Isogeometric Computational Modeling of Curvilinear Fiber Composites

Abstract

Recently, composite materials are broadly used in a wide range of industries. Composite materials are attractive in designing applications not only because of its outstanding specific mechanical performance but also its ability to tailor the material properties based on design-purpose. Conventional fiber-reinforced composite structures have utilized layup orientation to achieve a desired mechanical performance of a laminate. However, these structures are still limited to straight fibers, which are not necessarily placed in the optimal way to carry the load. Thanks to the advancement in manufacturing technology, emerging technologies such as Automated Fiber Placement (AFP) and Additive Manufacturing (AM) enable complex and large-scale structural designs, especially leveraging on Curvilinear Transverse Isotropy (CTI), in which fibers are deposited along curvilinear paths to optimize the load-carrying capability or other functional properties. In a geometrical modeling process, it is common to design structures using Computer-Aided Design (CAD) software e.g. AutoCAD, CATIA, SolidWorks, etc., and spline functions are often used to parameterize a geometry. However, in analysis, engineers use Finite Element (FE) software packages e.g. ABAQUS, ANSYS, NASTRAN, etc., in which the geometry does not follow the same definition from the CAD design. Thus, the transition process between CAD file and CAE file takes a huge amount of time for re-meshing, refinements, etc. In addition, FEM approximates a CAD model using polynomial basis/interpolation functions instead of spline functions. These facts result in inefficient time consumption and obtaining less accurate solution. In order to reduce these burdens, it is necessary to integrate the modeling routine and the analysis to obtain high convergence rate and greater precision of the solution. This integration between geometrical modeling and analysis is referred to as Isogeometric Analysis. First, the theoretical framework of NURBS-based Isogeometric Analysis will be introduced using variational method under the assumption of linear elasticity and plane stress condition. Then, in order to model CTI composites, new methods of computing stiffness matrix in each integration point on an element will be discussed. Second, the implementation framework will be explained using parallelization and vectorization for the element stiffness evaluation and the assemble routines in MATLAB environment. Once the IGA solver is built, multiple simulations will be conducted on a semi-circular notched plate of under tensile loading with different types of fiber configuration such as (1) curvilinear fibers following the holomorphic path defined by the conformal mapping, (2) concentric fibers following the semi-circular notch, (3) longitudinal straight fibers, and (4) transverse straight fibers. The IGA implementation will show that it converges much faster than the one from FEM. The mechanical behavior of each plate will be discussed and will be concluded that their mechanical behaviors strongly depend on the fiber orientation. In addition, an optimization study will also be presented for (1) the minimum stress concentration factor and (2) the minimum Tsai-Wu failure index varying the radius of the semi-circular notch. The optimal fiber paths will show the significant amount of reduction in terms of stress concentration. On the contrary, the optimal fiber paths for the minimum Tsai-Wu failure index will be converged to the longitudinal straight fiber configuration. This optimization study will also indicate that it is very difficult to conclude the optimal fiber path for the damage progress in terms of Tsai-Wu failure criterion, and thus, progressive failure analysis (PFA) is needed to identify the best fiber configuration.