This study presents a simplified, reduced-order finite element analysis (FEA) methodology developed to evaluate deformation, fretting damage, and life characteristics of multi-layer composite screen meshes used in shale shaker systems for solid control in drilling. Traditional screen development relies heavily on iterative physical testing, which is time-consuming and costly. To support faster screening of screen mesh concepts, a computationally efficient explicit FEA model based on localized domain reduction and layer homogenization was developed in ABAQUS to reproduce the deformation behavior of the screen mesh under representative operating loads. The model captures a small representative screen mesh area to reduce computational cost while preserving key woven-structure interactions. The middle layer mesh is simulated with elasto-plastic beam elements that represent realistic wire geometry, while the top layer is modeled using homogenized elasto-plastic shell properties. The bottom layer, significantly stiffer, is idealized as a rigid woven support. Thermal pretension resulting from manufacturing and pressure loading due to cyclic impact of fluid and mesh mass are included. A scaled monotonic pressure is applied to mimic vibration-induced cyclic loading. Simulation results show that the model successfully predicts the characteristic deformation mode observed in laboratory tests: wire openings in the middle layer occur above knuckle locations of the bottom mesh. Contact pressure distributions between mesh layers strongly correlate with observed worn areas. Two screen mesh configurations with different mesh densities were evaluated. Mesh A exhibits larger deformation and higher cumulative contact pressure, consistent with its shorter measured life. Mesh B, with thinner but denser bottom wires, shows reduced deformation magnitude (approximately half of Mesh A) and a contact-pressure-based damage metric about 40% lower, aligning with lab-reported life improvement. The study demonstrates that the sum of nodal contact pressures above a threshold provides a meaningful predictor of shale shaker screen life, enabling accelerated comparative evaluation of screen mesh designs.