Variety of fiber orientation tensors

Fiber orientation tensors are established descriptors of fiber orientation states in (thermo-)mechanical material models for fiber-reinforced composites. In this paper, the variety of fourth-order orientation tensors is analyzed and specified by parameterizations and admissible parameter ranges. The combination of parameterizations and admissible parameter ranges allows for studies on the mechanical response of different fiber architectures. Linear invariant decomposition with focus on index symmetry leads to a novel compact hierarchical parameterization, which highlights the central role of the isotropic state. Deviation from the isotropic state is given by a triclinic harmonic tensor with simplified structure in the orientation coordinate system, which is spanned by the second-order orientation tensor. Material symmetries reduce the number of independent parameters. The requirement of positive-semi-definiteness defines admissible ranges of independent parameters. Admissible parameter ranges for transversely isotropic and planar cases are given in a compact closed form and the orthotropic variety is visualized and discussed in detail. Sets of discrete unit vectors, leading to selected orientation states, are given.

Probing the Rheological Properties of Liquids Under Conditions of Elastohydrodynamic Lubrication Using Simulations and Machine Learning

In elastohydrodynamic lubrication (EHL), the lubricant experiences pressures in excess of 500 MPa and strain rates larger than $$10^5$$ 10 5 $$\text{s}^{-1}$$ s - 1 . The high pressures lead to a dramatic rise in the Newtonian viscosity and the high rates lead to large shear stresses and pronounced shear thinning. The extraction of accurate rheological properties using non-equilibrium molecular dynamics simulations (NEMD) has played a key role in improving our understanding of lubricant flow in EHL conditions. However, the high dimensionality of the output data generated by NEMD simulations often makes a deeper interrogation of the link between molecular-scale features and rheological properties challenging. In this paper, we explore the use of machine learning to analyze and visualize the high-dimensional output data generated in typical NEMD simulations. We show that dimension reduction of NEMD simulation data describing the shear flow of squalane enables a clear visualization of the transition from Newtonian to non-Newtonian shear thinning with increasing shear rate and provides a reliable assessment of the correlation between shear thinning and the evolution in molecular alignment. The end-to-end atom pairs dominate the largest variations in pair orientation tensor components for low-pressure systems (0.1, 100 MPa) and provide the clearest separation of the orientation tensors with rate. On the other hand, the side atom pairs dominate the largest variation in the tensor components for the high-pressure systems ($$P\ge 400$$ P ≥ 400 MPa) which exhibit an overall limited evolution in orientation tensors as a function of rate. Dimension reduction using all the six components of the orientation tensors of all 435 pairs associated with a squalane molecule shows that the decrease in viscosity with rate for low pressures is strongly correlated with changes in molecular alignment. However, for high pressures, shear thinning occurs at saturated orientational order.

Direct Fiber Simulation of a Compression Molded Ribbed Structure Made of a Sheet Molding Compound with Randomly Oriented Carbon/Epoxy Prepreg Strands—A Comparison of Predicted Fiber Orientations with Computed Tomography Analyses

Discontinuous fiber composites (DFC) such as carbon fiber sheet molding compounds (CF-SMC) are increasingly used in the automotive industry for manufacturing lightweight parts. Due to the flow conditions during compression molding of complex geometries, a locally varying fiber orientation evolves. Knowing these process-induced fiber orientations is key to a proper part design since the mechanical properties of the final part highly depend on its local microstructure. Local fiber orientations can be measured and analyzed by means of micro-computed tomography (µCT) and digital image processing, or predicted by process simulation. This paper presents a detailed comparison of numerical and experimental analyses of compression molded ribbed hat profile parts made of CF-SMC with 50 mm long randomly oriented strands (ROS) of chopped unidirectional (UD) carbon/epoxy prepreg tape. X-ray µCT scans of three entire CF-SMC parts are analyzed to compare determined orientation tensors with those coming from a direct fiber simulation (DFS) tool featuring a novel strand generation approach, realistically mimicking the initial ROS charge mesostructure. The DFS results show an overall good agreement of predicted local fiber orientations with µCT measurements, and are therefore precious information that can be used in subsequent integrative simulations to determine the part’s mesostructure-related anisotropic behavior under mechanical loads.

CFD Analysis of Turbulent Fibre Suspension Flow

A new model for turbulent fibre suspension flow is proposed by introducing a model for the fibre orientation distribution function (ODF). The coupling between suspended fibres and the fluid momentum is then introduced through the second and fourth order fibre orientation tensors, respectively. From the modelled ODF, a method to construct explicit expressions for the components of the orientation tensors as functions of the flow field is derived. The implementation of the method provides a fibre model that includes the anisotropic detail of the stresses introduced due to presence of the fibres, while being significantly cheaper than solving the transport of the ODF and computing the orientation tensors from numerical integration in each iteration. The model was validated and trimmed using experimental data from flow over a backwards facing step. The model was then further validated with experimental data from a turbulent fibre suspension channel flow. Simulations were also carried out using a Bingham viscoplastic fluid model for comparison. The ODF model and the Bingham model performed reasonably well for the turbulent flow areas, and the latter model showed to be slightly better given the parameter settings tested in the present study. The ODF model may have good potential, but more rigorous study is needed to fully evaluate the model.

Brief communication: Sampling c-axes distributions from the eigenvalues of ice fabric orientation tensors

For simulation purposes involving different realizations of ice fabrics, it can be necessary to generate arbitrarily large samples of c-axes based on the second-order orientation tensor, a commonly used descriptive statistics provided in publications of ice core measurements. This paper describes a sampling technique based on the combination of a vertical girdle and a single maximum Watson distributions.

FASTensor: A tensor framework for spatiotemporal description

Spatiotemporal description is a research field with applications in various areas such as video indexing, surveillance, human-computer interfaces, among others. Big Data problems in large databases are now being treated with Deep Learning tools, however we still have room for improvement in spatiotemporal handcraft description. Moreover, we still have problems that involve small data in which data augmentation and other techniques are not valid. The main contribution of this Ph.D. Thesis 1 is the development of a framework for spatiotemporal representation using orientation tensors enabling dimension reduction and invariance. This is a multipurpose framework called Features As Spatiotemporal Tensors (FASTensor). We evaluate this framework in three different applications: Human Action recognition, Video Pornography classification and Cancer Cell classification. The latter one is also a contribution of this work, since we introduce a new dataset called Melanoma Cancer Cell dataset (MCC). It is a small data that cannot be artificially augmented due the difficulty of extraction and the nature of motion. The results were competitive, while also being fast and simple to implement. Finally, our results in the MCC dataset can be used in other cancer cell treatment analysis.