The stress intensity factors and the electrical displacement intensity factor for functionally graded piezoelectric materials (FGPMs) are influenced by: (a) the spatial variation of the mechanical property and (b) the electrical and mechanical boundary conditions. In this work, a semi-analytical technique is proposed to study the fracture parameters of FGPMs subjected to far field traction and electrical boundary conditions. A scaled boundary finite element formulation for the analysis of functionally graded piezoelectric materials is developed. The formulation is linearly complete for uncracked polygons and can capture crack tip singularity for cracked polygons. These salient features enable the computation of the fracture parameters directly from their definition. Numerical examples involving cracks in FGPMs show the accuracy and efficiency of the proposed technique. © 2018 Elsevier Ltd

Sundararajan Natarajan

Department of Mechanical Engineering

Aladurthi L.N. Pramod

Ean Tat Ooi

Chongmin Song

Boundary conditions

Crack tips

finite element method

geometry

Numerical methods

Piezoelectric materials

Piezoelectricity

Stress intensity factors

Structural analysis

ELECTRICAL BOUNDARY CONDITIONS

Finite element formulations

FUNCTIONALLY GRADED PIEZOELECTRIC MATERIAL

INTENSITY FACTORS

PEIZOELECTRIC

POLYGONS

SCALED BOUNDARY FINITE ELEMENT METHOD

Semi-analytical techniques

Functionally graded materials

IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

Composite Structures

The development and the application of the scaled boundary finite element method for fracture analysis is reviewed. In this method, polygonal elements (referred to as subdomains) of arbitrary number of edges are constructed, with the only limitation that the whole boundary is directly visible from the scaling centre. The element solution is semi-analytical. When applied to two-dimensional linear fracture mechanics, any kinds of stress singularities are represented analytically without local refinement, special elements and enrichment functions. The flexibility of polygons to represent arbitrary geometric shapes leads to simple yet efficient remeshing algorithms to model crack propagation. Coupling procedures with the extended finite element method, meshless method and boundary element method to handle changes in the crack morphology have been established. These developments result in an efficient framework for fracture modelling. Examples of applications are provided to demonstrate their feasibility. © 2017 Elsevier Ltd

Fulltext

Engineering Fracture Mechanics

A review of the scaled boundary finite element method for two-dimensional linear elastic fracture mechanics

A crack propagation modelling technique combining the scaled boundary finite element method and quadtree meshes is developed. This technique automatically satisfies the compatibility requirement between adjacent quadtree cells irrespective of the presence of hanging nodes. The quadtree structure facilitates efficient data storage and rapid computations. Only a single cell is required to accurately model the stress field near crack tips. Crack growth is modelled by splitting the cells in the mesh into two. The resulting polygons are directly modelled by the scaled boundary formulation with minimal changes to the mesh. Four numerical examples demonstrate the salient features of the technique. © 2015.

Adaptation of quadtree meshes in the scaled boundary finite element method for crack propagation modelling

By leveraging the information of a typical CAD model in the analysis, the intensive process of discretization can be circumvented. This unification has led to the 'Isogeometric Analysis' (IGA) (Hughes etal., 2005). However, as the CAD model provides information only of the boundary, a 2D/3D stress analysis is still one major step away. In this work, the concepts of isogeometric analysis and the scaled boundary finite element method (SBFEM) are combined. The SBFEM requires only the boundary information and hence provides a seamless integration with the CAD modeling. Within the proposed framework, the NURBS basis functions are used to discretize the unknown fields in the circumferential direction, whilst analytical solution is sought in the radial direction. We further extend the framework to problems with singularities and to dynamic analysis. The accuracy and the convergence properties of the proposed method are demonstrated with benchmark problems in the context of linear elasticity and linear elastic fracture mechanics. © 2014 Elsevier B.V.

Computer Methods in Applied Mechanics and Engineering

Isogeometric analysis enhanced by the scaled boundary finite element method

This paper presents domain form of the interaction integrals based on three independent formulations for computation of the stress intensity factors and electric displacement intensity factor for cracks in functionally graded piezoelectric materials. Conservation integrals of J-type are derived based on the governing equations for piezoelectric media and the crack tip asymptotic fields of homogeneous piezoelectric medium as auxiliary fields. Each of the formulation differs in the way auxiliary fields are imposed in the evaluation of interaction integral and each of them results in a consistent form of the interaction integral in the sense that extra terms naturally appears in their derivation to compensate for the difference in the chosen crack tip asymptotic fields of homogeneous and functionally graded piezoelectric medium. The additional terms play an important role of ensuring domain independence of the presented interaction integrals. Comparison of the numerically evaluated intensity factors through the three consistent formulations with those obtained using displacement extrapolation method is presented by means of two examples. © 2008 Elsevier Ltd. All rights reserved.

International Journal of Solids and Structures

Interaction integrals for fracture analysis of functionally graded piezoelectric materials

A multi-material level set-based topology optimization of flexoelectric composites

Numerical estimation of stress intensity factors in cracked functionally graded piezoelectric materials – A scaled boundary finite element approach

Journal	Data powered by TypesetComposite Structures
Publisher	Data powered by TypesetElsevier Ltd
ISSN	02638223
Open Access	No