Continuum shape sensitivity analysis of mixed-mode fracture using fractal finite element method

• Published in: Engineering fracture mechanics Vol. 75; no. 10; pp. 2860 - 2906
• Main Authors: Reddy, R.M., Rao, B.N.
• Format: Journal Article
• Language: English
• Published: Tarrytown, NY Elsevier Ltd 01.07.2008; Oxford Elsevier
• Subjects: Crack; Exact sciences and technology; Fractal finite element method; Fracture mechanics (crack, fatigue, damage...); Fundamental areas of phenomenology (including applications); Linear-elastic fracture mechanics; Material derivative; Mixed-mode; Physics; Shape sensitivity analysis; Solid mechanics; Static elasticity (thermoelasticity...); Stress-intensity factor; Structural and continuum mechanics; Velocity field; Material derivative; Fractal finite element method; Shape sensitivity analysis; Mixed-mode; Velocity field; Stress-intensity factor; Linear-elastic fracture mechanics; Crack; Geometrical shape; J integral; Sensitivity analysis; Mode coupling; Rupture; Mechanical properties; Modeling; Crack propagation; Direct method; Finite element method; Perturbation method; Stress intensity factor; Fractal; Virtual work principle; Variational calculus; Finite difference method
• ISSN: 0013-7944; 1873-7315
• DOI: 10.1016/j.engfracmech.2008.01.001

This paper presents a new fractal finite element based method for continuum-based shape sensitivity analysis for a crack in a homogeneous, isotropic, and two-dimensional linear-elastic body subject to mixed-mode (modes I and II) loading conditions. The method is based on the material derivative concept of continuum mechanics, and direct differentiation. Unlike virtual crack extension techniques, no mesh perturbation is needed in the proposed method to calculate the sensitivity of stress-intensity factors. Since the governing variational equation is differentiated prior to the process of discretization, the resulting sensitivity equations predicts the first-order sensitivity of J-integral or mode-I and mode-II stress-intensity factors, K I and K II, more efficiently and accurately than the finite-difference methods. Unlike the integral based methods such as J-integral or M-integral no special finite elements and post-processing are needed to determine the first-order sensitivity of J-integral or K I and K II. Also a parametric study is carried out to examine the effects of the similarity ratio, the number of transformation terms, and the integration order on the quality of the numerical solutions. Four numerical examples which include both mode-I and mixed-mode problems, are presented to calculate the first-order derivative of the J-integral or stress-intensity factors. The results show that first-order sensitivities of J-integral or stress-intensity factors obtained using the proposed method are in excellent agreement with the reference solutions obtained using the finite-difference method for the structural and crack geometries considered in this study.