The behavior of third gradient materials is analyzed. They possess stress tensor fields of second, third and fourth order. Starting from the principle of virtual power, we derive the admissible boundary conditions. Those on free surfaces can only be obtained by the application of the divergence theorem of surfaces. On the other hand, such an application to fictitious internal cuts makes no sense although it is usually practiced. We prove that some of the boundary conditions on a free surface may be interpreted as the equilibrium conditions of a shell. So a crust shell exists on such a surface and a beam exists where patches of the surface meet. On the other hand, no such shells or beams can be found with fictitious surfaces in the interior of a continuum. Our finding does not depend on any specific constitutive assumption.

分析了第三种梯度材料的行为。它们具有二阶，三阶和四阶的应力张量场。从虚拟功率原理出发，我们得出了可容许的边界条件。自由表面上的那些只能通过应用表面的发散定理来获得。另一方面，尽管通常被实践为虚拟内部切割的这种应用是没有意义的。我们证明自由表面上的某些边界条件可以解释为壳的平衡条件。因此，在这样的表面上存在外壳，并且在表面的相交处存在梁。另一方面，在连续体内部找不到带有虚拟表面的此类壳或梁。我们的发现不依赖于任何特定的构成假设。