Averaged strain energy density estimated rapidly from nodal displacements by coarse fe analyses: cracks under mixed mode loadings

The strain energy density (SED) averaged over a structural volume allows to assess the fracture and fatigue behaviour of cracked components under mixed-mode loadings. To rapidly estimate the averaged SED , two approaches have been previously proposed: (i) the direct approach; (ii) the peak stress method (PSM) and nodal stress (NS) approach. In this paper the nodal displacement (ND) approach is presented to rapidly estimate the averaged SED from the nodal displacements by FE analyses. This method combines the advantages of all previous approaches, i.e. the use of coarse meshes able to capture the contributions of both stress intensity factors (SIFs) and higher order terms, without requiring geometrical modelling of the control volume. To validate the method, cracked plates and cracked bars under mixed-mode loadings have been analysed. The averaged SED values estimated by the ND approach agree with those calculated by the direct approach, within a range of applicability.