Efficiënte orderreductie voor de voorspelling van macroscopische mechanische eigenschappen van niet-lineair vezelversterkt composietmateriaal met verschillende ontwerpparameters

Over the last few decades, fiber reinforced polymer (FRP) composites have been widely used in various engineering applications. This is largely due to their ability to be tailored to achieve desirable mechanical properties, which make them suitable for use in aerospace, automotive, medical, energy, and other industries. However, designing such composite materials is often a repetitive and time-consuming process as numerous combinations of various design parameters must be evaluated until the desired mechanical properties at the structural level are achieved. As the demand for FRP composites continue to grow, it is crucial to be able to accurately predict the behavior of the composites. FRP composites exhibit a heterogeneous composition at micro- and mesoscale but can be regarded as homogeneous at the macroscale. As a result, predicting their behavior requires multiscale analysis. Computational homogenization has been developed for this purpose. It links the solution of two or more boundary value problems (BVP), for example, one at the macroscale and another at the microscale. The solution of the BVP at the macroscale defines the boundary conditions that are applied on the representative volume element (RVE) at the microscale. At the microscale, material behavior of both the matrix and the fiber is modeled. After solving the BVP at the microscale, the resulting microscopic stresses are averaged over the volume of the RVE to determine the macroscopic stress-strain relationship. This allows detailed microstructural information, such as the properties and geometrical arrangement of the constituents, to be accounted for in the macroscopic behavior. It becomes a useful tool for investigating the onset and propagation of damage occurring at the microscale, as the details of the stress and strain distributions throughout the microstructure can be resolved. However, it poses practical challenges due to its high computational cost, especially in material-by-design settings and when nonlinear effects are considered. Model order reduction (MOR) can be employed to reduce the computational cost. This work describes the development and capabilities of a MOR framework to accelerate the parametric study of unidirectional composite plies with a plastic constitutive material model for the matrix when the varying fiber distribution in the microstructure is the parameter of interest. It is logical to examine numerous realizations of fiber distribution for the comprehensive understanding of damage initiation and failure mechanisms in composite. While there are many studies that were carried out in such a way in the case of composites with linear elastic properties under various loading conditions, little attention was given to the similar study in the case of nonlinear composites. Nonlinear micromechanical analysis would typically be focused on limited realizations of fiber distributions since the nonlinear simulation is generally computationally expensive. it often requires fine numerical discretization to correctly represent the microstructure at the microscale. Numerous nonlinear simulations eventually results in prohibitive computational cost. While variation in local fiber arrangements has pronounced effect on damage initiation and failure mechanisms in composite, an attempt to reduce the computational cost for the parametric study of such a problem seems to be absent. The MOR framework used in this work is based on constructing the reduced order basis (ROB) using the proper orthogonal decomposition (POD), followed by the construction of the reduced order model through the Galerkin projection. Along the process of constructing the reduced order model (ROM) and utilizing it to achieve the computational gain, several challenges arise. From the start, the variation in fiber distributions leads to the variation in spatial discretizations which interrupts the usual POD-based procedure. In the case of nested refinement, it is straightforward to construct a common finite element mesh by laying each adapted mesh over each other. In the case of varying local refinements like the meshes for various fiber distributions, a common discretization space results in too fine discretizations. A premeshed RVE strategy is proposed to overcome this issue. Once the process can be continued, the propose microstructure ranking coupled with the convergence criteria are used to establish a representative ROM and determine the quality of the solution from the ROM. Lastly, the accuracy of the ROM solution and the computational efficiency are further improved by incorporating the concept of local ROB. The capability of this MOR framework is first demonstrated on a linear problem where both matrix and fiber are considered linear elastic. The application is then extended to a nonlinear problem in which the source of nonlinearity comes solely from the nonlinear constitutive model of matrix. Results from the finite element analysis and from the ROM are compared to assess the efficiency and accuracy of the proposed MOR framework which accounts for the variation of fiber distributions. In the linear case, the computational load during parametric studies is significantly reduced as the model dimension in the microscale analyses is smaller. For the nonlinear problem, notable computational gains are also achieved with the potential for further improvement through the second stage of reduction, the so-called hyper-reduction, in future work. In terms of accuracy, the stress distributions as well as global stress-strain responses from the ROM are shown to be in good agreement with those from the finite element analysis and. Discrepancies in global responses are generally less than 10\% , with most cases exhibiting differences of less than 5\%. These responses obtained from the ROM also fall within the scatter of experimental data reported in the literature. In terms of local responses, the ROM captures stress distributions in critical regions of the microstructures very well. Similar levels of discrepancy in stress fields are also observed in the literature when full-field experimental measurements are compared with numerical results from finite element analysis. Though the damage mechanism is not yet incorporated in this proposed framework, it is crucial to first demonstrate that the local stress distributions under different loading conditions can be obtained accurately as the prediction of the damage initiation and progression relies on the accurate prediction of local stress distributions. This work paves way for extending the approach to consider the process of damage initiation and evolution as the source of the nonlinearity in future work. When coupling with other MOR strategies that account for the variation of loading and material parameters, this could open new possibilities in the design and analysis of unidirectional-based composite.