Analysis of two cohesive zone models for crack propagation in notched beams using the BEM

Abstract

Crack propagation in a single-edge notched beam is analyzed with the three-point bending test. Two constitutive laws that describe the material softening in the cohesive zone were tested, and their results were compared. The dual boundary element method (DBEM) is employed with the traction boundary integral equation using the tangential differential operator. A constitutive law was introduced in the system of equations, and the cohesive forces were directly computed at each loading step. The results are compared with the experimental and numerical results available in the literature.

Analysis of the Crack Propagation in Fiber-Reinforced Concrete Specimens Using the Bem

“…4. This case was studied in [27] and it is repeated here because the formulation and the computer code were changed. The depth of the beam (d) is 0.2 m, the width is 0.05 m, and the length (l) is 2.0 m. The adopted ratio between notched depth and beam depth (a/d) was 0.5.…”

“…The present code is different to that used in [26], [27], which employed linear boundary elements and considered different DBEM equations. Furthermore, the formulation using eqns (4) and (5) was stable when the constitutive law employed two straight lines with reference to that presented in [27] without reducing or changing benefits on the direct computation of the cohesive forces at each incremental loading step. Figure 6: The notched beam subjected to the three-point bending test in [31].…”

“…The traction in the direction j on the crack surface  2 within the cohesive zone (t 2 j ) appeared in both integrals performed on crack surfaces  2 and  3 in eqns (4) and (5) because the traction t 3 j is equal to -t 2 j in the cohesive zone. The numerical implementation in the present study employed eqns (4) and (5), which is different to the formulation used in [26], [27].…”