FastDM4C: A Fast and Efficient Discrete Model for Composites

Abstract

The adoption of composite materials in the aerospace industry has enabled the achievement of structural performance levels and weight savings unimaginable even just twenty years ago. Yet, only a fraction of the true potential of these materials has been expressed to date due to lack of high-fidelity models which has resulted in the adoption of extremely conservative designs compared to metallic counterparts. In part this is because, in contrast to high performance metallic alloys, the fracturing behaviors of composites are way more complex and difficult to simulate. Fiber reinforced composites feature many interacting mechanisms spanning several material and structural length scales, from the fiber scale of few microns to the structural scale of a composite wing with a span of several meters. This makes the development of computational models for the design and optimization of composite structures extremely challenging owed to the conflicting need of being able to capture microdamage events at the fiber scale while still be efficient enough to simulate structures that are at least six orders of magnitude larger. This work attempts to address this challenging problem by formulating a novel discrete, sub-lamina-scale model aimed at providing an effective description of damage at the microscale while maintaining computational costs comparable to continuum, homogenized formulations. The proposed model is also based on the DM4C where the constitutive relationship of the discrete members representing the matrix are edge-based instead of 3D-based. Both DM4C FastDM4C have been proven successful and are providing tools to both academic and industry partners to pave the way for the full exploitation of the advantages of composites in aerospace structure design. In this new approach, composites are simulated as an assembly of Representative Unit Cells (RUC) of roughly the same dimensions of the average distance between splitting cracks. In contrast to traditional models, which homogenize the mechanical behavior of the fibers and matrix into an equivalent continuum, the new model simulates explicitly groups of fibers and surrounding matrix material leveraging a proper configuration of one-dimensional Finite Elements. The arrangement of the fiber- and matrix-elements within the RUC is designed to replicate the transversely-isotropic behavior of the lamina. One distinct regularized strain-softening constitutive law is utilized to describe the behavior of the fibers using a new element called Discrete Fiber Model (DFM). The matrix is instead modeled using three different implementations of the same edge-based constitutive formulation called Discrete Matrix Model (DM2) which is meant to capture pure matrix behavior, in-plane shear behavior, and interface behavior between different plies. A multiple stage optimization algorithm is developed to calibrate both elastic and fracture parameters of the model, both at the small scale (for elastic behavior) and at the large structure scale (for fracturing behavior) levying the use of a Machine Learning/Artificial Intelligence algorithm coupled with a relational database to store and process large number of simulations. Then, several simulations of the composite structures under highly non-linear behavior are used to validate the model and showcase its capability of capturing the inherent damage and fracture mechanisms of composite laminates. It will be shown that the proposed FastDM4C is capable of capturing the inherently complex damaging behavior of composites by comparing it to experimental results, while at the same time showing its numerical efficiency capable of running real engineering structures.