2004/10/12 by Jakob Knudsen, A.R. Massih, A. R. Massih · 6 citations
Engineering · Mathematics · Physics and Astronomy · #Composite material #Elastic modulus #Engineering #Force Microscopy Techniques and Applications #Geometry #Granular flow and fluidized beds #Materials science #Mathematics #Mechanics #Moduli #Modulus #Physics #Scaling #Shear (geology) #Shear modulus #Stiffness #Structural engineering #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.mtrl-sci #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.72.036129
published in Physical Review E 72(3), 036129 (American Physical Society) · 15 pages, 7 figures
arxiv created 2004/10/12 · openalex publication_date 2005/09/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We model an interface layer connecting two parts of a solid body by N parallel elastic springs connecting two rigid blocks. We load the system by a shear force acting on the top side. The springs have equal stiffness but are ruptured randomly when the load reaches a critical value. For the considered system, we calculate the shear modulus G as a function of the order parameter phi describing the state of damage, and also the "spalled"; material (burst) size distribution. In particular, we evaluate the relation between the damage parameter and the applied force and explore the behavior in the vicinity of material breakdown. Using this simple model for material breakdown, we show that damage, caused by applied shear forces, is analogous to a first-order phase transition. The scaling behavior of G with phi is explored analytically and numerically, close to phi=0 and phi=1 and in the vicinity of phi(c), when the shear load is close to but below the threshold force that causes material breakdown. Our model calculation represents a first approximation of a system subject to wear induced loads.