Constitutive model for shear transfer in cracked concrete

The capability of rough cracks in concrete to transmit significant amounts of shear has been well recognized for the past few decades. In spiteof extensive analysis and experimentation of interface shear, general constitutive models relating shear and normal stresses to corresponding displacements are scarce. A constitutive model for shear transfer (crack stiffness matrix) is desirable for the finite element modeling as well as for modeling mixed mode fracture problems. It is difficult to formulate the relation between stresses and displacements when all four parameters change during the test. To simplify the problem, normal and shear stresses were decoupled during testing in the study reported here. From the test data, expressions were formulated for shear stress versus slip and slip versus dilation at constant normal stresses. Coupling was incorporated by relating normal stresses to peak shear stresses by means of a "failure surface." Using the proposed crack stiffness matrix formulation, the predicted values were satisfactorily compared with the data of other tests where normal and shear stresses were coupled. The proposed model assumes total deformation theory. Unloading is not considered.