Construction Of Shape Function By Radial Point Interpolation Method For 1d Case

2014 ◽  
Vol 04 (11) ◽  
pp. 23-35
Author(s):  
A. Mjidila
Keyword(s):  
Shape Function ◽  
Interpolation Method ◽  
Radial Point Interpolation Method ◽  
Radial Point Interpolation ◽  
Point Interpolation Method ◽  
Point Interpolation

scholarly journals An interaction integral method for evaluating T-stress for two-dimensional crack problems using the extended radial point interpolation method

2015 ◽  
Vol 18 (2) ◽  
pp. 106-113
Author(s):  
Nha Thanh Nguyen ◽  
Hien Thai Nguyen ◽  
Minh Ngoc Nguyen ◽  
Thien Tich Truong
Keyword(s):  
Integral Method ◽  
Interpolation Method ◽  
Two Dimensional ◽  
Radial Point Interpolation Method ◽  
Interaction Integral ◽  
Crack Problems ◽  
Radial Point Interpolation ◽  
T Stress ◽  
Point Interpolation Method ◽  
Point Interpolation

The so-called T-stress, or second term of the William (1957) series expansion for linear elastic crack-tip fields, has found many uses in fracture mechanics applications. In this paper, an interaction integral method for calculating the T-stress for two-dimensional crack problems using the extended radial point interpolation method (XRPIM) is presented. Typical advantages of RPIM shape function are the satisfactions of the Kronecker’s delta property and the high-order continuity. The T-stress can be calculated directly from a path independent interaction integral entirely based on the J-integral by simply the auxiliary field. Several benchmark examples in 2D crack problem are performed and compared with other existing solutions to illustrate the correction of the presented approach.

scholarly journals Meshless Radial Point Interpolation Method for Hyperelastic Materials

10.29007/r7sp ◽  
2020 ◽  
Author(s):  
Trong Khiem Bui ◽  
Vu Tuong Nguyen ◽  
Thanh Nha Nguyen ◽  
Tich Thien Truong
Keyword(s):  
Large Deformation ◽  
Interpolation Method ◽  
Biological Tissues ◽  
Material Behavior ◽  
Nonlinear Material ◽  
Radial Point Interpolation Method ◽  
Hyperelastic Materials ◽  
Radial Point Interpolation ◽  
Point Interpolation Method ◽  
Point Interpolation

Hyperelastic materials are special types of material that tends to behavior elastically when they are subjected to very large strains. These materials show not only the nonlinear material behavior but also the large deformation and stress-strain relationship is derived from a strain energy density function. Hyperelastic materials are widely used in many applications such as biological tissues, polymeric foams, and moreover. Neo - Hookean is a material model for hyperelastic solid which contains only two material parameters: bulk modulus and shear modulus. In the field of numerical analysis, the radial point interpolation method (RPIM) is a well-known meshfree method based on Garlekin's weak form. With the property of “free of mesh”, the RPIM approach shows its advantage for large deformation problems. In this study, a meshless radial point interpolation method is applied to demonstrate the elastic response of rubber-like materials based on the Mooney- Rivlin model. The obtained results are compared with the reference solutions given by other methods to verify the accuracy of the proposed method.

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