Classification of smeared crack models based on material and structural properties

Abstract

The paper presents a classification of existing smeared crack models. A concise characterization of the classical models, i.e. the fixed crack and rotating crack model, with their more advanced successors in the form of the multiple fixed crack and the microplane model, identifies the underlying heuristic assumptions with respect to the orientation of the plane of degradation (POD). Following an analytical derivation, the critical PODs are uniquely identified for primary as well as for subsequent secondary cracking. Their direction is shown to depend solely on the character of the unilateral fracture criterion which is applied at the POD and on the character of the applied loading. The ductility of the response is found to play the key role for the orientation of the PODs in the process of secondary cracking. Therefore, it must be considered an important parameter whenever a specific material formulation for a numerical simulation is selected. The proposed analytical approach encompasses the classical models as physically relevant special cases and provides a smooth transition between them. Thus, the presented adaptive fixed crack model allows for a proper choice with respect to the relevant material characteristics and loading conditions.