Quasi-static analysis of mixed-mode crack propagation using the meshless local Petrov–Galerkin method

A numerical model for the two-dimensional nonlinear elastic–plastic problem is proposed based on the improved interpolating complex variable element free Galerkin (IICVEFG) method and the incremental tangent stiffness matrix method. The viability of the proposed model is verified through three elastic–plastic examples. The numerical analyses show that the IICVEFG method has good convergence. The solutions using the IICVEFG method are consistent with the solutions obtained from the finite element method using the ABAQUS program. Moreover, the IICVEFG method shows greater computing precision and efficiency than the non-interpolating meshless methods.

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“…Substitute Equations ( 27), (32) and (35) into Equation (15), then consider the arbitrary of δ . U(z) T .…”

Section: U(z)mentioning

confidence: 99%

“…Unlike conventional mesh-based numerical methods [10,11], the meshless method is built on discrete nodes, which does not cause mesh distortion. Therefore, the meshless method is more suitable for nonlinear large deformation and fracture problems, as well as complicated porous structures [12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Analysis of Elastic–Plastic Problems Using the Improved Interpolating Complex Variable Element Free Galerkin Method

et al. 2021

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“…Compared with the XFEM, the MLM improves the continuity of the interpolation [ 21 , 22 ]; however, it is difficult to apply the essential boundary conditions because the shape functions do not meet the nature of the Kronecker delta function [ 23 , 24 ]. Other MLMs, such as mesh-less local Petrov–Galerkin [ 25 ], partition of unity method [ 26 ] and so on, also have their own limitations in terms of long calculation time and efficiency.…”

Section: Introductionmentioning

confidence: 99%

Improved peridynamic model and its application to crack propagation in rocks

Zhou

Zhu

et al. 2022

R. Soc. open sci.

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The conventional bond-based peridynamics (BB-PD) model is suitable for simulating the failure mode of homogeneous elastic-brittle materials. However, the strain hardening and subsequent strain softening characteristics of rocks under loading cannot be reflected. In addition, the fracture mechanisms of rock materials under tension and compression are completely different. To solve these problems, this paper proposes an improved BB-PD model using different fracture criteria in the tensile and compression stages of the bond based on previous improved models, and a critical failure condition obeying the Weibull distribution is introduced to reflect the heterogeneity of the rock. The crack propagation processes of an intact rock specimen, rock specimen with a single pre-existing flaw and rock specimens with two and three pre-existing flaws under compressive loading are simulated using the model, and its feasibility is verified by comparing with the results of previous laboratory tests. Next, the effects of the inclination angle and length on the wing crack propagation length are studied. Finally, the changes in the crack aggregation modes under different rock bridge inclination angles are simulated. Eight types of crack aggregation modes are found, and the conditions under which they may occur are analysed. The improved model proposed can effectively simulate the crack propagation and coalescing processes and has a wide application prospect for rock fracture simulations.

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“…Belytschko et al proposed the popular element free Galerkin method (EFGM), in which the EFGM error estimation is given to make in-depth study on the numerical integration scheme, thereby laying the mathematical foundation of the method (Belytschko et al, 1994;Ventura et al, 2002). The meshless method is mainly suitable for solving deformation analysis of jointed rock mass (Hajiazizi and Graili, 2018), fluid-structure interactions (Hu et al, 2019), fracture analysis (Memari and Mohebalizadeh, 2019), diffusion problem (Tayefi et al, 2018) and large deformation problem (Lin et al, 2014), etc. This method has been widely used in multiple fields (Wang, 2012;Belytschko et al, 1995;Fouaidi et al, 2019;Li and Belytschko, 2001).…”

Section: Introductionmentioning

confidence: 99%

Meshless numerical method for the contact problems of joint surface

Wang

Shi

Cao

et al. 2022

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PurposeThe partition of unity of the standard meshless Galerkin method is used as basis in expressing the discontinuity of the contact surface displacement, particularly by adding discontinuous terms into the displacement mode, and constructing the discontinuous meshless displacement field function. In this study the contact surface equation is aimed to derive from the improved Coulomb friction contact model.Design/methodology/approachIn this paper based on the basic idea of meshless method, an improved moving least squares approximation function (expansion method based on out of unit division) is applied to the analysis of two-dimensional contact problems.FindingsOn the basis of this equation after discrete processing, it is combined with the discrete form of the virtual work equation with added contact conditions, and eventually transformed into a standard linear complementary problem. Moreover, it is solved by using the Lemke algorithm, and a corresponding example is provided in this research.Originality/valueThe proposed method can effectively control the mutual embedding of the contact surface, and the stress distribution that is the same as the actual situation can be obtained on the contact surface.

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Quasi-static analysis of mixed-mode crack propagation using the meshless local Petrov–Galerkin method

Cited by 19 publications

References 48 publications

Analysis of Elastic–Plastic Problems Using the Improved Interpolating Complex Variable Element Free Galerkin Method

Analysis of Elastic–Plastic Problems Using the Improved Interpolating Complex Variable Element Free Galerkin Method

Improved peridynamic model and its application to crack propagation in rocks

Meshless numerical method for the contact problems of joint surface

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