabot, G., and van Mier, J. G. M., editors, Fourth International Conference on Fracture Mechanics of Concrete and Concrete Structures, pages 301–306, Rotterdam. Balkema. Mon, 01 Jan 2001 00:00:00 GMT http://www.dspace.cam.ac.uk:80/handle/1810/236910 2001-01-01T00:00:00Z http://www.dspace.cam.ac.uk:80/handle/1810/236909 Title: Multi-level analysis of localisation problems Authors: Sluys, L J; Estrin, Y; Wells, G N Abstract: Localisation processes, such as shear banding and necking, have been investigated following a macroscopic and a microscopic approach. Both approaches have been formulated within a finite deformation plasticity framework. Additional terms have been used to regularise the problem and solve mesh dependency. In the macroscopic model viscosity is introduced as a means to control the thickness of the shear band, while in the microscopic model the nonlocal interaction of dislocations acts as a stabiliser. The micro-mechanical model is formulated in a crystal plasticity framework. A diffusion term that represents cross-slip of dislocations is included in the evolution equations for dislocation densities. The effect of the viscous term (macro-model) and the diffusion-like term (micro-model) in the constitutive relation on the resulting formation of localised shear modes is studied. An analysis of a strip in tension oriented for multiple slip is presented for both models. Description: In 2nd European Conference on Computational Mechanics (CDROM), Cracow, Poland. Thu, 31 May 2001 23:00:00 GMT http://www.dspace.cam.ac.uk:80/handle/1810/236909 2001-05-31T23:00:00Z http://www.dspace.cam.ac.uk:80/handle/1810/236908 Title: A novel technique for modelling interfaces in reinforced brittle materials Authors: Simone, A; Wells, G N; Sluys, L J Abstract: A novel numerical technique for the modelling of interfaces is introduced for the analysis of reinforced brittle materials. The method exploits the partition of unity property of finite element shape functions. By considering finite element shape functions as partitions of unity, extra degrees of freedom are added to the nodes at the interface between the matrix and reinforcement. A gradient-enhanced damage model is used to simulate the continuum response. Numerical results for a three-point bending test and a pull-out test are presented. The numerical procedure proposed here is suitable for a great variety of applications ranging from discrete cracking and steel-concrete interaction in concrete to delamination processes in composite materials. Description: In de Borst, R., Mazars, J., Pijaudier-Cabot, G., and van Mier, J. G. M., editors, Fourth International Conference on Fracture Mechanics of Concrete and Concrete Structures, pages 841–846, Rotterdam. Balkema. Mon, 01 Jan 2001 00:00:00 GMT http://www.dspace.cam.ac.uk:80/handle/1810/236908 2001-01-01T00:00:00Z http://www.dspace.cam.ac.uk:80/handle/1810/236907 Title: Analysis of delamination growth with discontinuous finite elements Authors: Remmers, Joris J C; Wells, G N; De Borst, R Abstract: Delamination is one of the most important failure mechanisms in laminates. Normally, it is modelled using interface elements. These elements are placed between two layers that are modelled with continuum elements. The interface elements are equipped with a softening or damage model in order to simulate debonding. This method has some drawbacks, both in a numerical and in a mechanical sense. A recent alternative is to simulate the crack by adding a discontinuous displacement mode to the continuum elements according to the partition of unity method. The elements do not contain the discontinuity prior to cracking, but when the ultimate stress in the bulk material is exceeded, delamination is initiated and additional degrees-of-freedom are activated. Beside this, a slightly different implementation is examined also. A discontinuity is predefined and has an initial dummy stiffness. Delamination is initiated when the tractions in the discontinuity exceed a threshold value. The results of both versions of this partition of unity model are compared mutually and with conventional interface elements by means of two examples. Description: In 2nd European Conference on Computational Mechanics (CDROM), Cracow, Poland. Thu, 31 May 2001 23:00:00 GMT http://www.dspace.cam.ac.uk:80/handle/1810/236907 2001-05-31T23:00:00Z http://www.dspace.cam.ac.uk:80/handle/1810/236906 Title: Strong embedded discontinuities for simulating fracture in quasi-brittle materials Authors: Alfaiate, J; Wells, G N; Sluys, L J Abstract: In this paper embedded strong discontinuities are used to model discrete cracking in materials like concrete. In the approach followed a discontinuous displacement field is considered