Two Dimensional Stress and Displacement Wave Propagation Under Shock Loading in Saturated Porous Materials with Two Dimensional Functionally Graded Materails Using MLPG Method

The meshless local Petrov-Galerkin (MLPG) method is employed for dynamic analysis of fully saturated porous materials under shock loading considering two directional functionally grading patterns in constitutive mechanical properties. To approximate the trial functions in the radial point interpolation method (RPIM), the radial basis functions (RBFs) are utilized. The mechanical properties are simulated using a non-linear grading model with the radial and axial exponent. The 2D propagation of displacement and stresses are tracked through radial and axial direction in a two dimensional domain for various grading patterns at different time instants. By employing the presented meshless technique, the effects of various grading patterns on maximum values of stresses and displacements are studied in detail. The variation in the value of radial exponent has a significant effect on the dynamic behavior of radial displacement and radial stress comparing to the variation in the value of axial exponent. The MLPG method has a high capability to track the stress and displacement wave fronts at every arbitrary time instant in 2D domain.