Mesh‐free simulation of ductile fracture

This paper is concerned with mesh‐free simulations of crack growth in ductile materials, which is a major technical difficulty in computational mechanics. The so‐called reproducing kernel particle method, which is a member of the mesh‐free method family, is used together with the Gurson–Tvergaard–Needleman constitutive model for simulation of ductile fracture. A study has been carried out to compare the proposed mesh‐free simulation with the available experimental results and previous finite element simulations for crack propagation in a three‐point‐bending steel specimen. The results show that the mesh‐free simulation agrees well with experimental results, and it is confirmed that the proposed method provides a convenient and yet accurate means for simulation of ductile fracture. Copyright © 2004 John Wiley & Sons, Ltd.     

Ductile tearing analyses of cracked TP304 pipes using the multiaxial fracture strain energy model and the Gurson–Tvergaard–Needleman model

Ductile crack growth behaviours of TP304 pipes containing different circumferential defects were investigated in the study. Finite element (FE) damage analysis of the ductile fracture was carried out based on an uncoupled multiaxial fracture strain energy (MFSE) model with only two model parameters, which can be calibrated by data from tensile tests and fracture toughness tests. For the purpose of comparison, the Gurson–Tvergaard–Needleman (GTN) model was also employed in the FE damage analysis. It is observed that the MFSE model can reproduce the ductile tearing experiments as excellently as the GTN model does. Despite its simplicity, the MFSE model can reasonably predict the magnitudes of the crack initiation load and maximum load, the load‐line displacement, the crack mouth opening displacement, the crack extension and the crack profiles in the full‐scale cracked pipe tests.     

Extended Voronoi cell finite element model for multiple cohesive crack propagation in brittle materials

This paper introduces an extended Voronoi cell finite‐element model (X‐VCFEM) for modelling cohesive crack propagation in brittle materials with multiple cracks. The cracks are modelled by a cohesive zone model and their incremental directions and growth lengths are determined in terms of the cohesive energy near the crack tip. Extension to VCFEM is achieved through enhancements in stress functions in the assumed stress hybrid formulation. In addition to polynomial terms, the stress functions include branch functions in conjunction with level set methods, and multi‐resolution wavelet functions in the vicinity of crack tips. The wavelet basis functions are adaptively enriched to accurately capture crack‐tip stress concentrations. Conditions and methods of stability are enforced in X‐VCFEM for improved convergence with propagating cracks. Two classes of problems are solved and compared with existing solutions in the literature for validation of the X‐VCFEM algorithms. The first set corresponds to results for static cracks, while in the latter set, the propagation of cohesive cracks are considered. Comparison of X‐VCFEM simulation results with results in literature for several fracture mechanics problems validates the effectiveness of X‐VCFEM. Copyright © 2005 John Wiley & Sons, Ltd.     

Voronoi cell finite element model based on micropolar theory of thermoelasticity for heterogeneous materials

In this paper, a new ‘Voronoi cell finite element model’ is developed for solving steady-state heat conduction and micropolar thermoelastic stress analysis problems in arbitrary heterogeneous materials. The method is based on the natural discretization of a multiple phase domain into basic structural elements by Dirichlet Tessellation. Tessellation process results in a network of polygons called Voronoi polygons. In this paper, formulations are developed for treating these polygons as elements in a finite element mesh. Furthermore, a composite Voronoi cell finite element model is developed to account for the presence of a second phase inclusion within a polygonal element. Various numerical examples are executed for validating the effectiveness of this model in the analysis of the temperature and stress fields for micropolar elastic materials. Effective material properties are derived for microstructures containing different distributions of second phase.     

Multiple cohesive crack growth in brittle materials by the extended Voronoi cell finite element model

This paper is aimed at modeling the propagation of multiple cohesive cracks by the extended Voronoi cell finite element model or X-VCFEM. In addition to polynomial terms, the stress functions in X-VCFEM include branch functions in conjunction with level set methods and multi-resolution wavelet functions in the vicinity of crack tips. The wavelet basis functions are adaptively enriched to accurately capture crack-tip stress concentrations. Cracks are modeled by an extrinsic cohesive zone model in this paper. The incremental crack propagation direction and length are adaptively determined by a cohesive fracture energy based criterion. Numerical examples are solved and compared with existing solutions in the literature to validate the effectiveness of X-VCFEM. The effect of cohesive zone parameters on crack propagation is studied. Additionally, the effects of morphological distributions such as length, orientation and dispersion on crack propagation are studied.     

On stabilized finite element methods for the Reissner–Mindlin plate model

Stabilized finite element formulation for the Reissner–Mindlin plate model is considered. Physical interpretation for the stabilization procedure for low‐order elements is established. Explicit interpolation functions for linear and bilinear stabilized MITC elements are derived. Some numerical examples including buckling and frequency analyses are presented. Copyright © 2007 John Wiley & Sons, Ltd.     

