Thermal fiber orientation tensors for digital paper physics

We estimate the orientation of wood fibers in porous networks like paper, paperboard or fiberboard by computing digital thermal conductivity experiments on micro-computed tomography (mCT) images with artificial isotropic thermal conductivity parameters. The accuracy of mechanical and thermal constitutive models for porous wood fiber based materials crucially depends on knowing the wood fiber orientation. Unfortunately, due to the high porosity, the micro-heterogeneity of wood fibers, the high carbon content of organic materials and the unknown additives present in industrial paper, mCT-scans often exhibit low contrast and strong artifacts. Conventional image processing approaches encounter difficulties, as they rely upon convex fiber cross sections. We propose a solution by circumventing the segmentation of single wood fibers in mCT images, by performing thermal conductivity simulations on binarized wood fiber structures, where an artificial isotropic thermal conductivity is associated to the fibers and the pore space is considered as isolating. The local and global temperature fluxes are assembled into a fiber orientation tensor. This method overcomes the limitations of the mentioned local image processing approaches, as individual fibers need not be resolved and convergence for increasing resolution is a consequence of abstract mathematical theory. We use our novel method to analyze large three-dimensional mCT-scans and a synchrotron scan of a paperboard sample, serving as the starting point of an accurate micromechanical modeling of the effective anisotropic mechanical behavior of paper and paperboard. These results are crucial for calculating the mechanical strength of deep-drawn paperboard, which will be accomplished in a subsequent article.