An efficient variable-node XFEM for modeling multiple crack growth: A Matlab object-oriented implementation

Multiple fatigue crack growth in pre-corroded 2024-T3 aluminum

We present a 3D forward modeling algorithm of marine controlled-source electromagnetic (CSEM) fields using finite element method based on unstructured meshes. As the unstructured mesh is incorporated, the algorithm can easily accommodate complex structures, such as dipping interfaces and rough topography. Secondary coupled-potential formulation of Maxwell's equations allows to avoid the singularities introduced by the sources. The primary electromagnetic fields excited by electric dipole source in layered isotropic media are derived from the semi-analytical formulas based on Schelkunoff potentials. To improve the accuracy and efficiency of the algorithm, we propose an effective local mesh refinement strategy, where the elements near the receiver locations and in the abnormal areas are refined using the volume constraints. We validate the finite element code against a 1D and 2D reservoir model and study the performance of the local mesh refinement strategy. The Canonical disc model illustrates the utility of the finite element method for 3D CSEM modeling. The bathymetry model study shows that the seafloor topography gives an important response which needs to be reproduced by numerical modeling to avoid the misinterpretation of measurements.

This paper deals with optimal control problems constrained by linear elliptic partial differential equations. The case where the right‐hand side of the Neumann boundary is controlled, is studied. The variational discretization concept for these problems is applied, and discretization error estimates are derived. On polyhedral domains, one has to deal with edge and corner singularities, which reduce the convergence rate of the discrete solutions, that is, one cannot expect convergence order two for linear finite elements on quasi‐uniform meshes in general. As a remedy, a local mesh refinement strategy is presented, and a priori bounds for the refinement parameters are derived such that convergence with optimal rate is guaranteed. As a by‐product, finite element error estimates in the H1(Ω)‐norm, L2(Ω)‐norm and L2(Γ)‐norm for the boundary value problem are obtained, where the latter one turned out to be the main challenge. Copyright © 2015 John Wiley & Sons, Ltd.

An explicit time integration algorithm to solve the two-dimensional Navier-Stokes equations on general N-sided polygons is presented. The integral form of the equations are descritized on a set of non-overlapping polygons yielding a data structure where the flow variables are stored at cell centers. An edge-base data structure is utilized to obtain maximum flexibility and allow the use of polygons with any number of faces. The edgebased data structure allowed the scheme to be extended to allow a local mesh refinement strategy in areas where flow solution errors were deemed to be the greatest. A Roe-Averaged Riemann solver is utilized to evaluate the numerical flux at the cell faces and higher order accuracy is achieved by linear reconstruction on the cell-averaged data and using a monotone preserving limiter to achieve smooth results near flow discontinuities.

In this paper, novel finite elements that include an arbitrary number of additional nodes on each edge of a quadrilateral element are proposed to achieve compatible connection of neighboring nonmatching meshes in plate and shell analyses. The elements, termed variable-node plate elements, are based on two-dimensional variable-node elements with point interpolation and on the Mindlin---Reissner plate theory. Subsequently the flat shell elements, termed variable-node shell elements, are formulated by further extending the plate elements. To eliminate a transverse shear locking phenomenon, the assumed natural strain method is used for plate and shell analyses. Since the variable-node plate and shell elements allow an arbitrary number of additional nodes and overcome locking problems, they make it possible to connect two nonmatching meshes and to provide accurate solutions in local mesh refinement. In addition, the curvature and strain smoothing methods through smoothed integration are adopted to improve the element performance. Several numerical examples are presented to demonstrate the effectiveness of the elements in terms of the accuracy and efficiency of the analyses.

Linear Elastic Fracture Mechanics (LEFM) provides a quantitative description of the crack motion that agrees well with observations in brittle materials as long as the crack growth is sufficiently slow. However, several issues remain unsolved: (i) experimental observations reveal that at high velocity, the crack speed is systematically smaller than the one predicted by LEFM [1] and (ii) above a given velocity, a dynamically growing crack creates a structure of its own as evidenced from roughening of fracture surfaces at high speed [2]. The aim of this work is to present a statistical study and a deterministic reconstruction of the morphology of the fracture surfaces in Plexiglas obtained under dynamic conditions.

