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Isogeometric boundary element methods for three dimensional static fracture and fatigue crack growth ; ; et al in Computer Methods in Applied Mechanics and Engineering (2016) Detailed reference viewed: 229 (13 UL)Stable 3D extended finite elements with higher order enrichment for accurate non planar fracture Agathos, Konstantinos ; ; Bordas, Stéphane in Computer Methods in Applied Mechanics and Engineering (2016), 306 An extended finite element method (XFEM) for three dimensional (3D) non-planar linear elastic fracture is introduced, which provides optimal convergence through the use of enrichment in a fixed area ... [more ▼] An extended finite element method (XFEM) for three dimensional (3D) non-planar linear elastic fracture is introduced, which provides optimal convergence through the use of enrichment in a fixed area around the crack front, while also improving the conditioning of the resulting system matrices. This is achieved by fusing a novel form of enrichment with existing blending techniques. Further, the adoption of higher order terms of theWilliams expansion is also considered and the effects in the accuracy and conditioning of the method are studied. Moreover, some problems regarding the evaluation of stress intensity factors (SIFs) and element partitioning are dealt with. The accuracy and convergence properties of the method as well as the conditioning of the resulting stiffness matrices are investigated through the use of appropriate benchmark problems. It is shown that the proposed approach provides increased accuracy while requiring, for all cases considered, a reduced number of iterations for the solution of the resulting systems of equations. The positive impact of geometrical enrichment is further demonstrated in the accuracy of the computed SIFs where, for the examined cases, an improvement of up to 40% is achieved. [less ▲] Detailed reference viewed: 105 (3 UL)A phase-field method for computational modeling of interfacial damage interacting with crack propagation in realistic microstructures obtained by microtomography Nguyen, Thanh Tung ; ; et al in Computer Methods in Applied Mechanics and Engineering (2016), 312 Detailed reference viewed: 66 (2 UL)A fast, certified and "tuning free" two-field reduced basis method for the metamodelling of affinely-parametrised elasticity problems ; ; Bordas, Stéphane in Computer Methods in Applied Mechanics and Engineering (2016), 298 This paper proposes a new reduced basis algorithm for the metamodelling of parametrised elliptic problems. The developments rely on the Constitutive Relation Error (CRE), and the construction of separate ... [more ▼] This paper proposes a new reduced basis algorithm for the metamodelling of parametrised elliptic problems. The developments rely on the Constitutive Relation Error (CRE), and the construction of separate reduced order models for the primal variable (displacement) and flux (stress) fields. A two field greedy sampling strategy is proposed to construct these two fields simultaneously and in an efficient manner: at each iteration, one of the two fields is enriched by increasing the dimension of its reduced space in such a way that the CRE is minimised. This sampling strategy is then used as a basis to construct goal-oriented reduced order modelling. The resulting algorithm is certified and “tuning free”: the only requirement from the engineer is the level of accuracy that is desired for each of the outputs of the surrogate. It is also shown to be significantly more efficient in terms of computational expense than competing methodologies. [less ▲] Detailed reference viewed: 160 (18 UL)Meshfree volume-averaged nodal projection method for nearly-incompressible elasticity using meshfree and bubble basis functions ; Hale, Jack ; in Computer Methods in Applied Mechanics and Engineering (2015), 285 We present a displacement-based Galerkin meshfree method for the analysis of nearly-incompressible linear elastic solids, where low-order simplicial tessellations (i.e., 3- node triangular or 4-node ... [more ▼] We present a displacement-based Galerkin meshfree method for the analysis of nearly-incompressible linear elastic solids, where low-order simplicial tessellations (i.e., 3- node triangular or 4-node tetrahedral meshes) are used as a background structure for numerical integration of the weak form integrals and to get the nodal information for the computation of the meshfree basis functions. In this approach, a volume- averaged nodal projection operator is constructed to project the dilatational strain into an approximation space of equal- or lower-order than the approximation space for the displacement field resulting in a locking-free method. The stability of the