Simple Remeshing Research Articles

Interlocked archimedean spirals for conversion of planar rigid panels into locally flexible panels with stiffness control

We present a relief cutting method to turn rigid planar surfaces into flexible ones using meander patterns that consist of interlocked Archimedean spirals. We have developed an approach to obtain all possible such 2D meander patterns with a set of simple remeshing processes. Our algorithm can be applied to any polygonal mesh to produce 2D meander patterns. Since these meander patterns are obtained by remeshing processes, we can control the local properties of the pattern with intensity of images to obtain different stiffness values in different regions. This approach provides a simple interface to construct desired patterns.

Quasi-Static Crack Propagation Modeling Using Shape-Free Hybrid Stress-Function Elements with Drilling Degrees of Freedom

A new plane shape-free multi-node singular hybrid stress-function (HS-F) element with drilling degrees of freedom, which can accurately capture the stress intensity factors at the crack tips, is developed. Then, a quasi-static 2D crack propagation modeling strategy is established by combination of the new singular element and a shape-free 4-node HS-F plane element with drilling degrees of freedom proposed recently. Only simple remeshing with an unstructured mesh is needed for each simulation step. Numerical results show that the proposed scheme is an effective and robust technique for dealing with the crack propagation problems.

Experimental and numerical study of the dependency of interface fracture in concrete–rock specimens on mode mixity

The interface between the concrete and the rock is usually considered the weakest link in concrete structures built on rock foundations. The fracture behaviour at the concrete–rock interface is influenced by many factors e.g. the material properties of the individual constituents, the fracture process zone at the interface and the mode mixity ratio. This paper investigates the dependency of the fracture behaviour of concrete–rock interfaces on the mode mixity ratio using experimental and numerical methods. The experimental program involves four-point-shearing of concrete–rock composite beams. It is designed to test a wide range of mode mixity ratio. Using linear elastic fracture mechanics theory, the fracture toughness and the fracture energy are first quantified in terms of the mode mixity ratio. The scaled boundary finite element method, which is known for its accuracy in modelling fracture, is used to compute the fracture toughness and fracture energy. Next, the crack propagation process of the concrete–rock composite beam is modelled using nonlinear fracture mechanics theory. The scaled boundary finite element method is coupled with interface elements to model the fracture process zone, which is a characteristic of fracture in quasi-brittle materials such as concrete and rock. A revised scaled boundary finite element method formulation using generalized coordinates is used to model the cohesive tractions. The cohesive crack at the interface is assumed to propagate when either the Mode 1 or the Mode 2 stress intensity factors change sign. A simple remeshing algorithm is used to propagate the crack at the interface. The numerical simulations are validated by the experimental measurements. The simulated crack propagation processes are described in terms of the mode mixity ratio.

A quasi-static crack propagation simulation based on shape-free hybrid stress-function finite elements with simple remeshing

In this paper, a new shape-free multi-node singular hybrid stress-function (HSF) element and a shape-free 8-node plane HSF element proposed recently are employed to simulate the quasi-static 2D crack propagation problem. Compared with other well-known methods, such new scheme exhibits four advantages: (i) for the singular element, the shape and the number of nodes can be flexibly adjusted as required; (ii) high precision for stress intensity factors (SIF) can be obtained due to the advantages of the HSF method; (iii) only simple remeshing with a very coarse mesh is needed for each simulation step; (iv) unstructured mesh containing extremely distorted elements can be used without losing precision. It demonstrates that the proposed scheme is an effective technique for dealing with crack propagation problems.

Dynamic crack propagation analysis using scaled boundary finite element method

The prediction of dynamic crack propagation in brittle materials is still an important issue in many engineering fields. The remeshing technique based on scaled boundary finite element method (SBFEM) is extended to predict the dynamic crack propagation in brittle materials. The structure is firstly divided into a number of superelements, only the boundaries of which need to be discretized with line elements. In the SBFEM formulation, the stiffness and mass matrices of the super-elements can be coupled seamlessly with standard finite elements, thus the advantages of versatility and flexibility of the FEM are well maintained. The transient response of the structure can be calculated directly in the time domain using a standard time-integration scheme. Then the dynamic stress intensity factor (DSIF) during crack propagation can be solved analytically due to the semi-analytical nature of SBFEM. Only the fine mesh discretization for the crack-tip super-element is needed to ensure the required accuracy for the determination of stress intensity factor (SIF). According to the predicted crack-tip position, a simple remeshing algorithm with the minimum mesh changes is suggested to simulate the dynamic crack propagation. Numerical examples indicate that the proposed method can be effectively used to deal with the dynamic crack propagation in a finite sized rectangular plate including a central crack. Comparison is made with the results available in the literature, which shows good agreement between each other.

Some applications of Loop-subdivision wavelet tight frames to the processing of 3D graphics

Multiresolution analysis based on subdivision wavelets is an important method of 3D graphics processing. Many applications of this method have been studied and developed, including denoising, compression, progressive transmission, multiresolution editing and so on. Recently Charina and Stockler firstly gave the explicit construction of wavelet tight frame transform for subdivision surfaces with irregular vertices, which made its practical applications to 3D graphics became a subject worthy of investigation. Based on the works of Charina and Stockler, we present in detail the wavelet tight frame decomposition and reconstruction formulas for Loop-subdivision scheme. We further implement the algorithm and apply it to the denoising, compression and progressive transmission of 3D graphics. By comparing it with the biorthogonal Loop-subdivision wavelets of Bertram, the numerical results illustrate the good performance of the algorithm. Since multiresolution analysis based on subdivision wavelets or subdivision wavelet tight frames requires the input mesh to be semi-regular, we also propose a simple remeshing algorithm for constructing meshes which not only have subdivision connectivity but also approximate the input mesh.