An enhanced cell‐based smoothed finite element method for the analysis of Reissner–Mindlin plate bending problems involving distorted mesh

In this work, an enhanced cell‐based smoothed finite element method (FEM) is presented for the Reissner–Mindlin plate bending analysis. The smoothed curvature computed by a boundary integral along the boundaries of smoothing cells in original smoothed FEM is reformulated, and the relationship between the original approach and the present method in curvature smoothing is established. To improve the accuracy of shear strain in a distorted mesh, we span the shear strain space over the adjacent element. This is performed by employing an edge‐based smoothing technique through a simple area‐weighted smoothing procedure on MITC4 assumed shear strain field. A three‐field variational principle is utilized to develop the mixed formulation. The resultant element formulation is further reduced to a displacement‐based formulation via an assumed strain method defined by the edge‐smoothing technique. As the result, a new formulation consisting of smoothed curvature and smoothed shear strain interpolated by the standard transverse displacement/rotation fields and smoothing operators can be shown to improve the solution accuracy in cell‐based smoothed FEM for Reissner–Mindlin plate bending analysis. Several numerical examples are presented to demonstrate the accuracy of the proposed formulation.Copyright © 2013 John Wiley & Sons, Ltd.     

A physically and geometrically nonlinear scaled‐boundary‐based finite element formulation for fracture in elastomers

This paper is devoted to the formulation of a plane scaled boundary finite element with initially constant thickness for physically and geometrically nonlinear material behavior. Special two‐dimensional element shape functions are derived by using the analytical displacement solution of the standard scaled boundary finite element method, which is originally based on linear material behavior and small strains. These 2D shape functions can be constructed for an arbitrary number of element nodes and allow to capture singularities (e.g., at a plane crack tip) analytically, without extensive mesh refinement. Mapping these proposed 2D shape functions to the 3D case, a formulation that is compatible with standard finite elements is obtained. The resulting physically and geometrically nonlinear scaled boundary finite element formulation is implemented into the framework of the finite element method for bounded plane domains with and without geometrical singularities. The numerical realization is shown in detail. To represent the physically and geometrically nonlinear material and structural behavior of elastomer specimens, the extended tube model and the Yeoh model are used. Numerical studies on the convergence behavior and comparisons with standard Q1P0 finite elements demonstrate the correct implementation and the advantages of the developed scaled boundary finite element. Copyright © 2014 John Wiley & Sons, Ltd.     

Anisotropic Gurson‐Tvergaard‐Needleman plasticity and damage model for finite element analysis of elastic‐plastic problems

Implementation and analysis of the anisotropic version of the Gurson‐Tvergaard‐Needleman (GTN) isotropic damage criterion are performed on the basis of Hill's quadratic anisotropic yield theory with the definition of an effective anisotropic coefficient to represent the elastic‐plastic behavior of ductile metals. This study aims to analyze the extension of the GTN model suitable for anisotropic porous metals and to investigate the GTN model extension. An anisotropic damage model is implemented using the user material subroutine in ABAQUS/standard finite element code. The implementation is verified and applied to simulate a uniaxial tensile test on a commercially produced aluminum sheet material for three‐dimensional and plane stress test cases. Spherical and ellipsoidal micro voids are considered in the matrix material, and their effects on the uniaxial stress‐strain response of the material are analyzed. Hill's quadratic anisotropic yield theory predicts substantially large damage evolution and a low stress‐strain curve compared with those predicted by the isotropic model. An approximate model for anisotropic materials is proposed to avoid increased damage evolution. In this approximate model, Hill's anisotropic constants are replaced with an effective anisotropy coefficient. All model‐generated stress‐strain predictions are compared with the experimental stress‐strain curve of AA6016‐T4 alloy.     

A rheological interface model and its space–time finite element formulation for fluid–structure interaction

This contribution discusses extended physical interface models for fluid–structure interaction problems and investigates their phenomenological effects on the behavior of coupled systems by numerical simulation. Besides the various types of friction at the fluid–structure interface the most interesting phenomena are related to effects due to additional interface stiffness and damping. The paper introduces extended models at the fluid–structure interface on the basis of rheological devices (Hooke, Newton, Kelvin, Maxwell, Zener). The interface is decomposed into a Lagrangian layer for the solid‐like part and an Eulerian layer for the fluid‐like part. The mechanical model for fluid–structure interaction is based on the equations of rigid body dynamics for the structural part and the incompressible Navier–Stokes equations for viscous flow. The resulting weighted residual form uses the interface velocity and interface tractions in both layers in addition to the field variables for fluid and structure. The weak formulation of the whole coupled system is discretized using space–time finite elements with a discontinuous Galerkin method for time‐integration leading to a monolithic algebraic system. The deforming fluid domain is taken into account by deformable space–time finite elements and a pseudo‐structure approach for mesh motion. The sensitivity of coupled systems to modification of the interface model and its parameters is investigated by numerical simulation of flow induced vibrations of a spring supported fluid‐immersed cylinder. It is shown that the presented rheological interface model allows to influence flow‐induced vibrations. Copyright © 2010 John Wiley & Sons, Ltd.     