and the deformation is localized at a surface of zero width. Both a damage law and a plasticity law are adopted to describe the constitutive relation between tractions and displacement jumps at the discontinuity surface. An algorithm is introduced to enforce the continuity of the crack path, permitting a clear identification of the discontinuities in the mesh. Both mode-I and mixed-mode cracking have been considered and the importance of the shear tractions on the global behaviour of a structure is assessed. With the formulation adopted it is concluded that: i) realistic crack patterns are obtained, similar to those found in experiments and ii) the dissipation of energy can be objectively found irrespective of the mesh that is used. Description: In de Borst, R., Mazars, J., Pijaudier-Cabot, G., and van Mier, J. G. M., editors, Fourth International Conference on Fracture Mechanics of Concrete and Concrete Structures, pages 749–756, Rotterdam. Balkema. Mon, 01 Jan 2001 00:00:00 GMT http://www.dspace.cam.ac.uk:80/handle/1810/236906 2001-01-01T00:00:00Z http://www.dspace.cam.ac.uk:80/handle/1810/236905 Title: A p-adaptive scheme for overcoming volumetric locking during isochoric plastic deformation Authors: Wells, G N; Sluys, L J Abstract: A p-adaptive scheme is developed in order to overcome volumetric locking in low order finite elements. A special adaptive scheme is used which is based on the partition of unity concept. This allows higher order polynomial terms to be added locally to the underlying finite element interpolations basis through the addition of extra degrees of freedom at existing nodes. During the adaptive process, no new nodes are added to the mesh. Volumetric locking is overcome by introducing higher order polynomial terms in regions where plastic flow occurs. The model is able to overcome volumetric locking for plane strain, axisymmetric and three-dimensional problems. Description: In 2nd European Conference on Computational Mechanics (CDROM), Cracow, Poland. Thu, 31 May 2001 23:00:00 GMT http://www.dspace.cam.ac.uk:80/handle/1810/236905 2001-05-31T23:00:00Z http://www.dspace.cam.ac.uk:80/handle/1810/236904 Title: Computational modelling of cracks in viscoplastic media Authors: Wells, G N; Sluys, L J; De Borst, R Abstract: A newly developed numerical model is used to simulate propagating cracks in a strain softening viscoplastic medium. The model allows the simulation of displacement discontinuities independently of a finite element mesh. This is possible using the partition of unity concept, in which fracture is treated as a coupled problem, with separate variational equations corresponding to the continuous and discontinuous parts of the displacement field. The equations are coupled through the dependence of the stress field on the strain state. Numerical examples show that allowing displacement discontinuities in a viscoplastic Von Mises material can lead to a failure mode that differs from a continuum-only model. Description: In Ravi-Chandar, K., Karihaloo, B.L., Kishi, T., Ritchie, R.O., Yokobori, Jr, A. T., and Yokobori, T., editors, Advances in Fracture Research - Proceedings of ICF10 (CDROM), Honolulu, Hawaii. Pergamon. Mon, 01 Jan 2001 00:00:00 GMT http://www.dspace.cam.ac.uk:80/handle/1810/236904 2001-01-01T00:00:00Z http://www.dspace.cam.ac.uk:80/handle/1810/236807 Title: Simulating discontinuities in a gradient-enhanced continuum Authors: Simone, A; Wells, G N; Sluys, L J Abstract: A continuum-discrete model for failure in quasi-brittle materials is presented. The continuum is regularised through the introduction of gradient terms into the constitutive model. At the transition to discrete failure, the problem fields are enhanced through the use of a discontinuous interpolation. The continuum model is able to simulate micro-cracking, while a traction-free discontinuity represents the macro crack. The discretisation procedure is described in detail. Description: In Dyskin, A. V., Hu, X., and Sahouryeh, E., editors, Proceeding of the International Conference on Structural Integrity and Fracture, pages 115–118, Lisse. Swets & Zeitlinger. Tue, 01 Jan 2002 00:00:00 GMT http://www.dspace.cam.ac.uk:80/handle/1810/236807 2002-01-01T00:00:00Z http://www.dspace.cam.ac.uk:80/handle/1810/236806 Title: Discontinuous Modelling of Crack Propagation in a Gradient-Enhanced Continuum Authors: Simone, A; Wells, G N; Sluys, L J Abstract: A numerical model for the description of the combined continuous/discontinuous failure in a regularised strain-softening continuum is proposed. The continuum is regularised through the introduction of gradient terms into the constitutive equations. At the transition to discrete failure, the problem fields are enhanced through