scholarly journals Modeling of Shear Crack Propagation in Rock Masses Using Mesh-Free LRPIM

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Qingbo Li ◽  
Nengxiong Xu ◽  
Weifeng Wan ◽  
Yazhe Li
Keyword(s):  
Crack Propagation ◽  
Interpolation Method ◽  
Shear Crack ◽  
Propagation Path ◽  
Crack Model ◽  
Rock Masses ◽  
Shear Cracks ◽  
Elastic Plastic ◽  
Mesh Free ◽  
Point Interpolation Method

The modeling of shear cracks in materials is critical in various engineering applications, such as the safety analysis of concrete structures and stability analysis of rock slopes. Based on the idea of Goodman element, the elastic-plastic constitutive model of the shear cracks is derived, and the elastic-plastic analysis of shear crack propagation is realized in the local radial basis point interpolation method (LRPIM). This method avoids the loss of accuracy caused by the mesh in the analysis of fracture propagation, and the crack propagation of rock brittle material is simulated. The investigation indicates that (1) the LRPIM results are close to the FDM results, which demonstrates that it is feasible to analyze shear cracks in rock masses. (2) Compared with the results of the built-in oblique crack model, when the LRPIM is used to analyze crack propagation, the results are close to the experimental results, showing that the LRPIM can model shear crack propagation in a rock mass. (3) The propagation path using the LRPIM is not sufficiently smooth, which can be explained as the crack tip stress and strain not being sufficiently accurate and still requiring further improvement.

scholarly journals Comparative modelling of crack propagation in elastic–plastic materials using the meshfree local radial basis point interpolation method and eXtended finite-element method

2019 ◽  
Vol 6 (11) ◽  
pp. 190543 ◽  
Author(s):  
Yazhe Li ◽  
Nengxiong Xu ◽  
Jinzhi Tu ◽  
Gang Mei
Keyword(s):  
Finite Element Method ◽  
Crack Propagation ◽  
Extended Finite Element Method ◽  
Interpolation Method ◽  
Extended Finite Element ◽  
Elastic Plastic ◽  
Plastic Materials ◽  
Point Interpolation Method ◽  
Point Interpolation ◽  
Elastic Plastic Materials

The modelling and understanding of crack propagation for elastic–plastic materials is critical in various engineering applications, such as safety analysis of concrete structures and stability analysis of rock slopes. In this paper, the local radial basis point interpolation method (LRPIM) combined with elastic–plastic theory and fracture mechanics is employed to analyse crack propagation in elastic–plastic materials. Crack propagation in elastic–plastic materials is compared using the LRPIM and eXtended finite-element method (XFEM). The comparative investigation indicates that: (i) the LRPIM results are close to the model test results, which indicates that it is feasible for analysing the crack growth of elastic–plastic materials; (ii) compared with the LRPIM, the XFEM results are closer to the experimental results, showing that the XFEM has higher accuracy and computational efficiency; and (iii) compared with the XFEM, when the LRPIM method is used to analyse crack propagation, the propagation path is not smooth enough, which can be explained as the crack tip stress and strain not being accurate enough and still needing further improvement.

The Natural Neighbor Radial Point Interpolation Method in Computational Fracture Mechanics: A 2D Preliminary Study

2017 ◽  
Vol 14 (04) ◽  
pp. 1750045 ◽  
Author(s):  
J. Belinha ◽  
J. M. C. Azevedo ◽  
L. M. J. S. Dinis ◽  
R. M. Natal Jorge
Keyword(s):  
Crack Propagation ◽  
Interpolation Method ◽  
Circumferential Stress ◽  
Crack Tip ◽  
Propagation Path ◽  
Radial Point Interpolation Method ◽  
Natural Neighbor ◽  
Radial Point Interpolation ◽  
Point Interpolation Method ◽  
Point Interpolation

In this work, the natural neighbor radial point interpolation method (NNRPIM) is extended to the numeric analysis of crack propagation problems. Here, the advanced discretization meshless technique is combined with a linear elastic crack growth algorithm. The algorithm simulates the crack propagation by displacing iteratively the crack tip, which consequently requires a local remeshing. In each iteration, it is estimated the stress state in the crack tip and afterwards the direction of the crack propagation is obtained considering the maximum circumferential stress criterion.The required local remeshing does not represent a numeric difficulty for the NNRPIM. The main advantage of the NNRPIM is its capability to fully discretize the problem domain using only an unstructured nodal distribution. Being a truly meshless method, the NNRPIM is able to define autonomously the nodal connectivity and the background integration mesh.The classic NNRPIM formulation permits to enforce the nodal connectivity by means of two kind of influence-cells: first degree influence-cells or second degree influence-cells. This work investigates the influence of the nodal connectivity on the simulated crack propagation path. Thus, demanding benchmark crack propagation examples are studied and the obtained results are compared with reference solutions available in the literature.

