Meshless local Petrov-Galerkin micromechanical analysis of structural composites

This study aims at the development of a micromechanical model for structural composites using the meshless local Petrov-Galerkin method (MLPG) to predict the stiffness properties, and the shear correction factors of structural composites from the analysis of the representative volume element (RVE). Micromechanical analysis of structural composites is possible due to the presence of the RVE also called the unit cell. On the microscale, comparable to the scale of unit cell, the composite is heterogeneous due to the presence of the reinforcing yarn and the matrix. However, on the macroscale, compared to the structural scale, the composite is assumed to be homogeneous and orthotropic. The homogeneous composite properties are then predicted from the properties of the constituent materials and their distribution.; The highlight of the study is the treatment of some challenging problems in the meshless local Petrov-Galerkin method-based micromechanical analysis of structural composites. The unit cell is discretized and periodic boundary conditions are set up and imposed between opposite end-faces of the unit cell, essential boundary conditions are enforced by the penalty method. The treatment of material discontinuities at the interfaces between different phases of the composite is presented by means of the direct imposition of interface boundary conditions. In addition, an algorithm for handling of periodic boundary conditions in the MLPG method using the multipoint constraint technique is also presented. The MLPG formulation is presented for the six linearly independent deformations of the unit cell. From the forces acting on the unit cell for each of the six deformations, the elastic constants of the composite can be computed.; In this study, a micromechanical model using both the finite element method and the MLPG method is suggested to predict the flexural stiffness properties and the shear correction factors for a class of composite beam problems including textile composite beams. Examples are presented to illustrate the effectiveness of the current method, and it is validated by comparing the results with available analytical and numerical solutions. The current method shows great potential for applications in micromechanics, especially for textile composites.