Based on the requirement of field engineering, we proposed a new numerical method for analyzing solid mechanics with Euler variables. By replacing Lagrange variables variables, there will be three items appearing in equation. We use fixed grid to calculate mechanics, and boundary material regiment describe movement material, after moves beyond element size, grids appear corresponding old which ...

Since early publications in the late 1980s and 1990s, finite volume method has been shown suitable for solid mechanics analyses. At present, there are several flavours of method, which can be classified a variety ways, such as grid arrangement (cell-centred vs. staggered vertex-centred), solution algorithm (implicit explicit), stabilisation strategy (Rhie–Chow Jameson–Schmidt–Turkel Godunov upw...

As Science & technology develop, many practical problems, such as the mathematical boundary layer theory or approximation of solution of various problems described by differential equations involving large or small parameters have become increasingly complex and therefore require the use of asymptotic methods. However, the theory of asymptotic analysis for differential operators has mainly been...

When a frictional interface is subject to a localized shear load, it is often (experimentally) observed that local slip events initiate at the stress concentration and propagate over parts of the interface by arresting naturally before reaching the edge. We develop a theoretical model based on linear elastic fracture mechanics to describe the propagation of such precursory slip. The model’s pre...

In this paper, we study the mechanics of the brain during closed head impact via numerical simulation. We propose a mathematical model of the human head, which consists of three layers: the rigid skull, the cerebrospinal fluid and the solid brain. The fluid behavior is governed by the Navier-Stokes equations, and the fluid and solid interact together according to the laws of mechanics. Numerica...