Non-planar crack growth analyses of multiple cracks in thin-walled structures

Multiple crack propagation in a strip caused by thermal shock

Fracture analysis of a single edge cracked strip under thermal shock

This paper summarizes three recent experimental works coauthored by the present author regarding the effect of crack instability/stability on fracture toughness, and also includes the necessary formulae for predicting stability. Two recent works have shown that unstable crack extension resulted in apparent increases in fracture toughness compared to that determined during stable crack growth. In the first investigation a quasi-brittle polymer, polymethylmethacrylate, was examined. In the second, a more brittle metallic material. tungsten, was tested. In both cases the transition from unstable to stable behavior was predicted based on stability analyses. The third investigation was conducted on a truly brittle ceramic material, hot pressed silicon nitride. These three papers showed that fracture toughness test results conducted on brittle materials vary according to whether the material fractures in an unstable or stable manner. Suggestions for achieving this important yet difficult phenomenon of stable crack growth, which is necessary when determining the fracture toughness variation occurring during unstable/stable crack advance, are presented, as well as recommendations for further research .

A method for modelling the growth of multiple cracks in linear elastic media is presented. Both homogeneous and inhomogeneous materials are considered. The method uses the extended finite element method for arbitrary discontinuities and does not require remeshing as the cracks grow; the method also treats the junction of cracks. The crack geometries are arbitrary with respect to the mesh and are described by vector level sets. The overall response of the structure is obtained until complete failure. A stability analysis of competitive cracks tips is performed. The method is applied to bodies in plane strain or plane stress and to unit cells with 2–10 growing cracks (although the method does not limit the number of cracks). It is shown to be efficient and accurate for crack coalescence and percolation problems. Copyright © 2004 John Wiley & Sons, Ltd.

SummaryAdaptive local refinement is one of the main issues for isogeometric analysis (IGA). In this paper, an adaptive extended IGA (XIGA) approach based on polynomial splines over hierarchical T‐meshes (PHT‐splines) for modeling crack propagation is presented. The PHT‐splines overcome certain limitations of nonuniform rational B‐splines–based formulations; in particular, they make local refinements feasible. To drive the adaptive mesh refinement, we present a recovery‐based error estimator for the proposed method. The method is based on the XIGA method, in which discontinuous enrichment functions are added to the IGA approximation and this method does not require remeshing as the cracks grow. In addition, crack propagation is modeled by successive linear extensions that are determined by the stress intensity factors under linear elastic fracture mechanics. The proposed method has been used to analyze numerical examples, and the stress intensity factors results were compared with reference results. The findings demonstrate the accuracy and efficiency of the proposed method.

Dynamic fracture analysis of the linearly uncoupled and coupled physical phenomena by the variable-node multiscale XFEM

For the purpose of realizing the brittle material's turning in ductile mode on the basis of optimizing the diamond cutting tool's geometrical parameters, the Linear Elastic Fracture Mechanics and Finite Element Method are applied to stimulate the stress distribution and micro-cracks' propagation in the cutting region generated under different rake angles and edge radius. The cutting experiments on single crystal silicon surface are then conducted to verify the stimulation results, which show that the propagation of micro-cracks can be restrained from atomic-size cracks when utilizing the diamond cutting tools with -15 degree to -25 degree rake angles. As a result of increasing the critical depth of cut value of brittle-ductile transition, the goal of ductile-mode turning can be achieved. In addition, with a smaller cutting edge radius, the turning of brittle material in ductile-mode can be easily realized, resulting in good diamond turned surface quality.

Mechanistic understanding of the fracture toughening in chemically strengthened glass—experiments and phase-field fracture modeling