Riv. Mat. Univ. Parma, Vol. 2, No. 1, 2011


Boundary element transient analysis of the dynamic T-stress and biaxiality ratio

Pages: 57-76
Received: 1 April 2010   
Accepted: 7 May 2010
Mathematics Subject Classification (2000): 65N38, 74R10.

Keywords: Dynamic T-stress, dynamic biaxiality ratio, symmetric-Galerkin boundary element method, elastodynamics, frequency analysis, transient responses.

Abstract: In this paper, we introduce a 2-D boundary integral equation (BIE) for determining the T-stress for cracks under dynamic loading conditions (dynamic T-stress or DTS). This BIE is only weakly singular and it can be used in the post-processing stage of a boundary element dynamic analysis of cracks. The formula can also be employed, in conjunction with any technique for the mode-I dynamic stress intensity (DSIF), for calculating the dynamic biaxiality ratio (DBR). In this work, the proposed BIE is formulated in the frequency domain so it can be used within the framework of the symmetric-Galerkin boundary element method for elastodynamics in the Fourier-space frequency domain. By applying the inverse fast Fourier transform to the frequency responses of the DTS and mode-I DSIF, the time histories (transient responses) of the DTS and DBR can be obtained. Numerical examples involving 2-D crack plates subjected to the Heaviside step loading are presented. The DTS results obtained from the aforementioned BIE are compared with some references available in the literature to validate the proposed technique.

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