The effect of mesh size on failure for shell structures

More than any other application, simulation of crash events depends on the precise representation of fracture. At the same time, practical considerations typically force the crash analyst to use shell elements for many types of thin-walled structures, such as cars, aircraft, and ships. For these reasons, improving the reliability of fracture for shell elements is of primary concern for analysis of crash in structures. Failure strain of shell elements depends strongly on the size of the element. Failure strain also depends on the state of stress, which has been characterized in terms of triaxiality for the plane stress condition (Xue and Wierzbicki, 2009). However, there is nothing written about how the failure strain depends on both the triaxiality and the element size together. As the necking drives the mesh size effect in shell elements and is more associated with some stress states than others (e.g. it is present in uniaxial tension, but not biaxial tension), it is anticipated that the mesh size effect will depend on stress state. This paper fills this gap by delivering an engineering framework with which to determine the effect of stress state and element size on failure strain. The framework is completely modular, taking in a yield criterion, a Forming Limit Diagram (FLD, used for necking prediction), a hardening relationship, and a failure locus (for a single element size) as input. To demonstrate the framework, an example is given in which the Swift (1952) condition is used to model necking in multiple state of stress, the Modified Mohr-Coulomb (MMC) model (Bai, 2010) is used for fracture modeling, and the power hardening law is used to model the hardening relationship. This framework is applied to a set of test data taken from the literature (Hwang et al. 2009). The example shows that the fracture associated with uniaxial tension should have a much larger dependence on failure strain than equi-biaxial tension, and that there is a nonlinear relationship between these two conditions.