An Enriched Equilibrium Finite Element Method for Crack Problems With Direct Access to Stress Intensity Factors and Strict Error Estimation

In this work, the functionally graded magneto-electro-elastic (FG-MEE) structures were used to study mechanical performance under a thermal environment using the thermo-mechanical-electro-magnetic enriched finite element method (TMEM-EFEM). Through enhancing the traditional solution space of the finite element method (FEM), additional degrees of freedom are introduced without modifying the mesh structure. Therefore, as a class of higher-order finite element methods, field variables with high gradients can be captured without a relatively finer mesh. The accuracy of TMEM-EFEM is improved by using interpolation covers. The feasibility of TMEM-EFEM is proven by numerical examples. The proposed TMEM-EFEM is proven to be accurate under the relatively coarse mesh. Through numerical examples, the high accuracy of TMEM-EFEM is demonstrated. Therefore, TMEM-EFEM can be a good alternative for the statics study of FG-MEE structures.

An enriched finite element method with interpolation cover functions for acoustic analysis in high frequencies

Magneto-electro-elastic (MEE) composites have promising application prospects due to the rapid response to the excitation of external electric or magnetic fields. Finite element simulation of the multi-physics coupling problems in MEE-based structures is significant. The enriched finite element method (EFEM) is derived from the standard finite element method (FEM), with finite element shape functions improved by interpolation covers. Considering the complex mechanical-electro-magnetic multi-physics coupling mechanism of MEE-based structures, the mechanical-electro-magnetic coupling enriched finite element method (MEM-EFEM) was proposed. The method is well worked for investigating the mechanical-electro-magnetic multi-physics coupling issues to calculate the generalized displacement (displacement components, electric and magnetic potential) with 3-node triangular elements. In a set of numerical experiments involving the static analysis of MEE-based structures, MEM-EFEM outperforms the regular FEM. When it comes to the same solution accuracy level, the number of elements used by MEM-EFEM is lower than that of the standard FEM, suggesting that MEM-EFEM has better convergence and accuracy on this subject. Besides, the MEM-EFEM solution accuracy can be enhanced by mesh refinement. Overall, the MEM-EFEM has the potential to be used in engineering practice to solve the static responses of MEE-based structures on mechanical-electro-magnetic multi-physics coupling issues.

Elastodynamic problems are investigated in this work by employing the enriched finite element method (EFEM) with various enrichment functions. By performing the dispersion analysis, it is confirmed that for elastodynamic analysis, the amount of numerical dispersion, which is closely related to the numerical error from the space domain discretization, can be suppressed to a very low level when quadric polynomial bases are employed to construct the local enrichment functions, while the amount of numerical dispersion from the EFEM with other types of enrichment functions (linear polynomial bases or first order of trigonometric functions) is relatively large. Consequently, the present EFEM with a quadric polynomial enrichment function shows more powerful capacities in elastodynamic analysis than the other considered numerical techniques. More importantly, the attractive monotonic convergence property can be broadly realized by the present approach with the typical two-step Bathe temporal discretization technique. Three representative numerical experiments are conducted in this work to verify the abilities of the present approach in elastodynamic analysis.

This paper presents a novel numerical method for simulating the transport and dispersion of pollutants in the Mediterranean sea. The governing mathematical equations consist of a barotropic ocean model with friction terms, bathymetric forces, Coriolis and wind stresses coupled to an advection–diffusion equation with anisotropic dispersion tensor and source terms. The proposed numerical solver uses a multilevel adaptive semi-Lagrangian finite element method that combines various techniques, including the modified method of characteristics, finite element discretization, coupled projection scheme based on a rotational pressure correction algorithm, and an adaptive L2-projection. The approach employs the gradient of the concentration as an error indicator for enrichment adaptations and increasing the number of quadrature points where needed without refining the mesh. The method is shown to provide accurate and efficient simulations for pollution transport in the Mediterranean sea. The proposed approach distinguishes itself from the well-established adaptive finite element methods for incompressible viscous flows by retaining the same structure and dimension of linear systems during the adaptation process.