method is provided via bubble-like basis functions. Because the notion of an ‘ele- ment’ or ‘cell’ is not present in the computation of the meshfree basis functions such low-order tessellations can be used regardless of the order of the approximation spaces desired. First- and second-order meshfree basis functions are chosen as a particular case in the proposed method. Numerical examples are provided in two and three dimensions to demonstrate the robustness of the method, its ability to avoid volumetric locking in the nearly-incompressible regime, and its improved performance when compared to the MINI finite element scheme on the simplicial mesh. [less ▲] Detailed reference viewed: 251 (53 UL)A fast, certified and "tuning-free" two-field reduced basis method for the metamodelling of parametrised elasticity problems ; ; Bordas, Stéphane in Computer Methods in Applied Mechanics and Engineering (2015) This paper proposes a new reduced basis algorithm for the metamodelling of parametrised elliptic problems. The developments rely on the Constitutive Relation Error (CRE), and the construction of separate ... [more ▼] This paper proposes a new reduced basis algorithm for the metamodelling of parametrised elliptic problems. The developments rely on the Constitutive Relation Error (CRE), and the construction of separate reduced order models for the primal variable (displacement) and flux (stress) fields. A two-field Greedy sampling strategy is proposed to construct these two fields simultaneously and efficient manner: at each iteration, one of the two fields is enriched by increasing the dimension of its reduced space in such a way that the CRE is minimised. This sampling strategy is then used as a basis to construct goal-oriented reduced order modelling. The resulting algorithm is certified and "tuning-free": the only requirement from the engineer is the level of accuracy that is desired for each of the outputs of the surrogate. It is also one order of magnitude more efficient in terms of computational expenses than competing methodologies. [less ▲] Detailed reference viewed: 388 (12 UL)Stable 3D extended finite elements with higher order enrichment for accurate non planar fracture ; ; Bordas, Stéphane in Computer Methods in Applied Mechanics and Engineering (2015) We present an extended finite element method (XFEM) for 3D nonplanar linear elastic fracture. The new approach not only provides optimal convergence using geometrical enrichment but also enables to ... [more ▼] We present an extended finite element method (XFEM) for 3D nonplanar linear elastic fracture. The new approach not only provides optimal convergence using geometrical enrichment but also enables to contain the increase in conditioning number characteristic of enriched finite element formulations: the number of iterations to convergence of the conjugate gradient solver scales similarly to and converges faster than the topologically-enriched version of the standard XFEM. This has two advantages: (1) the residual can be driven to zero to machine precision for at least 50% fewer iterations than the standard version of XFEM; (2) additional enrichment functions can be added without significant deterioration of the conditioning. Numerical examples also show that our new approach is up to 40% more accurate in terms of stress intensity factors, than the standard XFEM. [less ▲] Detailed reference viewed: 230 (10 UL)Geometry-Independent Field approximaTion: CAD-Analysis Integration, geometrical exactness and adaptivity ; ; et al in Computer Methods in Applied Mechanics and Engineering (2014) In isogeometric analysis (IGA), the same spline representation is employed for both the geometry of the domain and approximation of the unknown fields over this domain. This identity of the geometry and ... [more ▼] In isogeometric analysis (IGA), the same spline representation is employed for both the geometry of the domain and approximation of the unknown fields over this domain. This identity of the geometry and field approximation spaces was put forward in the now classic 2005 paper [20] as a key advantage on the way to the integration of Computer Aided Design (CAD) and subsequent analysis in Computer Aided Engineering (CAE). [20] claims indeed that any change to the geometry of the domain is automatically inherited by the approximation of the field variables, without requiring the regeneration of the mesh at each change of the domain geometry. Yet, in Finite Element versions of IGA, a parameterization of the interior of the domain must still be constructed, since CAD only provides information about the boundary. The identity of the boundary and field representation decreases the flexibility in which this parameterization can be generated and somewhat constrains the