Fractal finite element method based shape sensitivity analysis of mixed-mode fracture

• Published in: Finite elements in analysis and design Vol. 44; no. 15; pp. 875 - 888
• Main Authors: Reddy, R.M., Rao, B.N.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.11.2008; 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; Similarity solution; Modeling; Continuum; Direct method; Finite element method; Stress intensity factor; Fractal; Mixed problem; Finite difference method
• ISSN: 0168-874X; 1872-6925
• DOI: 10.1016/j.finel.2008.06.011

In this paper, 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, is presented. The method is based on the material derivative concept of continuum mechanics, and direct differentiation. 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. Three 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.