On the computation of mixed-mode stress intensity factors in functionally graded materials

Extended finite element modeling of deformable porous media with arbitrary interfaces

Enriched finite element methods have gained traction in recent years for modeling problems with material interfaces and cracks. By means of enrichment functions that incorporate a priori behavior about the solution, these methods decouple the finite element (FE) discretization from the geometric configuration of such discontinuities. Taking advantage of this greater flexibility, recent studies have proposed the adoption of Non-Uniform Rational B-Splines (NURBS) to preserve the interfaces' exact geometries throughout the analysis. In this article, we investigate NURBS-based geometries in the context of the Discontinuity-Enriched Finite Element Method (DE-FEM) based on linear field approximations. While optimal convergence is retained for problems with weak discontinuities without singularities, representing exact geometry via NURBS does not yield noticeable improvements when extracting stress intensity factors of cracked specimens. For low-order elements, we conclude that the benefits of exact geometry representation do not outweigh the increased complexity in formulation and implementation. The choice of linear FEs hinders the accuracy of the proposed formulation, suggesting that its full potential may only be unleashed by increasing the field representation order.

An enriched finite element method is presented to numerically solve the eigenvalue problem on electromagnetic waveguides governed by the Helmholtz equation. In this work, a highly efficient, simple and precise higher order subparametric method was developed using a 2D automated mesh generator performed with JuliaFEM. The transcendence computerized discretization code in Julia is developed for the present work. For curved waveguide structures, meshes with one side and curving higher orders are proposed with triangular elements with parabolic arcs. The technique is shown for distinct waveguide constructions, and the results are compared with the strongest numerical or analytical results available. The results demonstrate that the proposed methodology is effective and accurate for generating finite element simulations for complex structures with black holes and irregular topology due to no curvature loss. This article presents a finding cutoff frequency performed with JuliaFEM—an open-source program. Analysis results produced by commercial software are considered for the comparison and show that the calculation results between the two programs do not differ significantly. This procedure can be used to achieve the most effective transmission of energy for electromagnetic applications.

Singular perturbation theory is used to solve the integral equations which occur when treating finite-length crack problems in porous elastic materials. The method provides the stress intensity factors which characterize the near crack tip stress and displacement fields for small times. The method also gives the stress and pore pressure fields on the fracture plane for small times relative to the diffusive time scale. In this paper, the authors treat crack problems which are unmixed in the pore pressure boundary condition on the fracture plane. The Abelian result that small times correspond, in Laplace transform space, to large values of the transform variable is used to formulate the problems in terms of a small parameter. Rescaling on this small parameter leads to inner problems which are eigensolutions of the semi-infinite problems treated earlier by the authors. The outer solutions are given by elastic eigensolutions together with appropriate fluid dipole responses. These outer solutions give the complete stress and pore pressure fields except in the neighbourhood of the crack tips; in this region the outer solutions are asymptotically matched with inner solutions. The full outer solutions are given here as an asymptotic expansion for small times and enable the development of the outer fields to be followed in real time. A reciprocal theorem in Laplace transform space is used to check the small-time solutions. The inner problem is rescaled to a semi-infinite crack problem, so eigensolutions of this semi-infinite problem are used together with the known asymptotic behaviour of the real solution to identify the stress intensity factor. The stress intensity factor is then related to an integral involving the inner limit of the outer solution together with the eigensolution of the semi-infinite problem. Using this integral, we recover the result for the stress intensity factor found using singular perturbation theory. A ‘nearly’ invariant integral analogous to the invariant M integral used in elastostatics is derived. Unfortunately, the poroelastic analogue is not invariant, although it is used to verify the small-time results.

Adaptive Gaussian process regression as an alternative to FEM for prediction of stress intensity factor to assess fatigue degradation in offshore pipeline

Application of virtual crack closure integral method for interface cracks in low- k integrated circuit devices under thermal load

A new numerical approach for fluid-structure interaction of viscous fluid flow and flexible structures of negligible thickness (e.g. membranes, plates) on a topologically fixed fluid discretization is presented. The linear elastic and geometrically nonlinear structure is embedded [1] into the flow field described by the incompressible Navier-Stokes equations using locally enriched space-time (EST) finite elements [2], [3] to consider resulting strong and weak discontinuities in the fluid field appropriately [4]. Since the formulation of fluid, structure and coupling conditions uniformly uses velocities as unknowns and the integration of governing equations is perfomed on the deformed space-time mesh, the simulation of the strongly coupled physical domains becomes very comfortable and results in a monolithic system [5]. Numerical examples of fluid-stucture interaction processes show the ability of the developed numerical method to describe those situations of coupled systems for that common mesh moving strategies are not useful applicable and would require the introduction of time-consuming remeshing algorithms.

