Papers by Keyword: Extended Finite Element Method (XFEM)

Abstract: Woven glass fibre-reinforced polymer composite materials are widely used in different sectors, replacing traditional construction materials with their advantages in lightweight construction, high strength-to-weight ratio, etc., and especially their ability to impart transverse stiffness to the structure. The objective of the current investigation is to introduce a side edge notch to the laminate and study the failure pattern. The effect of crack length on the failure pattern and strength of the laminate is also studied here using the extended Finite Element Method (XFEM). Maximum stress criteria based on bilinear traction separation law are utilised for crack initiation, and critical energy release criteria are used for crack opening and propagation. The results show the effectiveness of XFEM in capturing failure patterns in the laminate for all the considered cases.

Abstract: Computational prediction of damage in cement-based composites, as steel fibre reinforced ones, under mechanical, thermal, etc. loads, manifested as creation of micro-fractured zones, followed by potential initiation and evolution of macroscopic cracks, is a rather delicatematter, due to the necessity of bridging between micro- and macro-scales. This short paper presents a relatively simple approach, using certain extension of the finite element technique, open to possible generalizations. Such model admits proper verification of its existence andconvergence results, from the physical and mathematical formulation up to software implementation of relevant algorithms. Its practical applicability is documented on computational examples.

Abstract: The paper presents results of numerical investigation of fracture behaviour of initially notched beams made of foamed concrete. Extended Finite Element Method (XFEM) was used to simulate the damage and fracture process of the beams subjected to three-point bending. Subsequently, the numerical models were validated by a series of static loading tests. Numerical models simulate correctly the fracture behaviour of beams observed during testing. XFEM method and computer simulation technologies allow for reliable approximation of load–bearing capacity and damage mechanisms of beams made of foamed concrete, which provides some foundations for realistic structural applications.

Abstract: 5XXX aircraft skin aluminum alloy needs relatively high fatigue performance to sustain complex pneumatic loading in service. Stress intensity factors are important parameters to compute fatigue crack propagation rate. XFEM was used to calculate the crack tip stress, as well as stress intensity factors (SIF) and fatigue crack propagation rate on the 5E62 alloy. Simulation results showed that the values of SIF calculated by XFEM were quite close to the theoretical values. Both the values of crack tip stress and SIF increase as crack length increasing in Paris region, resulting the increasing of fatigue crack growth rate. Fatigue crack propagation rate calculated by XFEM are consistent with the theoretical values and experimental values in Paris region.

Abstract: The extended finite element method (XFEM) is the most effective numerical method to solve discontinuous dynamic problems so far. It makes research within a standard finite element framework and needs not mesh repartition to geometric and physical interface, so it reserves all merits of the conventional finite element method (CFEM). The XFEM was applied to the penetration process for concrete target in the paper, and the displacement mode of elements with cracks and fracture criterion were presented. Then the weak solutions of control equations were discretized in different areas. The numerical examples for steel rod penetrating in the concrete target concluded that the method and program were reasonable and effective. The effect discipline of crack growth to the concrete material penetration process was summarized, and it would establish theoretic base for the further application of the XFEM.

Abstract: Composite solid propellant is a particulate composite with high volume fraction and wide size distribution, macroscopic mechanical behavior of SP is strongly depended on its mesostructure. This work presents a numerical analysis of mesostructure damage for SP based on XFEM and CZM method. A simplified physical model is used for the validation of the proposed method. It is shown that the result of crack extension agrees with experiment of Micro CT scan on the whole. Numerical simulations also indicate the fact that initiation of SP damage takes place at the interface of particle and matrix. At last, the relations of macroscopic strain and stress of SP with 55% volume fraction and 65% volume fraction AP are predicted based on mesostructure simulation and compared with experiments.

Abstract: A scheme is presented for the free vibration analysis of beam-like structures containing a crack with the extended finite element method (XFEM). The scheme is compared with the traditional scheme with the finite element method. The natural frequency of a cantilever beam is analyzed using both the methods and the results are compared. A new method for the damage identification of a cantilever beam containing a crack is then presented.

Abstract: Theoretical, experimental and simulation researches are investigated to study the phenomenon of edge chipping in laser assisted milling (LAML) of silicon nitride ceramics. To consider the crack evolution and influencing factors of edge chipping, the Extended Finite Element Method (XFEM) is used to model the process of chipping crack with the advantage of independent of the mesh and needless to remesh with the crack growth. The chipping width measured from experiments are loaded as initial boundary conditions to build the XFEM model, and the results show the edge chipping reduces with cutting forces decreasing and edge toughness increasing. The model reveals the edge chipping of workpiece reduces at elevated temperature through softening and toughening mechanisms.

Abstract: The extended finite element method (X-FEM) is reviewed and some new developments for fracture analysis of structures is presented. The X-FEM is an extension to the classical finite element method (FEM), using the concepts of partition of unity and meshless approaches. It is specifically designed to improve the performance of the conventional finite element method, while keeping the computational costs at an acceptable level, and avoiding the cumbersome remeshing of FEM in crack propagation problems. The simplicity, flexibility in handling several cracks and crack propagation patterns on a fixed mesh, and the level of accuracy with minimum additional degrees of freedom have transformed X-FEM into the most efficient numerical procedure in the arena of computational fracture mechanics.

Abstract: The extended finite element method (XFEM) allows the entire crack to be represented independently from the mesh, which means re-mesh is unnecessary in model crack growth, reduces the computational time drastically. However, fatigue crack growth simulation has been computationally challenged by lots of analog computations in crack growth. Therefore, a new reanalysis algorithm based on incremental Cholesky factorization is derived. In this paper, we consider a variant of XFEM in which an exponent discontinuous function is used to simulate the crack through unit. Then the corresponding formula of XFEM with inclusion and crack problem with a new reanalysis algorithm is derived. In the end, we use the new reanalysis algorithm and an optimization algorithm to predict the angle of crack initiation from a hole in a plate with inclusion. It shows that the algorithm is effective.