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# Scholarly Works - Engineering - Computational Mechanics

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Item Open Access Supporting material for the paper 'CO2 dissolution in a background hydrological flow'(2015-12) Unwin, H. Juliette T.; Wells, Garth N.Show more Supporting computer code to reproduce the examples in: Unwin, H. Juliette T., Wells, Garth N. and Woods, Andrew W. CO2 dissolution in a background hydrological flow, Journal of Fluid Mechanics, http://arxiv.org/abs/1506.04433.Show more Item Open Access FEniCS in Linux Containers(2015-06-29) Hale, Jack S.; Li, Lizao (Larry); Wells, Garth N.Show more Item Open Access Supporting material for the paper 'Compaction around a rigid, circular inclusion in partially molten rock'(2014-04-25) Alisic, Laura; Rudge, John F.; Katz, Richard F.; Wells, Garth N.; Rhebergen, SanderShow more Supporting computer code for the paper 'Compaction around a rigid, circular inclusion in partially molten rock'.Show more Item Open Access Compaction around a rigid, circular inclusion in partially molten rock(2013-12-11) Alisic, Laura; Rudge, John F; Katz, Richard F; Wells, Garth N; Rhebergen, Sander; Rudge, John [0000-0002-9399-7166]; Wells, Garth [0000-0001-5291-7951]Show more Conservation laws that describe the behavior of partially molten mantle rock have been established for several decades, but the associated rheology remains poorly understood. Constraints on the rheology may be obtained from recently published experiments involving deformation of partially molten rock around a rigid, spherical inclusion. These experiments give rise to patterns of melt segregation that exhibit the competing effects of pressure shadows and melt-rich bands. Such patterns provide an opportunity to infer rheological parameters through comparison with models based on the conservation laws and constitutive relations that hypothetically govern the system. To this end, we have developed software tools to simulate finite strain, two-phase flow around a circular inclusion in a configuration that mirrors the experiments. Simulations indicate that the evolution of porosity is predominantly controlled by the porosity-weakening exponent of the shear viscosity and the poorly known bulk viscosity. In two-dimensional simulations presented here, we find that the balance of pressure shadows and melt-rich bands observed in experiments only occurs for bulk-to-shear-viscosity ratio of less than about five. However, the evolution of porosity in simulations with such low bulk viscosity exceeds physical bounds at unrealistically small strain due to the unchecked, exponential growth of the porosity variations. Processes that limit or balance porosity localization should be incorporated in the formulation of the model to produce results that are consistent with the porosity evolution in experiments.Show more Item Open Access Expressive and scalable finite element simulation beyond 1000 cores(HECToR: UK National Supercomputing Service, 2013) Richardson, Chris J.; Wells, Garth N.Show more The FEniCS Project is a widely used, open-source problem solving environment for partial differential equations that allows users to specify equations in mathematical symbolic form via a domain-specific language, and solve them using the finite element method. The FEniCS Problem solving environment provides C++ and Python interfaces, and relies on automated code generation to reconcile expressive input with high performance. Because of the generic nature of the software, many different scientific problems are being addressed using FEniCS/DOLFIN, including geodynamics, heat flow, elasticity, electromagnetics, flow in porous media, Navier--Stokes equations and acoustics. The key aims of this project were to enhance the applicability and usability of DOLFIN, the core finite element library in the FEniCS Project, on parallel architectures. DOLFIN already supported fully distributed computation via MPI, but lacked some important infrastructure for enabling large scale parallel computation. This included a lack of (i) scalable parallel I/O and (ii) parallel mesh refinement. In addition, (iii) DOLFIN did not support threaded operations in combination with MPI. Implementation of the three aforementioned points formed the objectives of this project. All three objectives have been realised and exceeded, and the computer code developed is publicly available. Outcomes of this project are either already in a release of DOLFIN or are in development repositories and will be included in the next release, and are already being used in a number of research projects, including projects supported by UK research councils.Show more Item Open Access Supporting material for the paper 'Unified Form Language: A domain-specific language for weak formulations of partial differential equations'(2012-11) Alnaes, Martin S.; Logg, Anders; Oelgaard, Kristian B.; Rognes, Marie E.; Wells, Garth N.Show more Supporting computer code for the paper 'Unified Form Language: A domain-specific language for weak formulations of partial differential equations'Show more Item Open Access Supporting computer code for the paper 'Energy stable and momentum conserving hybrid finite element method for the incompressible Navier--Stokes equations'(2012) Labeur, Robert Jan; Wells, Garth N.Show more 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.Show more Item Open Access Computer code in support of paper 'Optimal control with stochastic PDE constraints and uncertain controls'(2011) Rosseel, Eveline; Wells, Garth N.Show more 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.'Show more Item Open Access Application of continuum laws in discontinuity analysis based on a regularised displacement jump(European Council of Computational Mechanics, 1999) Wells, GN; Sluys, LJ; Wells, Garth [0000-0001-5291-7951]Show more 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.Show more Item Open Access Embedded discontinuities for softening solids(Elsevier, 1999-12-06) Wells, GN; Sluys, LJ; Wang, CM; Lee, KH; Ang, KK; Wells, Garth [0000-0001-5291-7951]Show more 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.Show more Item Open Access Discrete analysis of localisation in three-dimensional solids(ECCOMAS, 2000) Wells, GN; Sluys, LJ; Wells, Garth [0000-0001-5291-7951]Show more 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.Show more Item Open Access Time scale in concrete fracture: a model based on partitions of unity(Balkema, 2001) Van Zijl, GPA; Wells, GN; Borst, RD; Wells, Garth [0000-0001-5291-7951]Show more 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.Show more Item Open Access Multi-level analysis of localisation problems(2001) Sluys, LJ; Estrin, Y; Wells, GN; Wells, Garth [0000-0001-5291-7951]Show more 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.Show more Item Open Access A novel technique for modelling interfaces in reinforced brittle materials(Balkema, 2001) Simone, A; Wells, GN; Sluys, LJ; Borst, RD; Wells, Garth [0000-0001-5291-7951]Show more 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.Show more Item Open Access Analysis of delamination growth with discontinuous solid-like shell elements(MCB University Press, 2004) Remmers, JJC; De Borst, R; Wells, GN; Ransing, RS; Wells, Garth [0000-0001-5291-7951]Show more 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.Show more Item Open Access Strong embedded discontinuities for simulating fracture in quasi-brittle materials(Balkema, 2001) Alfaiate, J; Wells, GN; Sluys, LJ; Borst, RD; Wells, Garth [0000-0001-5291-7951]Show more 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.Show more Item Open Access A p-adaptive scheme for overcoming volumetric locking during isochoric plastic deformation(Kraków : Fundacja Zdrowia Publicznego "Vesalius", 2001) Wells, GN; Sluys, LJ; Waszczyszyn, Z; Pamin, J; Wells, Garth [0000-0001-5291-7951]Show more 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.Show more Item Open Access Computational modelling of cracks in viscoplastic media(Elsevier Science, 2001) Wells, GN; Sluys, LJ; De Borst, R; Ravi Chandar, K; Wells, Garth [0000-0001-5291-7951]Show more 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.Show more Item Open Access Simulating discontinuities in a gradient-enhanced continuum(Balkema, 2002) Simone, A; Wells, GN; Sluys, LJ; Dyskin, AV; Hu, X; Sahouryeh, E; Wells, Garth [0000-0001-5291-7951]Show more 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.Show more Item Open Access Discontinuous modelling of crack propagation in a gradient-enhanced continuum(2002) Simone, A; Wells, GN; Sluys, LJ; Wells, Garth [0000-0001-5291-7951]Show more 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.Show more