Relationship between contact size (A) and static friction (f) has been studied for rigid crystalline systems. We built a series of systems with two identical surfaces but different orientations and investigated the effects of the size and shape of the contact area on static friction. In these systems, there are numerous nontrivial commensurate contacts. Our results confirmed that the relationship between A and f was determined by both commensurability and shape of the contact. For commensurate contacts, f ∝ A independent of the shape. For incommensurate contacts, generally f ∝ A⁰ for regular shapes or f ∝ A^1/4 for irregular shapes; however, in very few cases of regular shapes, f ∝ A^1/2. Moreover, in above systems, commensurability of a contact can be easily changed by a perturbation of the misfit angle. Therefore, if the perturbation caused by the lateral force and the deformation of the surface are considered (as is the case in real systems), further research is necessary.

对于刚性晶体系统，已经研究了接触尺寸（A）和静摩擦（f）之间的关系。我们建立了一系列具有两个相同表面但方向不同的系统，并研究了接触面积的大小和形状对静摩擦的影响。在这些系统中，有许多不平凡的对应联系人。我们的结果证实，A和f之间的关系由可比性和接触形状决定。对于相称的触点，f ∝ A与形状无关。对于不相称的接触，对于常规形状，通常为f ∝ A ⁰或fα甲^1/4为不规则形状; 然而，在极少数规则形状的情况下，f ∝ A ^1/2。此外，在以上系统中，通过失配角的扰动可以容易地改变接触的可比性。因此，如果考虑到由横向力和表面变形引起的扰动（在实际系统中就是这种情况），则有必要进行进一步的研究。