modeling and simulation process, because an approximation able to represent the domain geometry accurately need not be adequate to also approximate the field variables accurately, in particular when the solution is not smooth. We propose here a new paradigm called Geometry-Independent Field approximaTion (GIFT) where the spline spaces used for the geometry and the field variables can be chosen and adapted independently while preserving geometric exactness and tight CAD integration. GIFT has the following features: (1) It is possible to flexibly choose between different spline spaces with different properties to better represent the solution of the problem, e.g. the continuity of the solution field, boundary layers, singularities, whilst retaining geometrical exactness of the domain boundary. (2) For multi-patch analysis, where the domain is composed of several spline patches, the continuity condition between neighboring patches on the solution field can be automatically guaranteed without additional constraints in the variational form. (3) Refinement operations by knot insertion and degree elevation are performed directly on the spline space of the solution field, independently of the spline space of the geometry of the domain, which makes the method versatile. GIFT with PHT-spline solution spaces and NURBS geometries is used to show the effectiveness of the proposed approach. Keywords : Super-parametric methods, Isogeometric analysis (IGA), Geometry-independent Spline Space, PHT-splines, local refinement, adaptivity [less ▲] Detailed reference viewed: 1109 (30 UL)A multiscale quasicontinuum method for lattice models with bond failure and fiber sliding Beex, Lars ; ; in Computer Methods in Applied Mechanics and Engineering (2014), 269 Structural lattice models incorporating trusses and beams are frequently used to mechanically model fibrous materials, because they can capture (local) mesoscale phenomena. Physically relevant lattice ... [more ▼] Structural lattice models incorporating trusses and beams are frequently used to mechanically model fibrous materials, because they can capture (local) mesoscale phenomena. Physically relevant lattice computations are however computationally expensive. A suitable multiscale approach to reduce the computational cost of large-scale lattice computations is the quasicontinuum (QC) method. This method resolves local mesoscale phenomena in regions of interest and coarse grains elsewhere, using only the lattice model. In previous work, a virtual-power-based QC framework is proposed for lattice models that include local dissipative mechanisms. In this paper, the virtual-power-based QC method is adopted for lattice models in which bond failure and subsequent frictional fiber sliding are incorporated – which are of significant importance for fibrous materials such as paper, cardboard, textile and electronic textile. Bond failure and fiber sliding are nonlocal dissipative mechanisms and to deal with this nonlocality, the virtual-power-based QC method is equipped with a mixed formulation in which the kinematic variables as well as the internal history variables are interpolated. Previously defined summation rules can still be used to sample the governing equations in this QC framework. Illustrative examples are presented. [less ▲] Detailed reference viewed: 152 (9 UL)Explicit finite deformation analysis of isogeometric membranes ; ; et al in Computer Methods in Applied Mechanics and Engineering (2014) NURBS-based isogeometric analysis was first extended to thin shell/membrane structures which allows for finite membrane stretching as well as large deflection and bending strain. The assumed non-linear ... [more ▼] NURBS-based isogeometric analysis was first extended to thin shell/membrane structures which allows for finite membrane stretching as well as large deflection and bending strain. The assumed non-linear kinematics employs the Kirchhoff-Love shell theory to describe the mechanical behaviour of thin to ultrathin structures. The displacement fields are interpolated from the displacements of control points only, and no rotational degrees of freedom are used at control points. Due to the high order Ck (k ≥ 1) continuity of NURBS shape functions the Kirchhoff-Love theory can be seamlessly implemented. An explicit time integration scheme is used to compute the transient response of membrane structures to time-domain excitations, and a dynamic relaxation method is employed to obtain steady-state solutions. The versatility and good performance of the present formulation is demonstrated with the aid of a number of test cases, including a square membrane strip under static pressure, the inflation of a spherical shell under internal pressure, the inflation of a square airbag and the