Towards fully automatic modelling of the fracture process in quasi-brittle and ductile materials: a unified crack growth criterion

Fully automatic finite element (FE) modelling of the fracture process in quasi-brittle materials such as concrete and rocks and ductile materials such as metals and alloys, is of great significance in assessing structural integrity and presents tremendous challenges to the engineering community. One challenge lies in the adoption of an objective and effective crack propagation criterion. This paper proposes a crack propagation criterion based on the principle of energy conservation and the cohesive zone model (CZM). The virtual crack extension technique is used to calculate the differential terms in the criterion. A fully-automatic discrete crack modelling methodology, integrating the developed criterion, the CZM to model the crack, a simple remeshing procedure to accommodate crack propagation, the J2 flow theory implemented within the incremental plasticity framework to model the ductile materials, and a local arc-length solver to the nonlinear equation system, is developed and implemented in an in-house program. Three examples, i.e., a plain concrete beam with a single shear crack, a reinforced concrete (RC) beam with multiple cracks and a compact-tension steel specimen, are simulated. Good agreement between numerical predictions and experimental data is found, which demonstrates the applicability of the criterion to both quasi-brittle and ductile materials.

Modelling cohesive crack growth using a two-step finite element-scaled boundary finite element coupled method

A two-step method, coupling the finite element method (FEM) and the scaled boundary finite element method (SBFEM), is developed in this paper for modelling cohesive crack growth in quasi-brittle normal-sized structures such as concrete beams. In the first step, the crack trajectory is fully automatically predicted by a recently-developed simple remeshing procedure using the SBFEM based on the linear elastic fracture mechanics theory. In the second step, interfacial finite elements with tension-softening constitutive laws are inserted into the crack path to model gradual energy dissipation in the fracture process zone, while the elastic bulk material is modelled by the SBFEM. The resultant nonlinear equation system is solved by a local arc-length controlled solver. Two concrete beams subjected to mode-I and mixed-mode fracture respectively are modelled to validate the proposed method. The numerical results demonstrate that this two-step SBFEM-FEM coupled method can predict both satisfactory crack trajectories and accurate load-displacement relations with a small number of degrees of freedom, even for crack growth problems with strong snap-back phenomenon. The effects of the tensile strength, the mode-I and mode-II fracture energies on the predicted load-displacement relations are also discussed.

Finite element modelling of multiple cohesive discrete crack propagation in reinforced concrete beams

This paper presents a finite element (FE) model for fully automatic simulation of multiple discrete crack propagation in reinforced concrete (RC) beams. The discrete cracks are modelled based on the cohesive/fictitious crack concept using nonlinear interface elements with a bilinear tensile softening constitutive law. The model comprises an energy-based crack propagation criterion, a simple remeshing procedure to accommodate crack propagations, two state variable mapping methods to transfer structural responses from one FE mesh to another, and a local arc-length algorithm to solve system equations characterised by material softening. The bond-slip behaviour between reinforcing bars and surrounding concrete is modelled by a tension-softening element. An example RC beam with well-documented test data is simulated. The model is found capable of automatically modelling multiple crack propagation. The predicted cracking process and distributed crack pattern are in close agreement with experimental observations. The load–deflection relations are accurately predicted up to a point when compressive cracking becomes dominant. The effects of bond-slip modelling and the efficiency and effectiveness of the numerical algorithms, together with the limitations of the current model, are also discussed.

Fully automatic modelling of cohesive discrete crack propagation in concrete beams using local arc-length methods

A finite element model for fully automatic simulation of multi-crack propagation in concrete beams is presented. Nonlinear interface elements are used to model discrete cracks with concrete tensile behaviour represented by the cohesive crack model. An energy-based crack propagation criterion is used in combination with a simple remeshing procedure to accommodate crack propagation. Various local arc-length methods are employed to solve the material-nonlinear system equations characterised by strong snap-back. Three concrete beams, including a single-notched three-point bending beam (mode-I fracture), a single-notched four-point shear beam (mixed-mode fracture) and a double-notched four-point shear beam (mixed-mode fracture), are modelled. Comparisons of the numerical results with experimental data show that this model is capable of fully automatically modelling concrete tensile fracture process with accurate pre/post-peak load–displacement responses and crack trajectories. Its mesh-objective nature, together with the high efficiency of the energy crack propagation criterion, makes using coarse meshes to obtain reasonably accurate simulations possible. The local arc-length numerical algorithms are found to be capable of tracking complex equilibrium paths including strong snap-back with high robustness, generality and efficiency.

Quasilinear formulation with a simple remeshing scheme for the finite element based simulation of dopant diffusion in silicon

The weighted residual formulation of the finite-element method is used to solve the nonlinear diffusion equation which describes dopant diffusion. Discretisation in the time domain is carried out using the Crank-Nicolson implicit scheme. A remeshing scheme based on a continuity criterion obtained by comparing the concentration values of adjacent nodes is used to introduce or eliminate nodes in the spatial domain as the diffusion proceeds in time. This scheme which uses an average diffusivity across each element has been successfully applied to the simulation of As diffusion in Si, and overcomes the oscillation and instability which would otherwise occur if a uniform mesh with the same number of nodes were used.