关于线性非局部弹性理论的应力边界条件

On Stress Boundary Conditions in the Nonlocal Linear Elasticity Theories

应力边界条件的提法是线性非局部弹性理论尚未解决的一个理论问题。文中针对这一问题进行了研究，所导出的应力边界条件包含了物体微观结构的长程相互作用，这个结果不仅解释了在裂纹混合边界值问题中非线性局部弹性理论方程的解在常应力边界条件下不存在的问题，而且可以自然地得到裂纹尖端的分子内聚力模型。

Stress boundary condition in the nonlocal linear elasticity theories is an unsolved problem. In this paper, this problem is studied. The stress boundary conditions which contain the effect of the longdistance action of microstructures of matter are given. This result not only answers the problem that the solution of the nonlocal linear elasticity theories under the boundary conditions with constant stress does not exist in the crack problem with mixed boundary conditions, but also naturally gives a modol of molecular cohesive stress on the tip of crack.