*2.5. Simulation*

To determine plasma pressure profiles, experimental rear free-velocity profiles were predicted using simulation. The laser shock propagation simulation was carried out using the commercial FE code ABAQUS 6.14 [19]. A 2D axisymmetric model was developed. Since laser shock is a high-speed process, an explicit solver is used while considering the dynamic effects.

### 2.5.1. Target Geometry and Boundary Conditions

Figures 3 and 4 respectively show the target configuration and the mesh used for simulation. The target was modeled as a planar shell with a 1 mm width and a 7.5 mm length. It was meshed by means of CAX4R elements (Continuum, 4-node bilinear axisymmetric, quadrilateral, reduced integration, hourglass control). To improve the accuracy of the FE solutions, a refinement mesh was used in the treated area with the use of a BIAS function in the X direction (Figure 4). As the element dimensions decreased, the obtained results became more stable. A decrease between experimental and numerical rear free-velocity profiles as observed. The treated region was refined with small elements of 1 μm × 1 μm dimensions. For the boundary condition, one node of the bottom surface was fixed (Figure 3).

**Figure 3.** Target used for the laser shock peening (LSP) finite element (FE) modeling: (**a**) geometry and (**b**) 2D axisymmetric FE model.

**Figure 4.** Mesh refinement used for the LSP simulation.
