Extended isogeometric dynamic and static fracture analysis for cracks in piezoelectric materials using NURBS

Bui, Tinh Quoc

doi:10.1016/j.cma.2015.07.005

Cited by 167 publications

(31 citation statements)

References 73 publications

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“…There are three classical criteria for mixed-mode brittle fracture in propagation analysis: the maximum tangential stress, the maximum energy release rate, and the minimum strain energy density. For this purpose, energy-based criteria are used widely in fracture mechanics [44][45][46][47][48][49]. Let us consider the energy release rate.…”

Section: Calculation Of Sifsmentioning

confidence: 99%

Development of a new semi-analytical method in fracture mechanics problems based on the energy release rate

2016

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The existence of crack and notch is a considerable and serious subject in the failure study of solids and structures. As most of cracked domain problems do not have closed-form solutions, numerical methods are dominant approaches dealing with fracture mechanics problems. In fracture mechanics and failure analysis, cracked media energy and consequently stress intensity factors (SIFs) play a crucial and significant role. Based on linear elastic fracture mechanics, the SIFs may be estimated using the energy release rate, as an indirect approach. This study presents the development of a new semi-analytical method to model cracked media. In this method, only the boundaries of problems are discretized using specific higher-order subparametric elements and higher-order Chebyshev mapping functions. Implementing the weighted residual method and using Clenshaw-Curtis quadrature yield diagonal Euler's differential equations. Therefore, when the local coordinate origin is located at the crack tip, the geometry of crack problems is implemented directly without further processing. In order to present crack boundary conditions, a modified form of nodal force function is presented. Validity and accuracy of the proposed method is fully illustrated by four benchmark problems, whose results agree very well with those of other numerical and/or analytical solutions existing in the literature.

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Section: Calculation Of Sifsmentioning

confidence: 99%

Development of a new semi-analytical method in fracture mechanics problems based on the energy release rate

2016

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“…[54][55][56][57][58][59][60][61][62][63] ) that can solve the crack problems faster than the finite element method can also be used for future fracture studies of heterogeneous asphalt mixtures. [54][55][56][57][58][59][60][61][62][63] ) that can solve the crack problems faster than the finite element method can also be used for future fracture studies of heterogeneous asphalt mixtures.…”

Section: Crack Growth Pathmentioning

confidence: 99%

Heterogeneity effects on mixed‐mode I/II stress intensity factors and fracture path of laboratory asphalt mixtures in the shape of SCB specimen

Aliha

Ziari

Mojaradi

et al. 2019

Fatigue Fract Eng Mat Struct

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Edge cracked semi-circular shape specimen subjected to three point bend loading is a favourite test specimen for determining fracture toughness of asphalt mixtures. However, in the vast majority of previous experimental works, the homogeneous medium assumption has been considered for determining the stress intensity factor and geometry factors of asphalt mixtures tested with this test configuration. As a more realistic model and in order to consider the effects of heterogeneity on corresponding values of stress intensity factors, the asphalt mixture was modelled as a two-phase aggregate/mastic heterogeneous mixture and its fracture behaviour was investigated using numerical models of asymmetric semi-circular bend (ASCB) specimens. The generation and packing algorithm was employed to randomly distribute the aggregates with different shapes and sizes inside the mastic part. The effect of the mechanical properties of asphalt mixture (elastic modulus and the Poisson's ratios of aggregates and mastic), coarse aggregates distribution and crack length were studied on modes I and II geometry factors by means of extensive twodimensional finite element analyses. Moreover, the effect of the elastic modulus of asphalt mixture components was evaluated on the fracture path using the maximum tangential stress criterion. It was shown that crack tip location, elastic modulus of aggregates and mastic are the most important affecting parameters on the magnitude of modes I and II geometry factors. It was also shown that the geometry factors are not sensitive to the Poisson's ratios of aggregates and mastic. In addition, fracture cracking path is affected by the elastic modulus of the asphalt mixture components such that, depending on the difference between the stiffness of stiffer coarse aggregates and softer NOMENCLATURE: K I , K II , stress intensity factors of modes I and II; K Ic , K IIc , critical stress intensity factors of modes I and II; Y I , Y II , geometry factors of modes I and II; P, applied load; P c , critical fracture load; R, radius of the SCB specimen; t, thickness of the SCB specimen; E, Young's modulus; E agg , Young's modulus of aggregates; E mastic , Young's modulus of mastic; E interface , Young's modulus of interface; D, distribution of aggregates in the SCB sample; Xi, Yi, Cartesian coordinate of new generated aggregate; R i , radius of new generated aggregate; X j , Y j , Cartesian coordinate of generated aggregate in the previous steps; R j , radius of generated aggregate in the previous steps; a, crack length; S 1 , S 2 , bottom support distances; S 1 /R, S 2 /R, bottom support distances over the radius ratios; A ij , area of aggregate j in group i; A i max , maximum summation area of aggregates in group i; A i min , minimum summation area of aggregates in group i; SCB, semicircular bending sample; MTS, maximum tangential stress; HMA, hot mix asphalt; SIF, stress intensity factor

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“…In general, stress analysis of cracked smart structures under dynamic loads is complicated and only those with simple geometries may be handled analytically. Some numerical techniques, such as extended finite element method and boundary integral equation method, have also been extended to study the fracture behaviour of cracked piezoelectric media …”

Section: Introductionmentioning

confidence: 99%

Multiple interfacial cracks in dissimilar piezoelectric layers under time harmonic loadings

Ayatollahi

Fartash

2018

Fatigue Fract Eng Mat Struct

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In this study, the dislocation‐based model is developed to study the interaction between time‐harmonic elastic waves and multiple interface cracks in 2 bonded dissimilar piezoelectric layers. In this model, cracks are represented by a distribution of so‐called electro‐elastic dislocations whose density is to be determined by satisfying the boundary conditions. Using the Fourier transform, this formulation leads to 2 singular integral equations, which can be solved numerically for the densities of electro‐elastic dislocations on a crack surface. The formulation is used to determine dynamic field intensity factors for multiple interface cracks without limitation of number of cracks. The dynamic field intensity factors are then calculated for both permeable and impermeable crack, and finally, numerical results are presented to illustrate the variation of these quantities with the electromechanical coupling, crack spacing, and the frequency of loading.

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Extended isogeometric dynamic and static fracture analysis for cracks in piezoelectric materials using NURBS

Cited by 167 publications

References 73 publications

Development of a new semi-analytical method in fracture mechanics problems based on the energy release rate

Development of a new semi-analytical method in fracture mechanics problems based on the energy release rate

Heterogeneity effects on mixed‐mode I/II stress intensity factors and fracture path of laboratory asphalt mixtures in the shape of SCB specimen

Multiple interfacial cracks in dissimilar piezoelectric layers under time harmonic loadings

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