Weight function determinations for shear cracks in reinforced concrete beams based on finite element method

Abstract

An efficient approach of evaluating the weight functions for the generally load applied faces of shear cracked RC beams with varying shear span/beam depth ratios is presented using the corresponding weight functions for the RC beams with two shear span/beam depth ratios. The shear cracked RC beam under applied load can be considered as an oblique edge crack elastic geometry under mixed load conditions if the nonlinear bridging force is evaluated according to a crack bridging model separately. With pure bend load conditions, both Mode I and II weight functions for the oblique edge crack geometries with three shear span/beam depth ratios for different crack length/beam depth ratios are evaluated through applying the Virtual Crack Extension technique with symmetric mesh around the crack-tip into finite element analysis, where all weigh function components exhibit orderly trends with respect to the changing shear span/beam depth. As a result, the weight functions for the shear crack RC beams with the other shear span/beam depth ratios can be calculated following the orderly trends. Since the crack-tip singular behaviors of fracture problems is observed only in the primary crack-face nodal 2 weight functions, to facilitate application, the primary crack-face weight functions are formulated accurately as a function of crack length and distance away from the crack-tip employing the fitting and interpolation methods.

A review and verification of analytical weight function methods in fracture mechanics

“…27 Deng and Matsumoto presented numerical WF for shear cracked beam by using FEM with VCE and fitting/interpolation technique in which a large amount of work was required. 28 Another useful numerical WF approach is the boundary element method (BEM). 17,90-93 Lorenzo et al made BEM analysis for WFs that were fitted in a standard form and used for analysis of CODs and strip-yield cracks.…”

“…More recent developments on the WF determination by using FEM can be found in the book “Finite Elements in Fracture mechanics” by Kuna . Deng and Matsumoto presented numerical WF for shear cracked beam by using FEM with VCE and fitting/interpolation technique in which a large amount of work was required . Another useful numerical WF approach is the boundary element method (BEM) .…”

“…The numerical methods are still being developed in the recent literatures. 10,27,28 Among these, the most extensively used FEM has very powerful meshing and computational capability for complex crack geometries. However, the amount of work and time needed for meshing and numerical computation for many crack configurations coupled with large number of crack length steps and subsequent curve fitting is very substantial.…”

“…Subsequent numerical WFMs mainly include the finite element method (FEM), boundary element method (BEM), boundary collocation method (BCM), and etc. The numerical methods are still being developed in the recent literatures . Among these, the most extensively used FEM has very powerful meshing and computational capability for complex crack geometries.…”

Weight function calculation method for analyzing mixed-mode shear cracks in reinforced concrete beams

“…Therefore, this study aims at proposing a method of calculating WFs for shear cracked RC beams based on a virtual crack extension (VCE) technique in finite element method [20][21][22]. Actually, exploiting the mixed mode WFs from this method, the authors have successfully predicted the fatigue life and determined the dominant degradation mechanisms of RC slabs under a moving wheel-type load focusing on the propagation and failure along a couple of critical punching shear cracks [23,24].…”