2015/10/13 by Michael Moshe, Eran Sharon, Raz Kupferman · 1 citation
Biochemistry, Genetics and Molecular Biology · Engineering · Mathematics · Physics and Astronomy · #Adhesion, Friction, and Surface Interactions #Airy function #Cellular Mechanics and Interactions #Classical mechanics #Composite material #Curvature #Elasticity (physics) #Engineering #Force Microscopy Techniques and Applications #Geometry #Materials science #Mathematical analysis #Mathematics #Mechanics #Physics #Point (geometry) #Scalar field #Shear stress #Stress (linguistics) #Stress field #Structural engineering #cond-mat.soft
paper · pdf · doi:10.1103/physreve.92.062403
10 pages, 4 figures
arxiv created 2015/10/13 · openalex publication_date 2015/12/07 · arxiv updated 2016/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.