inflation of a rubber balloon. The mechanical contribution of the bending stiffness is also evaluated. [less ▲] Detailed reference viewed: 604 (7 UL)Nitsche’s method method for mixed dimensional analysis: conforming and non-conforming continuum-beam and continuum-plate coupling ; ; et al in Computer Methods in Applied Mechanics and Engineering (2014) A Nitche’s method is presented to couple different mechanical models. They include coupling of a solid and a beam and of a solid and a plate. Both conforming and non-conforming formulations are presented ... [more ▼] A Nitche’s method is presented to couple different mechanical models. They include coupling of a solid and a beam and of a solid and a plate. Both conforming and non-conforming formulations are presented. In a non-conforming formulation, the structure domain is overlapped by a refined solid model which is needed to either get more accuracy or to capture highly nonlinear events. Applications can be found in multi-dimensional analyses in which parts of a structure are modeled with solid elements and others are modeled using a coarser model with beam and/or plate elements. Discretisations are performed using both standard Lagrange elements and high order NURBS (Non Uniform Rational Bsplines) based isogeometric elements. We present various examples to demonstrate the performance of the method. [less ▲] Detailed reference viewed: 297 (18 UL)Quasicontinuum-based multiscale approaches for plate-like beam lattices experiencing in-plane and out-of-plane deformation Beex, Lars ; ; et al in Computer Methods in Applied Mechanics and Engineering (2014), 279 The quasicontinuum (QC) method is a multiscale approach that aims to reduce the computational cost of discrete lattice computations. The method incorporates small-scale local lattice phenomena (e.g. a ... [more ▼] The quasicontinuum (QC) method is a multiscale approach that aims to reduce the computational cost of discrete lattice computations. The method incorporates small-scale local lattice phenomena (e.g. a single lattice defect) in macroscale simulations. Since the method works directly and only on the beam lattice, QC frameworks do not require the construction and calibration of an accompanying continuum model (e.g. a cosserat/micropolar description). Furthermore, no coupling procedures are required between the regions of interest in which the beam lattice is fully resolved and coarse domains in which the lattice is effectively homogenized. Hence, the method is relatively straightforward to implement and calibrate. In this contribution, four variants of the QC method are investigated for their use for planar beam lattices which can also experience out-of-plane deformation. The different frameworks are compared to the direct lattice computations for three truly multiscale test cases in which a single lattice defect is present in an otherwise perfectly regular beam lattice. [less ▲] Detailed reference viewed: 424 (14 UL)Isogeometric boundary element analysis using unstructured T-splines ; ; et al in Computer Methods in Applied Mechanics and Engineering (2013), 254 We couple collocated isogeometric boundary element methods and unstructured analysis-suitable T-spline surfaces for linear elastostatic problems. We extend the definition of analysis-suitable T-splines to ... [more ▼] We couple collocated isogeometric boundary element methods and unstructured analysis-suitable T-spline surfaces for linear elastostatic problems. We extend the definition of analysis-suitable T-splines to encompass unstructured control grids (unstructured meshes) and develop basis functions which are smooth (rational) polynomials defined in terms of the Bézier extraction framework and which pass standard patch tests. We then develop a collocation procedure which correctly accounts for sharp edges and corners, extraordinary points, and T-junctions. This approach is applied to several three-dimensional problems, including a real-world T-spline model of a propeller. We believe this work clearly illustrates the power of combining new analysis-suitable computer aided design technologies with established analysis methodologies, in this case, the boundary element method. © 2012 Elsevier B.V. [less ▲] Detailed reference viewed: 431 (14 UL)A partitioned model order reduction approach to rationalise computational expenses in nonlinear fracture mechanics ; ; et al in Computer Methods in Applied Mechanics and Engineering (2013), 256 We propose in this paper a reduced order modelling technique based on domain partitioning for parametric problems of fracture. We show that coupling domain decomposition and projection-based model order ... [more ▼] We propose in this paper a reduced order modelling technique based on domain partitioning for