The stress intensity factors or strain energy release rate are typically used to characterise the stress field in the vicinity of a crack in fracture mechanics. One way to obtain the strain energy release rate in elastic–plastic fracture mechanics is from the stress and deformation field around the crack tip through the calculation of the J integral. The J-integral is contour independent, although the contour must start and end from a traction-free surface, such as the crack surface. Using Green’s theorem, the J-integral can be formulated as a surface or area integral, which makes it convenient for implementation in finite element method (FEM). More importantly, the J-integral calculation is insensitive to uncertainty of the exact crack tip location, can be applied for linear elastic analysis with small scale yielding and in an improved formulation for elastic plastic fracture. In short, the J-integral is an indispensable tool in the study of fracture mechanics. Despite the J-integral being widely used in FEM, including availability in most commercial FEM codes, there is currently no algorithm to calculate the J-integral in the Smoothed Particle Hydrodynamics (SPH) method. This is somewhat surprising since the SPH method, due to its meshless nature, has inherent advantages in dealing with cracks compared to mesh based methods such as FEM. In this paper we will therefore address this deficiency and develop an algorithm for calculation of the J integral in the SPH method. The implementation of his new alghorithm is based on a new definition of the weighting function q 1 , as appropriately normalised kernel function, which inherently satisfies all the specific requirements on q 1 : The function is sufficiently smooth in the J-integral area, it is equal to unit inside contour path of the integral and zero outside of the path. A further element of novelty is that in the current implementation, the gradient of this function is evaluated analytically rather than through a numerical approximation. The verification and validation of developed algorithm is based on simulation of the standard single edge notch tension test (SENT) under the plain strain conditions. The SPH results are compared to the FEM results for stress and displacement fields in the vicinity of the crack tip, as well as the J integral solutions. The SPH results demonstrated convergence and were within 2% of the converged FEM solutions. The validation also allows for the definition of simple guidelines for the definition of the J-integral area to achieve accurate results. The implementation is currently developed for linear elastic fracture mechanics applications, but its generalisation and application to elastic plastic fracture mechanics, including the combination with elastic plastic constitutive models is straightforward. • New algorithm to calculate J-Integral developed in Smoothed Particle Hydrodynamics (SPH). • New approach for calculating gradient of J-Integral weighting function q 1 analytically. • Confirmed accuracy of J-integral results from SPH compared to FEM results.

An explosion clad plate composed of copper and mild steel is dealt with as a typical example of the bonded dissimilar plate. Tensile tests are carried out using rectangular plate specimens extracted from the clad plate. An artificial through-the-thickness edge crack or parallel cracks are made in each specimen. The cracks are close and perpendicular to the explosive interface. When a tensile load is applied perpendicularly to the crack plane, stress field near cracks, stress intensity factor, crack opening displacement and fracture strength are examined by experiment as well as elasto-plastic finite element analysis. The stress field and the stress intensity factor are evaluated by an infrared stress imaging system. The effects of the material inhomogeneity, the residual stress, the change of material characteristics and the interaction of parallel cracks on the stress field, the stress intensity factor, the deformation behavior and the fracture strength are revealed. The lower strength material ahead of the bonded interface increases the stress intensity factor and the crack opening displacement. The higher strength material ahead of the bonded interface decreases the stress intensity factor and the crack opening displacement. The effects of the material inhomogeneity and the interaction of parallel cracks on the crack opening displacement can be explained from the square of stress intensity factor at the low applied stress level. The brittle fracture strength of the inhomogeneous specimen can be evaluated from the stress intensity factor and linear elastic fracture mechanics criterion.