This paper computationally investigates heterogeneity in the distribution of foam fraction in chemically expanding blown polyurethane foam. The experimentally observed disparity in the volumes of expanded foam when an equal mass of the foaming mixture was injected into tubes of different dimensions motivated this study. To understand this phenomenon, attributed to local variations in the thermal and rheological properties of the expanding system, we explore available data from free-rise foam-expansion experiments in different geometries. Inspired by the mathematical framework for the microstructure modelling of bubble growth in viscous liquids, we study the reacting mixture as a continuum and formulate appropriate mathematical models that account for spatial inhomogeneity in the foam-expansion process. The nonlinear coupled system of partial differential equations governing flow was numerically solved using finite-volume techniques, and the associated results are presented and discussed with graphical illustrations. The proximity of the foaming-mixture core to the external environment and the thickness of a thermal-diffusion layer formed near the bounding geometry was seen to influence the distribution of the foam fraction. Our simulations showed an average spatial variation of about 1.1% in the distribution of solid foam fraction from the walls to the core, as verified with data from $\mu$ CT scan analysis of the expanded foam. This also reflects the distribution of void fraction in the foam matrix. The models were validated with experimental data, and our results favourably compared with the experiment observations.

In many textiles and fiber structures, the behavior of the material is determined by the structural arrangements of the fibers, their thickness and cross-section, as well as their material properties. Textiles are thin plates made of thin long yarns in frictional contact with each other that are connected via a rule defined by a looping diagram. The yarns themselves are stretchable or non-stretchable. All these structural parameters of a textile define its macroscopic behavior. Its folding is determined by all these parameters and the kind of the boundary fixation or loading direction. The next influencing characteristic is the value of the loading. The same textile can behave similar to a shell and work just for bending, or behave as a membrane with large tension deformations under different magnitudes of the loading forces. In our research, bounds on the loading and frictional parameters for both types of behavior are found. Additionally, algorithms for the computation of effective textile properties based on the structural information are proposed. Further focus of our research is the nature of folding, induced by pre-strain in yarns and some in-plane restriction of the textile movements, or by the local knitting or weaving pattern and the yarn’s cross-sections. Further investigations concern different applications with spacer fabrics. Structural parameters influencing the macroscopic fabric behavior are investigated and a way for optimization is proposed. An overview of our published mathematical and numerical papers with developed algorithms is given and our numerical tools based on these theoretical results are demonstrated.

Products made of polyurethane foam are manufactured by the chemical reaction of various low-viscosity raw materials and additives. The diversity of different formulations to meet the requirements of the market makes the characterization of their processing and flow properties important for a simple and error-free production. The modeling and simulation of such processes are equally of great importance. This provides additional findings without the expense of real tests and makes it easier to design components. The work described in this paper was carried out against this background. An experimental setup using a rheometer was developed to determine the flow and curing properties of reacting polyurethane foam reproducibly with comparable expansion conditions to industrial processes. The experiment was mathematically modelled to investigate the rheology of reacting polyurethane foams. The mathematical framework consists of coupled, non-linear, partial differential equations for the dynamics and the heat transfer processes in the system. These are solved numerically in 3D using finite volume techniques under adequate physical conditions. The accuracy of two viscosity laws according to the state of the art and their novel combination were investigated in this context. The proposed viscosity model of this study provides accurate results compared to the experiment.

Simulation-based prediction of mechanical properties is highly desirable for optimal choice and treatment of leather. Nowadays, this is state-of-the-art for many man-made materials. For the natural material leather, this task is however much more demanding due to the leather’s high variability and its extremely intricate structure. Here, essential geometric features of the leather’s meso-scale are derived from 3D images obtained by micro-computed tomography and subsumed in a parameterizable structural model. That is, the fiber-bundle structure is modeled. The structure model is combined with bundle properties derived from tensile tests. Then the effective leather visco-elastic properties are simulated numerically in the finite element representation of the bundle structure model with sliding contacts between bundles. The simulation results are validated experimentally for two animal types, several tanning procedures, and varying sample positions within the hide. Finally, a complete workflow for assessing leather quality by multi-scale simulation of elastic and visco-elastic properties is established and validated.

This paper covers the mechanical simulation of woven textiles on the yarn level with an investigation of the influence of the sliding between yarns and changing yarn cross-sections under loading. An experimental validation of the simulation tools for a range of chosen woven structures with different weaving types and thicknesses of multifilament glass fibre yarns is provided. The main focus of the paper is the classification of the folding mechanisms in textiles.