parametric problems of fracture. We show that coupling domain decomposition and projection-based model order reduction permits to focus the numerical effort where it is most needed: around the zones where damage propagates. No a priori knowledge of the damage pattern is required, the extraction of the corresponding spatial regions being based solely on algebra. The efficiency of the proposed approach is demonstrated numerically with an example relevant to engineering fracture. © 2012 Elsevier B.V. [less ▲] Detailed reference viewed: 330 (13 UL)An adaptive singular ES-FEM for mechanics problems with singular field of arbitrary order ; ; Bordas, Stéphane et al in Computer Methods in Applied Mechanics and Engineering (2013), 253 This paper presents a singular edge-based smoothed finite element method (sES-FEM) for mechanics problems with singular stress fields of arbitrary order. The sES-FEM uses a basic mesh of three-noded ... [more ▼] This paper presents a singular edge-based smoothed finite element method (sES-FEM) for mechanics problems with singular stress fields of arbitrary order. The sES-FEM uses a basic mesh of three-noded linear triangular (T3) elements and a special layer of five-noded singular triangular elements (sT5) connected to the singular-point of the stress field. The sT5 element has an additional node on each of the two edges connected to the singular-point. It allows us to represent simple and efficient enrichment with desired terms for the displacement field near the singular-point with the satisfaction of partition-of-unity property. The stiffness matrix of the discretized system is then obtained using the assumed displacement values (not the derivatives) over smoothing domains associated with the edges of elements. An adaptive procedure for the sES-FEM is proposed to enhance the quality of the solution with minimized number of nodes. Several numerical examples are provided to validate the reliability of the present sES-FEM method. © 2012 Elsevier B.V. [less ▲] Detailed reference viewed: 373 (8 UL)Extended finite element method with edge-based strain smoothing (ESm-XFEM) for linear elastic crack growth ; ; Bordas, Stéphane et al in Computer Methods in Applied Mechanics and Engineering (2012), 209-212 This paper presents a strain smoothing procedure for the extended finite element method (XFEM). The resulting "edge-based" smoothed extended finite element method (ESm-XFEM) is tailored to linear elastic ... [more ▼] This paper presents a strain smoothing procedure for the extended finite element method (XFEM). The resulting "edge-based" smoothed extended finite element method (ESm-XFEM) is tailored to linear elastic fracture mechanics and, in this context, to outperform the standard XFEM. In the XFEM, the displacement-based approximation is enriched by the Heaviside and asymptotic crack tip functions using the framework of partition of unity. This eliminates the need for the mesh alignment with the crack and re-meshing, as the crack evolves. Edge-based smoothing (ES) relies on a generalized smoothing operation over smoothing domains associated with edges of simplex meshes, and produces a softening effect leading to a close-to-exact stiffness, "super-convergence" and "ultra-accurate" solutions. The present method takes advantage of both the ES-FEM and the XFEM. Thanks to the use of strain smoothing, the subdivision of elements intersected by discontinuities and of integrating the (singular) derivatives of the approximation functions is suppressed via transforming interior integration into boundary integration. Numerical examples show that the proposed method improves significantly the accuracy of stress intensity factors and achieves a near optimal convergence rate in the energy norm even without geometrical enrichment or blending correction. [less ▲] Detailed reference viewed: 126 (2 UL)A two-dimensional Isogeometric Boundary Element Method for elastostatic analysis ; Bordas, Stéphane ; et al in Computer Methods in Applied Mechanics and Engineering (2012), 209-212 The concept of isogeometric analysis, where functions that are used to describe geometry in CAD software are used to approximate the unknown fields in numerical simulations, has received great attention ... [more ▼] The concept of isogeometric analysis, where functions that are used to describe geometry in CAD software are used to approximate the unknown fields in numerical simulations, has received great attention in recent years. The method has the potential to have profound impact on engineering design, since the task of meshing, which in some cases can add significant overhead, has been circumvented. Much of the research effort has been focused on finite element implementations of the isogeometric concept, but at present, little