a discontinuous interpolation based on the partition of unity concept. The discretisation procedure is described in detail and numerical examples illustrate the performance of the combined continuous/discontinuous approach. Description: In Mang, H. A., Rammerstorfer, F. G., and Eberhardsteiner, J., editors, Proceedings of the Fifth World Congress on Computational Mechanics (WCCM V), Austria. Vienna University of Technology. Sun, 30 Jun 2002 23:00:00 GMT http://www.dspace.cam.ac.uk:80/handle/1810/236806 2002-06-30T23:00:00Z http://www.dspace.cam.ac.uk:80/handle/1810/236805 Title: Analysis of delamination growth with discontinuous solid-like shell elements Authors: Remmers, Joris J C; Wells, G N; De Borst, R Abstract: In this contribution a new finite element is presented for the simulation of delamination growth in thin layered composite materials. The element is based on the solid-like shell element, a volume element that can be used in very thin applications due to a higher order displacement field in thickness direction. The delamination crack is incorporated in this element as a jump of the displacement field by means of the partition of unity method. The kinematics of the element as well as the finite element formulation are described. The performance of the element is demonstrated by means of two examples. Description: In Mang, H. A., Rammerstorfer, F. G., and Eberhardsteiner, J., editors, Proceedings of the Fifth World Congress on Computational Mechanics (WCCM V), Austria. Vienna University of Technology. Tue, 01 Jan 2002 00:00:00 GMT http://www.dspace.cam.ac.uk:80/handle/1810/236805 2002-01-01T00:00:00Z http://www.dspace.cam.ac.uk:80/handle/1810/236804 Title: A Précis of Some Recent Developments in Computational Failure Mechanics Authors: De Borst, R; Askes, Harm; Gutiérrez, Miguel A; Remmers, Joris J C; Wells, G N Abstract: A concise overview is given of various numerical methods that can be used to analyse localisation and failure in engineering materials. The importance of the cohesive-zone approach is emphasised and various ways of incorporating the cohesive-zone methodology in discretisation methods are discussed. Next, a simple continuum damage (decohesion) model which preserves well-posedness of boundary value problems via gradient enhancement is recalled. Using a meshless method the importance of the higher-order gradient terms is assessed. Finally, the model is used in finite element reliability analyses to quantify the probability of the emergence of various possible failure modes. Description: In Mang, H. A., Rammerstorfer, F. G., and Eberhardsteiner, J., editors, Proceedings of the Fifth World Congress on Computational Mechanics (WCCM V), Austria. Vienna University of Technology. Tue, 01 Jan 2002 00:00:00 GMT http://www.dspace.cam.ac.uk:80/handle/1810/236804 2002-01-01T00:00:00Z http://www.dspace.cam.ac.uk:80/handle/1810/236802 Title: Discontinuities in regularised media Authors: Simone, A; Wells, G N; Sluys, L J Abstract: Discontinuous interpolation of the problem fields in non-local and rate-dependent media is considered. The necessity of discontinuities in the analysis of failure processes and some of the requirements for the introduction of discontinuities in regularised media are discussed. The regularisation properties of a novel rate-dependent elastoplastic damage continuum model are presented. Description: In Onate, E. and Owen, D. R. J., editors, VII International Conference on Computational Plasticity (COMPLAS 2003), Barcelona, Spain. Wed, 01 Jan 2003 00:00:00 GMT http://www.dspace.cam.ac.uk:80/handle/1810/236802 2003-01-01T00:00:00Z http://www.dspace.cam.ac.uk:80/handle/1810/236801 Title: A combined experimental-numerical study to cyclic behaviour of limestone Authors: De Proft, K; Wells, G N; Sluys, L J; De Wilde, W P Abstract: In this paper, a combined experimental-computational study of double-edge notched stone specimen subject to cyclic tensile loading is presented. In the experimental part, the load-deformation response and the local displacement field are recorded. Both experimental results are used to validate a numerical model for the description of fracture within finite elements. The model uses displacement discontinuities to model cracks. These discontinuities are implemented using the partition of unity property of finite element shape functions. In the discontinuity, a combined damage-plasticity cohesive law is used. Numerical simulations are compared with experimental observations. Description: In E. Oñate and D.R.J. Owen (Eds), VII International Conference on Computational Plasticity (COMPLAS 2003), Barcelona, Spain. Wed, 01 Jan 2003 00:00:00 GMT http://www.dspace.cam.ac.uk:80/handle/1810/236801 2003-01-01T00:00:00Z