Visualizing gradients in composite design and fabrication

Greater access to computer resources has prompted scientists, engineers, and designers in all disciplines to go beyond the “number crunching” paradigm and establish visual tools and methodologies that are discipline-independent. The tools most commonly used in mechanics and material science are visualizations of gradients in scalar properties (zeroth-order tensors) and various stress glyphs (second-order tensors). Inherent to the study of these properties is the eigenvalue problem whose eigenvalues (zeroth-order tensors) and eigenvectors (first-order tensors) can be used to characterize physical properties that are second, fourth, and higher order tensors. For example, when the eigenvalue problem models a stress state (a second order tensor), it is possible to create glyphs that visualize the stress state and scalar gradients that visualize its individual components. In this article, we describe two cases of visualizing scalar gradients to study residual stresses and cure properties in complex three-dimensional composite structures, then we show how the need to study the distribution of these properties in a continuum leads to the development of visual tools that allow researchers to see gradients in three, four, and five dimensions. Elsewhere we review the visualization of second-order tensors applied to mechanics and material science, and also extend these representations to fourth-order tensors. These visual tools provide more information for the kinds of analysis we describe here