ON THE CHOICE OF BOUNDARY CONDITIONS IN PROBLEMS OF THE LOCAL GRADIENT APPROACH IN THERMOMECHANICS

摘要

Within the framework of the local gradient approach in thermomechanics, we formulate key systems of equations of a mathematical model that describes the behavior of elastic bodies with regard for effects of a local heterogeneity. In this case, we choose the displacement vector and vector of local mass displacement or the stress tensor and the vector of local mass displacement as key functions. Based on this, we obtain and analyze solutions of the problems of the equilibrium state of a stretched layer. The problem of choice of boundary conditions in the problems of the local gradient approach is discussed. It is shown that the size effects, including the ultimate strength, depend substantially on the boundary conditions and that the assignment of the density or the divergence of the vector of local mass displacement is physically justified.