has been seen on the application to the Boundary Element Method. The current paper proposes an Isogeometric Boundary Element Method (BEM), which we term IGABEM, applied to two-dimensional elastostatic problems using Non-Uniform Rational B-Splines (NURBS). We find it is a natural fit with the isogeometric concept since both the NURBS approximation and BEM deal with quantities entirely on the boundary. The method is verified against analytical solutions where it is seen that superior accuracies are achieved over a conventional quadratic isoparametric BEM implementation. © 2011 Elsevier B.V. [less ▲] Detailed reference viewed: 231 (7 UL)A locking-free meshfree method for the simulation of shear-deformable plates based on a mixed variational formulation Hale, Jack ; in Computer Methods in Applied Mechanics and Engineering (2012), 241-244 The problem of shear-locking in the thin-plate limit is a well known issue that must be overcome when discretising the Reissner-Mindlin plate equations. In this paper we present a shear-locking-free ... [more ▼] The problem of shear-locking in the thin-plate limit is a well known issue that must be overcome when discretising the Reissner-Mindlin plate equations. In this paper we present a shear-locking-free method utilising meshfree maximum-entropy basis functions and rotated Raviart-Thomas-Nédélec elements within a mixed variational formulation. The formulation draws upon well known techniques in the finite element literature. Due to the inherent properties of the maximum-entropy basis functions our method allows for the direct imposition of Dirichlet (essential) boundary conditions, in contrast to methods based on moving least squares basis functions. We present benchmark problems that demonstrate the accuracy and performance of the proposed method. © 2012. [less ▲] Detailed reference viewed: 212 (19 UL)Finite element analysis on implicitly defined domains: An accurate representation based on arbitrary parametric surfaces ; ; et al in Computer Methods in Applied Mechanics and Engineering (2011), 200(5-8), 774-796 In this paper, we present some novel results and ideas for robust and accurate implicit representation of geometric surfaces in finite element analysis. The novel contributions of this paper are threefold ... [more ▼] In this paper, we present some novel results and ideas for robust and accurate implicit representation of geometric surfaces in finite element analysis. The novel contributions of this paper are threefold: (1) describe and validate a method to represent arbitrary parametric surfaces implicitly; (2) represent arbitrary solids implicitly, including sharp features using level sets and boolean operations; (3) impose arbitrary Dirichlet and Neumann boundary conditions on the resulting implicitly defined boundaries. The methods proposed do not require local refinement of the finite element mesh in regions of high curvature, ensure the independence of the domain's volume on the mesh, do not rely on boundary regularization, and are well suited to methods based on fixed grids such as the extended finite element method (XFEM). Numerical examples are presented to demonstrate the robustness and effectiveness of the proposed approach and show that it is possible to achieve optimal convergence rates using a fully implicit representation of object boundaries. This approach is one step in the desired direction of tying numerical simulations to computer aided design (CAD), similarly to the isogeometric analysis paradigm. © 2010 Elsevier B.V. [less ▲] Detailed reference viewed: 478 (9 UL)Isogeometric analysis using polynomial splines over hierarchical T-meshes for two-dimensional elastic solids ; ; Bordas, Stéphane et al in Computer Methods in Applied Mechanics and Engineering (2011), 200(21-22), 1892-1908 Isogeometric analysis has become a powerful alternative to standard finite elements due to its flexibility in handling complex geometries. One of the major drawbacks of NURBS-based isogeometric finite ... [more ▼] Isogeometric analysis has become a powerful alternative to standard finite elements due to its flexibility in handling complex geometries. One of the major drawbacks of NURBS-based isogeometric finite elements is the inefficiency of local refinement. In this study, we present an alternative to NURBS-based isogeometric analysis that allows for local refinement. The idea is based on polynomial splines and exploits the flexibility of T-meshes for local refinement. The shape functions satisfy important properties such as non-negativity, local support and partition of unity. Several numerical examples are used to demonstrate the reliability of the present method. [less ▲] Detailed reference viewed: 134 (2 UL) |
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