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 analysisof fully saturated porous materials under shock loading considering two directional functionally gradingpatterns in constitutive mechanical properties. To approximate the trial functions in the radial pointinterpolation method (RPIM), the radial basis functions (RBFs) are utilized. The mechanical propertiesare simulated using a non-linear grading model with the radial and axial exponent. The 2D propagationof displacement and stresses are tracked through radial and axial direction in a two dimensional domainfor 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 studiedin detail. The variation in the value of radial exponent has a significant effect on the dynamic behaviorof radial displacement and radial stress comparing to the variation in the value of axial exponent. TheMLPG method has a high capability to track the stress and displacement wave fronts at every arbitrarytime instant in 2D domain.