A continuum shape sensitivity method for fracture analysis of isotropic functionally graded materials

Abstract

This paper presents a new continuum shape sensitivity method for calculating mixed-mode stress-intensity factors for a stationary crack in two-dimensional, linearelastic, isotropic FGMs with arbitrary geometry. The method involves the material derivative concept taken from continuum mechanics, the mutual potential energy release rate, and direct differentiation. Since the governing variational equation is differentiated prior to discretization, resulting sensitivity equations are independent of approximate numerical techniques, such as the finite element method, boundary element method, mesh-free method, or others. The discrete form of the mutual potential energy release rate is simple and easy to calculate, as it only requires multiplication of displacement vectors and stiffness sensitivity matrices. By judiciously selecting the velocity field, the method only requires displacement response in a subdomain close to the crack tip, thus making the method computationally efficient. Seven finite-element based numerical examples, which comprise mode-I and mixed-mode deformations and/or single or multiple interacting cracks, are presented to evaluate the accuracy of the fracture parameters calculated by the proposed method. Comparisons have been made between stress-intensity factors predicted by the proposed method and available reference solutions in the literature, generated either analytically or numerically using various other fracture integrals or analyses. Excellent agreement is obtained between the results of the proposed method and previously obtained solutions. Therefore, shape sensitivity analysis provides an attractive alternative to fracture analysis of cracks in homogeneous and non-homogeneous materials.

Damage detection with genetic algorithms taking into account a crack contact model

“…Changes in the natural frequencies was the first and more studied criterion [20,5,16,12], and the detection of many cracks with this technique was reported in [5,16,10,12] . Some attempts to detect the damage from the inverse problem were included in studies [14,17]. Anyway, the bad conditioning makes the detection difficult to be tackled as a pure inverse problem.…”

A completely meshless analysis of cracks in isotropic functionally graded materials

“…The results for crack length a = 3.5 units are given in Table 6, which are obtained by using 21 nodes along the x 1 -axis and 41 nodes along the x 2 -axis plus 24 extra nodes located in three rings around the crack tip. The present MLPG results are compared with the EFG results by Rao and Rahman [16] and the FEM results by Rao and Rahman [16] (using 880 elements and 2711 nodes). Also, the variation of the first and second modes of SIFs versus the crack length of the edge-cracked problem is plotted in Figs 10 and 11,…”

Effect of Mechanical Heterogeneity on the Structural Integrity of HTPB Propellant Grain

“…For complex structural components of heterogeneous materials, this approach has problems with the complicated construction of element stiffness matrices and heavy workload. Other methods for dealing with material heterogeneity, such as mesh-free methods [ 18 , 19 ], microelement methods [ 20 , 21 , 22 ], and extended multi-scale finite element methods [ 23 , 24 , 25 ], are still computationally expensive and difficult to apply to complex models.…”

“…Therefore, an isoparametric finite element has been developed and solve problems involving mechanically heterogeneous materials [14][15][16][17]. Ho approach still requires interpolating material properties at each Gaussian point from the nodal material properties of the element using isoparametric tions, which need to construct the element stiffness matrices related to coord complex structural components of heterogeneous materials, this approach ha with the complicated construction of element stiffness matrices and heavy Other methods for dealing with material heterogeneity, such as mesh-fre [18,19], microelement methods [20][21][22], and extended multi-scale finite eleme [23][24][25], are still computationally expensive and difficult to apply to complex Therefore, the gradient finite element method was used to evaluate the e mechanical heterogeneity of propellant mechanical performance on the grain integrity. In a case-bonded SRM, the propellant grain undergoes various cons introduced during curing and cooling, resulting in heterogeneous mechanical Therefore, the mechanical heterogeneity of propellant grain is constructed by the spatial distribution of constant strains, and the effect of mechanical hetero the structural integrity of the propellant grain is investigated.…”