Self-diffusion of polymers in cartilage as studied by pulsed field gradient NMR

Pulsed field gradient (PFG) nuclear magnetic resonance (NMR) was used to investigate the self-diffusion behaviour of polymers in cartilage. Polyethylene glycol and dextran with different molecular weights and in different concentrations were used as model compounds to mimic the diffusion behaviour of metabolites of cartilage. The polymer self-diffusion depends extremely on the observation time: The short-time self-diffusion coefficients (diffusion time Delta approximately 15 ms) are subjected to a rather non-specific obstruction effect that depends mainly on the molecular weights of the applied polymers as well as on the water content of the cartilage. The observed self-diffusion coefficients decrease with increasing molecular weights of the polymers and with a decreasing water content of the cartilage. In contrast, the long-time self-diffusion coefficients of the polymers in cartilage (diffusion time Delta approximately 600 ms) reflect the structural properties of the tissue. Measurements at different water contents, different molecular weights of the polymers and varying observation times suggest that primarily the collagenous network of cartilage but also the entanglements of the polymer chains themselves are responsible for the observed restricted diffusion. Additionally, anomalous restricted diffusion was shown to occur already in concentrated polymer solutions

Single-File Diffusion of Externally Driven Particles

We study 1-D diffusion of $N$ hard-core interacting Brownian particles driven by the space- and time-dependent external force. We give the exact solution of the $N$-particle Smoluchowski diffusion equation. In particular, we investigate the nonequilibrium energetics of two interacting particles under the time-periodic driving. The hard-core interaction induces entropic repulsion which differentiates the energetics of the two particles. We present exact time-asymptotic results which describe the mean energy, the accepted work and heat, and the entropy production of interacting particles and we contrast these quantities against the corresponding ones for the non-interacting particles

A 3D modelling approach for fluid progression during process simulation of wet compression moulding - Motivation & approach

Wet compression moulding (WCM) provides large-scale production potential for continuous fibre-reinforced structural components due to simultaneous infiltration and draping during moulding (viscous draping). Due to thickness-dominated infiltration of the laminate, comparatively low cavity pressures are sufficient – a considerable economic advantage. Experimental and numerical investigations prove strong mutual dependencies between the physical mechanisms, especially between resin flow and textile forming. Understanding and suitable modelling of these occurring physical mechanisms is crucial for process development and final part design. While existing modelling approaches are suitable for infiltration of preformed fabrics within various liquid moulding technologies, such as CRTM/RTM or VARI, WCM requires a fully coupled simulation approach for resin progression and concurrent stack deformation. Thus, the key challenge is to efficiently link these two aspects in a suitable framework. First, this work demonstrates that a three-dimensional approach for fluid progression during moulding is needed to capture WCM-process boundary conditions. In this regard, a novel test bench is used to investigate the impact of infiltration on the transversal compaction behaviour of a woven fabric. Moreover, the test setup is applied to determine the in-plane permeability values of the same material corresponding to the beforehand applied compaction states. Results are verified by comparison with an existing linear test setup. In the second part, initial steps towards a three dimensional extension of an existing 2D modelling approach are outlined. For this purpose, a macroscopic FE-based three-dimensional formulation of Darcy’s law is utilized within a User-Element in Abaqus/Explicit. Essential mechanisms within the element are presented. Additional control volumes (FE/CV) are applied to ensure mass conservation. Eventually, it is demonstrated, that the simulation model can predict the average fluid pressure beneath a punch during pre-infiltrated compaction experiments. Finally, major benefits and forthcoming steps for a fully-coupled 3D modelling approach for WCM are outlined

Capabilities of macroscopic forming simulation for large-scale forming processes of dry and impregnated textiles

Forming of continuously fibre-reinforced polymers (CoFRP) has a significant impact on the structural performance of composite components, underlining the importance of forming simulation for CoFRP product development processes. For an integrated development of industrial composite components, efficient forming simulation methods are in high demand. Application-oriented method development is particularly crucial for industrial needs, where large and complex multi-layer components are manufactured, commercial FE software is used, and yet high prediction accuracy is required. To meet industrial demands, this contribution gives an insight in macroscopic forming simulation approaches that utilize the FE software Abaqus in combination with user-defined material models and finite elements. Three CoFRP forming technologies are considered, which are in industrial focus due to their suitability for mass production: textile forming of dry unidirectional non-crimp fabrics (UD-NCF), thermoforming of pre-impregnated UD tapes and wet compression moulding (WCM). In addition to the highly anisotropic, large-strain material behaviour that composite forming processes have in common, the three process technologies face various process-specific modelling challenges. UD-NCFs require material models that capture the deformation behaviour and the slippage of the stitching. Thermoforming of UD tapes is highly rate- and temperature-dependent, calling for rheological membrane and bending modelling. Moreover, a thermomechanical approach including crystallisation kinetics enables the prediction of potential phase-transition during forming and resulting defects in the semi-crystalline thermoplastic matrix. For simultaneous forming and infiltration in wet compression moulding, a finite Darcy-Progression-Element is superimposed with the membrane and shell elements for forming simulation, capturing infiltration-dependent material properties. The three outlined technologies illustrate the complexity and importance of further simulation method development to support future process development

Direct Bundle Simulation approach for the compression molding process of Sheet Molding Compound

The manufacturing process of Sheet Molding Compounds (SMC) induces a reorientation of fibers during the flow, which influences local properties and is of interest for structural computations. Typically, the reorientation is described with an evolution equation for the second order fiber orientation tensor, which requires a closure approximation and multiple empirical parameters to describe long fibers. However, CT scans of SMC microstructures show that fiber bundles stay mostly intact during molding. Treating hundreds of fibers in such a bundle as one instance enables direct simulation on component scale. This work proposes a direct simulation approach, in which bundle segments experience Stokes’ drag forces and opposing forces are applied to the fluid field. The method is applied to specimens with a double-curved geometry and compared to CT scans. The Direct Bundle Simulation provides increased accuracy of fiber orientations and enables prediction of fiber-matrix separation with affordable computational effort at component scale

Experimental and numerical investigation of the shear behaviour of infiltrated woven fabrics

Wet compression moulding (WCM) as a promising alternative to resin transfer moulding (RTM) provides high-volume production potential for continuously fibre reinforced composite components. Lower cycle times are possible due to the parallelisation of the process steps draping, infiltration and curing during moulding. Although experimental and theoretical investigations indicate a strong mutual dependency arising from this parallelisation, no material characterisation set-ups for textiles infiltrated with low viscous fluids are yet available, which limits a physical-based process understanding and prevents the development of proper simulation tools. Therefore, a modified bias-extension test set-up is presented, which enables infiltrated shear characterisation of engineering textiles. Experimental studies on an infiltrated woven fabric reveal both, rate- and viscosity-dependent shear behaviour. The process relevance is evaluated on part level within a numerical study by means of FE-forming simulation. Results reveal a significant impact on the global and local shear angle distribution, especially during forming