scholarly journals Biaxial Shear Crack Propagation Modes of Rock-Like Specimens with Prefabricated Fissures and Their Strength Characteristics

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Nai-Zhong Xu ◽  
Chang-Qing Liu ◽  
You-Jian Wang ◽  
Hong-Bin Dang
Keyword(s):  
Shear Strength ◽  
Crack Propagation ◽  
Shear Crack ◽  
Crack Coalescence ◽  
Strength Characteristics ◽  
Propagation Mode ◽  
Peak Shear Strength ◽  
Shear Cracks ◽  
Tensile Shear ◽  
Dip Angle

A biaxial shear test is performed on prefabricated, single-fissure type, cubic rock-like specimens by using the TZW-500 rock direct shear apparatus to study the shear strength characteristics, crack coalescence, and propagation modes of the specimens with different geometric parameters. Results show that the crack coalescence and propagation modes of the rock-like specimens with prefabricated fissures can be divided into four types, namely, single main shear crack coalescence mode, main shear crack coalescence and secondary tensile-shear crack propagation mode, main shear crack coalescence and secondary shear crack propagation mode, and main shear crack coalescence and secondary tensile crack propagation mode. All modes are affected by the dip angle α and length l of the prefabricated fissure. When the dip angle of the prefabricated fissure is α∈[0°, 20°) or (70°, 90°], the cracks center on shear failure, and most shear cracks propagate along one end of the prefabricated fissure. At α∈(30°, 50°), the cracks bear the tensile-shear combined action, and the shear cracks propagate along the two ends of the prefabricated fissure. The peak shear strength of the rock-like specimens with prefabricated fissures is also closely related to the dip angle α and length l of the fissure. With the increase in dip angle α of the prefabricated fissure, the peak shear strength of each rock-like specimen decreases initially then increases, and the peak shear strength curve presents a similar “U” shape. At α∈[30°, 60°], the peak shear strength is within the peak-valley interval. When the length l of the prefabricated fissure is increased, the peak shear strength experiences a gradual reduction. When l > 20 mm, the peak shear strength is greatly influenced by l, but the influence is minimal when l ≥ 20 mm. At the same dip angle α and fissure length of l ≥ 20 mm, the correlation between peak shear strength and fissure width b is low.

scholarly journals A computational homogenization analysis of materials using the stabilized mesh-free method based on the radial basis functions

2020 ◽  
Vol 14 (1) ◽  
pp. 65-76
Author(s):  
Ho Le Huy Phuc ◽  
Le Van Canh ◽  
Phan Duc Hung
Keyword(s):  
Radial Basis Functions ◽  
Interpolation Method ◽  
Computational Homogenization ◽  
Basis Functions ◽  
Computational Aspect ◽  
Mesh Free ◽  
Kronecker Delta ◽  
Radial Basis ◽  
Point Interpolation Method ◽  
Mesh Free Method

This study presents a novel application of mesh-free method using the smoothed-radial basis functions for the computational homogenization analysis of materials. The displacement field corresponding to the scattered nodes within the representative volume element (RVE) is split into two parts including mean term and fluctuation term, and then the fluctuation one is approximated using the integrated radial basis function (iRBF) method. Due to the use of the stabilized conforming nodal integration (SCNI) technique, the strain rate is smoothed at discreted nodes; therefore, all constrains in resulting problems are enforced at nodes directly. Taking advantage of the shape function satisfies Kronecker-delta property, the periodic boundary conditions well-known as the most appropriate procedure for RVE are similarly imposed as in the finite element method. Several numerical examples are investigated to observe the computational aspect of iRBF procedure. The good agreement of the results in comparison with those reported in other studies demonstrates the accuracy and reliability of proposed approach. Keywords: homogenization analysis; mesh-free method; radial point interpolation method; SCNI scheme.

Elastic-plastic analysis of multi-material structures using edge-based smoothed point interpolation method

2018 ◽  
Vol 233 (4) ◽  
pp. 1289-1298
Author(s):  
SZ Feng ◽  
YH Cheng ◽  
AM Li
Keyword(s):  
Interpolation Method ◽  
Shape Functions ◽  
Integral Domains ◽  
Elastic Plastic ◽  
Plastic Analysis ◽  
Point Interpolation Method ◽  
Point Interpolation ◽  
Triangular Elements ◽  
Standard Finite Element Method ◽  
Edge Based

An edge-based smoothed point interpolation method is formulated to deal with elastic-plastic analysis of multi-material structures. The problem domain is discretized using triangular elements and field functions are approximated using point interpolation method shape functions. Edge-based smoothing domains are constructed based on the edge of triangular cells and smoothing operations are then performed in these integral domains. Numerical examples with different kinds of material models are investigated to fully verify the validity of the present method. It is observed that all edge-based smoothed point interpolation method models can achieve much better accuracy and higher convergence rate than the standard finite element method, when dealing with elastic-plastic analysis of multi-material structures.

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