A numerical method for the solid mechanics with Euler variables

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 have been out region disappear. this way, could calculated grids. Then did some test cases, get result that is right used mechanic problems.