title: Elastic interactions between two-dimensional geometric defects.
abstract: 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.
authors.affiliation: Department of Physics, Syracuse University, Syracuse, New York 13244-1130, USA and Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA.
authors.forename: Michael
authors.initials: M
authors.lastname: Moshe
authors.affiliation: Racah Institute of Physics, The Hebrew University, Jerusalem.
authors.forename: Eran
authors.initials: E
authors.lastname: Sharon
authors.affiliation: Einstein Institute of Mathematics, The Hebrew University, Jerusalem.
authors.forename: Raz
authors.initials: R
authors.lastname: Kupferman