Analytical and numerical evaluation of crack-tip plasticity of an axisymmetrically loaded penny-shaped crack

Penny-Shaped Dugdale Crack in a Transverse Isotropic Medium

“…which is consistent with that predicted by Chaiyat et al (2008). The CSD due to the external load (10) can be generally expressed in terms of special functions as well.…”

A unified treatment of axisymmetric adhesive contact problems using the harmonic potential function method

“…An illuminating discussion on using the harmonic function method to solve axisymmetric mixed boundary value problems and many useful expressions have been provided by Barber (1983). Also, some important contributions to fracture mechanics have recently been made by Chaiyat et al (2008) and Jin et al (2008) utilizing this method. The current formulation of non-adhesive and adhesive contact problems is greatly facilitated by the findings of these studies.…”

“…(3) and an expression similar to Eq. (4) (containing sin(xt) rather than cos(xt)) were employed earlier to solve penny-shaped and other internal crack problems (Kassir and Sih, 1975;Chen and Keer, 1993;Chaiyat et al, 2008). This harmonic function is adopted in the current study to solve non-adhesive and adhesive contact problems involving axisymmetric punches of arbitrary shapes and BCs of both types.…”

“…On the other hand, the harmonic potential function method for axisymmetric elasticity problems developed by Green (1949) and Collins (1959Collins ( , 1963 and elaborated in Green and Zerna (1968) has been found to exhibit significant advantages in solving axisymmetric half-space problems with mixed boundary conditions (e.g., Barber, 1983;Chaiyat et al, 2008;Jin et al, 2008). However, this method has not been systematically explored for its use in studying adhesive contact problems of axisymmetric elastic bodies, for which the JKR model, the DMT model, and the M-D model and its variants have been developed using the Hertz theory (1882) or Sneddon's (1965) solution.…”

Extended displacement discontinuity method for nonlinear analysis of penny-shaped cracks in three-dimensional piezoelectric media

“…This model assumes that the elastic-plastic material is ideal, and that the stress in the yielding zone is constant and equal to the yield value. Fracture mechanics based on the Dugdale model have been studied extensively and have been applied to twodimensional (2D) [5][6][7][8][9][10][11], as well as three-dimensional (3D) situation [12][13][14]. Extending the Dugdale model to piezoelectric materials, Gao and Barnett [15] and Gao et al [16] proposed a strip polarization saturation (PS) model in which the piezoelectric material is treated as mechanically brittle and electrically ductile and the electric displacement is equal to the polarization saturation value in the electric yielding zone.…”