This contribution focuses on gradient formulations for the prediction of the static failure load of V-notched and cracked components made of brittle materials. A weighted average of the local equivalent stress, called non-local equivalent stress, is first considered and subsequently approximated by a gradient expansion up to the spatial second-order derivative. A distinguishing characteristic of the present approach is that the non-local equivalent stress is calculated by solving a differential equation of implicit type. The numerical solution for a V-notch in the presence of Neumann's boundary conditions is presented. Moreover, the analytical solutions of an one-dimensional case is proposed. Finally, the static failure loads predicted by to the present formulation through the finite element technique are compared with the experimentally determined ones.
An implicit gradient stress failure condition
Tovo R.;Livieri P.;Benvenuti E.
2005
Abstract
This contribution focuses on gradient formulations for the prediction of the static failure load of V-notched and cracked components made of brittle materials. A weighted average of the local equivalent stress, called non-local equivalent stress, is first considered and subsequently approximated by a gradient expansion up to the spatial second-order derivative. A distinguishing characteristic of the present approach is that the non-local equivalent stress is calculated by solving a differential equation of implicit type. The numerical solution for a V-notch in the presence of Neumann's boundary conditions is presented. Moreover, the analytical solutions of an one-dimensional case is proposed. Finally, the static failure loads predicted by to the present formulation through the finite element technique are compared with the experimentally determined ones.I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
