Analysis of Mixed‐Mode Fracture in Concrete

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Abstract
A smeared crack model that covers tensile softening in mode I and shear softening in mode II fracture is described. In addition, the model provides for unloading and reloading and for multiple crack formation. Particular forms of tension and shear softening functions and relations with more conventional models are discussed. Two examples involving mixed‐mode fracture in notched, unreinforced concrete beams have been included to demonstrate the versatility of the model. The results indicate that the addition of shear softening is essential to obtain realistic results in the post‐peak regime since the classical approach based on a constant shear retention factor then results in a too stiff behavior. The results furthermore demonstrate that snap‐back behavior may occur in strain‐softening concrete under quasistatic loading conditions. Attention is also given to the possibility of hour‐glass formation when constitutive laws involving softening are deployed in a finite element model.

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