An extended finite element formulation for contact in multi‐material arbitrary Lagrangian–Eulerian calculations

Multi‐material Eulerian and arbitrary Lagrangian–Eulerian methods were originally developed for solving hypervelocity impact problems, but they are attractive for solving a broad range of problems having large deformations, the evolution of new free surfaces, and chemical reactions. The contact, separation, and slip between two surfaces have traditionally been addressed by the mixture theory, however the accuracy of this approach is severely limited. To improve the accuracy, an extended finite element formulation is developed and example calculations are presented. As a side benefit, the mixture theory is eliminated from the multi‐material formulation, eliminating the issues associated with the equilibration time between adjacent materials. By design, the new formulation is relatively simple to implement in existing multi‐material codes, parallelizes without difficulty, and has a low memory burden. Copyright © 2006 John Wiley & Sons, Ltd.     

Dimensional model reduction in non‐linear finite element dynamics of solids and structures

A general approach to the dimensional reduction of non‐linear finite element models of solid dynamics is presented. For the Newmark implicit time‐discretization, the computationally most expensive phase is the repeated solution of the system of linear equations for displacement increments. To deal with this, it is shown how the problem can be formulated in an approximation (Ritz) basis of much smaller dimension. Similarly, the explicit Newmark algorithm can be also written in a reduced‐dimension basis, and the computation time savings in that case follow from an increase in the stable time step length. In addition, the empirical eigenvectors are proposed as the basis in which to expand the incremental problem. This basis achieves approximation optimality by using computational data for the response of the full model in time to construct a reduced basis which reproduces the full system in a statistical sense. Because of this ‘global’ time viewpoint, the basis need not be updated as with reduced bases computed from a linearization of the full finite element model. If the dynamics of a finite element model is expressed in terms of a small number of basis vectors, the asymptotic cost of the solution with the reduced model is lowered and optimal scalability of the computational algorithm with the size of the model is achieved. At the same time, numerical experiments indicate that by using reduced models, substantial savings can be achieved even in the pre‐asymptotic range. Furthermore, the algorithm parallelizes very efficiently. The method we present is expected to become a useful tool in applications requiring a large number of repeated non‐linear solid dynamics simulations, such as convergence studies, design optimization, and design of controllers of mechanical systems. Copyright © 2001 John Wiley & Sons, Ltd.     

Efficient hyper‐reduced‐order model (HROM) for thermal analysis in the moving frame

The hyper‐reduced‐order model (HROM) is proposed for the thermal calculation with a constant moving thermal load. Firstly, the constant velocity transient process is simplified to a steady‐state process in the moving frame. Secondly, the control volume is determined by the temperature rate, and the thermal equilibrium equation in the moving frame is derived by introducing an advective term containing the loading velocity. Thirdly, the HROM is performed on the control volume with a moving frame formulation. This HROM has been applied to the thermal loading on brick and ring disk specimens with a CPU gain of the order of 7 (10⁷). In addition, two strategies are proposed for the HROM to improve its precision. Moreover, the high efficiency and high accuracy are kept for the parametric studies on thermal conductivity and amplitude of heat flux based on the developed HROM. Copyright © 2016 John Wiley & Sons, Ltd.     

A domain decomposition method for a two‐phase transport model of polymer electrolyte fuel cell containing micro‐porous layer

In this paper, a nonlinear Dirichlet–Robin iteration‐by‐subdomain domain decomposition method is studied for a multidimensional, multiphysics, and multiphase model of polymer electrolyte fuel cell (PEFC) containing micro‐porous layer (MPL). Across the interface of gas diffusion layer and MPL in PEFC, it is well known that the capillary pressure is continuous, whereas liquid saturation is discontinuous, by which the liquid‐water removal in the porous electrodes can be significantly enhanced. We design a type of non‐overlapping domain decomposition method to deal with water transport in such multi‐layer diffusion media, where Kirchhoff transformation and its inverse techniques are employed to conquer the discontinuous and degenerate water diffusivity in the coexisting single‐phase and two‐phase regions. In addition, the conservation equations of mass, momentum, charge, and hydrogen and oxygen transport are also solved by the combined finite element–upwind finite volume method (FEM/FVM) to overcome the dominated convection effect in gas channels. Numerical simulations demonstrate that the presented techniques are effective in obtaining a fast and convergent nonlinear iteration for such a 3D PEFC model within around 50 steps, in contrast with the oscillatory and nonconvergent iteration conducted by standard FEM/FVM. A series of numerical convergence tests are also carried out to verify the efficiency and accuracy of the present numerical techniques. Copyright © 2012 John Wiley & Sons, Ltd.