Investigating Stress Intensity Factor and Fatigue Life Using Extended Isogeometric Analysis Based on Bézier Extraction of NURBS

Journal of Solid Mechanics

مقاله 7، دوره 14، شماره 3، آذر 2022، صفحه 377-397   

نوع مقاله: Research Paper

شناسه دیجیتال (DOI): 10.22034/jsm.2021.1929984.1696

نویسندگان

M. M Shoheib¹؛ Sh Shahrooi^{* 1}؛ M Shishehsaz²؛ M Hamzehei¹

¹Department of Mechanical Engineering, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran

²Department of Mechanical Engineering, Faculty of Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran

چکیده

In this paper, the extended isogeometric analysis based on Bézier extraction of NURBS is applied for Investigating stress intensity factor and fatigue life in the two-dimensional crack problems with thermal and mechanical cyclic loading. By transforming NURBS function to linear combination of Bernstein functions defined over C⁰-continuous Bézier elements, the extended isogeometric analysis can be implemented in the extended finite element method framework. Grid points around the crack line and crack tip are identified by the level set representation. Then, discontinuous enrichment functions are added to the isogeometric analysis approximation. Thus, this method does not require remeshing. The interaction integral method and Paris law has been used to extract stress intensity factor and evaluate fatigue life, respectively. Numerical examples are examined to validate the efficiency of the proposed method. The effect of adaptive refinement strategies on computational cost and convergence is studied. Numerical examples showed that the presented method produces highly accurate results, yet it is beneficial to implement.  

کلیدواژه‌ها

XIGA analysis؛ Bézier extraction operator؛ Cyclic load؛ Stress intensity factor؛ Fatigue life

مراجع

1.  Sancho J.M., Planas J., Cendón D.A., Reyes E., Gálvez J., 2007, An embedded crack model for finite element analysis of concrete fracture, Engineering Fracture Mechanics 74(1-2): 75-86.
2.  Rabczuk T., Gracie R., Song J.H., Belytschko T., 2010, Immersed particle method for fluid–structure interaction, International Journal for Numerical Methods in Engineering 81(1): 48-71.
3.  Chessa J., Belytschko T., 2003, An enriched finite element method and level sets for axisymmetric two‐phase flow with surface tension, International Journal for Numerical Methods in Engineering 58(13): 2041-2064.
4.  Duddu R., Bordas S., Chopp D., Moran B., 2008, A combined extended finite element and level set method for biofilm growth, International Journal for Numerical Methods in Engineering 74(5): 848-870.
5.  Bordas S., Moran B., 2006, Enriched finite elements and level sets for damage tolerance assessment of complex structures, Engineering Fracture Mechanics 73(9): 1176-1201.
6.  Rabczuk T., Belytschko T., 2005, Adaptivity for structured meshfree particle methods in 2D and 3D, International Journal for Numerical Methods in Engineering 63(11): 1559-1582.
7.  Rabczuk T., Zi G., 2007, A meshfree method based on the local partition of unity for cohesive cracks, Computational Mechanics 39(6): 743-760.
8.  Rabczuk T., Xiao S.P., Sauer M., 2006, Coupling of mesh‐free methods with finite elements: basic concepts and test results, Communications in Numerical Methods in Engineering 22(10): 1031-1065.
9.  Nguyen-Thanh N., Nguyen-Xuan H., Bordas S.P.A., Rabczuk T., 2011, Isogeometric analysis using polynomial splines over hierarchical T-meshes for two-dimensional elastic solids, Computer Methods in Applied Mechanics and Engineering 200(21-22): 1892-1908.
10.  Bhardwaj G., Singh S., Singh I., Mishra B., Rabczuk T., 2016, Fatigue crack growth analysis of an interfacial crack in heterogeneous materials using homogenized XIGA, Theoretical and Applied Fracture Mechanics 85: 294-319.
11.  Bhardwaj G., Singh I., Mishra B., Bui T., 2015, Numerical simulation of functionally graded cracked plates using NURBS based XIGA under different loads and boundary conditions, Composite Structures 126: 347-359.
12.  Tran L.V., Ferreira A., Nguyen-Xuan H., 2013, Isogeometric analysis of functionally graded plates using higher-order shear deformation theory, Composites Part B: Engineering 51: 368-383.
13.  Huang X., Liu Y., Huang X., 2019, Analytical characterizations of crack tip plastic zone size for central-cracked unstiffened and stiffened plates under biaxial loading, Engineering Fracture Mechanics 206: 1-20.
14.  Gadallah R., Osawa N., Tanaka S., Tsutsumi S., 2018, A novel approach to evaluate mixed-mode SIFs for a through-thickness crack in a welding residual stress field using an effective welding simulation method, Engineering Fracture Mechanics 197: 48-65.
15.  Yuan H., Liu W., Xie Y., 2019, Mode-I stress intensity factors for cracked special-shaped shells under bending, Engineering Fracture Mechanics 207: 131-148.
16.  Cimrman R., Novák M., Kolman R., Tůma M., Plešek J., Vackář J., 2018, Convergence study of isogeometric analysis based on Bézier extraction in electronic structure calculations, Applied Mathematics and Computation 319: 138-152.
17.  Nguyen L.B., Thai C.H., Zenkour A., Nguyen-Xuan H., 2019, An isogeometric Bézier finite element method for vibration analysis of functionally graded piezoelectric material porous plates, International Journal of Mechanical Sciences 157: 165-183.
18.  Singh A.K., Jameel A., Harmain G., 2018, Investigations on crack tip plastic zones by the extended iso-geometric analysis, Materials Today: Proceedings 5(9): 19284-19293.
19.  Yin S., Yu T., Bui T.Q., Zheng X., Gu S., 2019, Static and dynamic fracture analysis in elastic solids using a multiscale extended isogeometric analysis, Engineering Fracture Mechanics 207: 109-130.
20.  Piegl L., Tiller W., 2012, The NURBS Book, Springer Science & Business Media, Berlin/Heidelberg, Germany.
21.  Shi J., Chopp D., Lua J., Sukumar N., Belytschko T., 2010, Abaqus implementation of extended finite element method using a level set representation for three-dimensional fatigue crack growth and life predictions, Engineering Fracture Mechanics 77(14): 2840-2863.
22.  Sutradhar A., Paulino G.H., 2004, Symmetric Galerkin boundary element computation of T-stress and stress intensity factors for mixed-mode cracks by the interaction integral method, Engineering Analysis with Boundary Elements 28(11): 1335-1350.
23.  Bremberg D., Faleskog J., 2015, A numerical procedure for interaction integrals developed for curved cracks of general shape in 3-D, International Journal of Solids and Structures 62: 144-157.
24.  de Klerk A., Visser A., Groenwold A.A., 2008, Lower and upper bound estimation of isotropic and orthotropic fracture mechanics problems using elements with rotational degrees of freedom, Communications in Numerical Methods in Engineering 24(5): 335-353.
25.  Sutradhar A., Paulino G. H., 2004, Symmetric Galerkin boundary element computation of T-stress and stress intensity factors for mixed-mode cracks by the interaction integral method, Engineering Analysis with Boundary Elements 28(11): 1335-1350.
26. Bayesteh H., Afshar A., Mohammdi S., 2015, Thermo-mechanical fracture study of inhomogeneous cracked solids by the extended isogeometric analysis method, European Journal of Mechanics-A/Solids 51: 123-139.
27. Dowling N.E., 1999, Mechanical Behavior of Materials: Engineering Methods for Deformation, Fracture, and Fatigue, Pearson, London, United Kingdom.