COMPARING VARIATIONAL CRITERIA USED TO PREDICT THE PATH OF A CRACK

摘要

The present paper discusses a problem of searching of a path of a brittle crack which appears in a two-dimensional body as a cause of an external load. The contours of the body and the external load are given. A global criterion approach is applied to find the crack path. This approach proposes that the path can be found as a solution of a variational problem. This means that the solution is a geodesic line in some space with a specially selected metric function. The choice of this function requires special attention. The application of two possible weight functions is discussed. The first weight function equals to a maximum principal tension stress, the second equals to the energy required for the crack to grow. This energy is calculated using the Winkler-Zimmerman foundation. Several particular solutions for an infinite plate with a circular hole, subjected to an external load, are discussed. Approximate solutions are obtained as finite series with unknown coefficients. This method allowed to replace the variational problem by a problem of search of a minimum of a function of many variables. The solutions, obtained using each of the two weight functions, are compared with each other, several known exact solutions and some experimental data.