Moshe Michael, Sharon Eran, Kupferman Raz
Department of Physics, Syracuse University, Syracuse, New York 13244-1130, USA and Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA.
Racah Institute of Physics, The Hebrew University, Jerusalem.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Dec;92(6):062403. doi: 10.1103/PhysRevE.92.062403. Epub 2015 Dec 7.
In this paper, we introduce a methodology applicable to a wide range of localized two-dimensional sources of stress. This methodology is based on a geometric formulation of elasticity. Localized sources of stress are viewed as singular defects-point charges of the curvature associated with a reference metric. The stress field in the presence of defects can be solved using a scalar stress function that generalizes the classical Airy stress function to the case of materials with nontrivial geometry. This approach allows the calculation of interaction energies between various types of defects. We apply our methodology to two physical systems: shear-induced failure of amorphous materials and the mechanical interaction between contracting cells.
在本文中，我们介绍了一种适用于广泛的局部二维应力源的方法。该方法基于弹性的几何公式。局部应力源被视为与参考度量相关的曲率的奇异缺陷——点电荷。存在缺陷时的应力场可以使用标量应力函数来求解，该函数将经典的艾里应力函数推广到具有非平凡几何形状的材料的情况。这种方法允许计算各种类型缺陷之间的相互作用能。我们将我们的方法应用于两个物理系统：非晶材料的剪切诱导破坏和收缩细胞之间的机械相互作用。
