Describing and Modeling Rough Composites Surfaces by Using Topological Data Analysis and Fractional Brownian Motion.

Many composite manufacturing processes employ the consolidation of pre-impregnated preforms. However, in order to obtain adequate performance of the formed part, intimate contact and molecular diffusion across the different composites' preform layers must be ensured. The latter takes place as soon as the intimate contact occurs and the temperature remains high enough during the molecular reptation characteristic time. The former, in turn, depends on the applied compression force, the temperature and the composite rheology, which, during the processing, induce the flow of asperities, promoting the intimate contact. Thus, the initial roughness and its evolution during the process, become critical factors in the composite consolidation. Processing optimization and control are needed for an adequate model, enabling it to infer the consolidation degree from the material and process features. The parameters associated with the process are easily identifiable and measurable (e.g., temperature, compression force, process time, ⋯). The ones concerning the materials are also accessible; however, describing the surface roughness remains an issue. Usual statistical descriptors are too poor and, moreover, they are too far from the involved physics. The present paper focuses on the use of advanced descriptors out-performing usual statistical descriptors, in particular those based on the use of homology persistence (at the heart of the so-called topological data analysis-TDA), and their connection with fractional Brownian surfaces. The latter constitutes a performance surface generator able to represent the surface evolution all along the consolidation process, as the present paper emphasizes.

A parametric metamodel of the vehicle frontal structure accounting for material properties and strain-rate effect: application to full frontal rigid barrier crash test.

In the automotive industry, building parametric surrogate models is a fundamental tool to evaluate, in real time, the performance of newly designed car components. Such models allow to compute any Quantity of Interest -QoI-, such as a specific safety protocol index, for any choice of material and/or geometrical parameters characterizing the component, within the stringent real time constraint. For instance, they can be exploited to guarantee safer designs (e.g., maximizing energy absorption by the crash boxes) or to reduce manufacturing costs (e.g., minimizing the mass of a specific structure under some safety protocol constraints). In general, these parametric simulation tools allow a significant gain in terms of manufacturing costs and time delays during the investigation phase. In this study, we focus on the vehicle frontal structure system considering its performance in a full-frontal crash scenario. In the front structure system we parameterize the crash boxes (left and right) and the inner/outer side front members (left and right, front and rear) with respect to the part thickness and the material parameters characterizing the Krupkowski plasticity curve. Moreover, Strain Rate Effect is also taken into account via Neural Network based regressions, whose training dataset comes from experimental data. The parametric metamodel is built via Non-Intrusive PGD -NI-PGD- strategies, relying on a sparse sampling of the parametric space, and allowing a quite reduced number of High Fidelity -HiFi- simulations. A novel strategy based on clustering and classification, known as Multi-PGD, is also applied and numerically verified.

Data-Driven Modelling of Polyethylene Recycling under High-Temperature Extrusion.

Two main problems are studied in this article. The first one is the use of the extrusion process for controlled thermo-mechanical degradation of polyethylene for recycling applications. The second is the data-based modelling of such reactive extrusion processes. Polyethylenes (high density polyethylene (HDPE) and ultra-high molecular weight polyethylene (UHMWPE)) were extruded in a corotating twin-screw extruder under high temperatures (350 °C < T < 420 °C) for various process conditions (flow rate and screw rotation speed). These process conditions involved a decrease in the molecular weight due to degradation reactions. A numerical method based on the Carreau-Yasuda model was developed to predict the rheological behaviour (variation of the viscosity versus shear rate) from the in-line measurement of the die pressure. The results were successfully compared to the viscosity measured from offline measurement assuming the Cox-Merz law. Weight average molecular weights were estimated from the resulting zero-shear rate viscosity. Furthermore, the linear viscoelastic behaviours (Frequency dependence of the complex shear modulus) were also used to predict the molecular weight distributions of final products by an inverse rheological method. Size exclusion chromatography (SEC) was performed on five samples, and the resulting molecular weight distributions were compared to the values obtained with the two aforementioned techniques. The values of weight average molecular weights were similar for the three techniques. The complete molecular weight distributions obtained by inverse rheology were similar to the SEC ones for extruded HDPE samples, but some inaccuracies were observed for extruded UHMWPE samples. The Ludovic® (SC-Consultants, Saint-Etienne, France) corotating twin-screw extrusion simulation software was used as a classical process simulation. However, as the rheo-kinetic laws of this process were unknown, the software could not predict all the flow characteristics successfully. Finally, machine learning techniques, able to operate in the low-data limit, were tested to build predicting models of the process outputs and material characteristics. Support Vector Machine Regression (SVR) and sparsed Proper Generalized Decomposition (sPGD) techniques were chosen to predict the process outputs successfully. These methods were also applied to material characteristics data, and both were found to be effective in predicting molecular weights. More precisely, the sPGD gave better results than the SVR for the zero-shear viscosity prediction. Stochastic methods were also tested on some of the data and showed promising results.

Study of Concentrated Short Fiber Suspensions in Flows, Using Topological Data Analysis.

The present study addresses the discrete simulation of the flow of concentrated suspensions encountered in the forming processes involving reinforced polymers, and more particularly the statistical characterization and description of the effects of the intense fiber interaction, occurring during the development of the flow induced orientation, on the fibers' geometrical center trajectory. The number of interactions as well as the interaction intensity will depend on the fiber volume fraction and the applied shear, which should affect the stochastic trajectory. Topological data analysis (TDA) will be applied on the geometrical center trajectories of the simulated fiber to prove that a characteristic pattern can be extracted depending on the flow conditions (concentration and shear rate). This work proves that TDA allows capturing and extracting from the so-called persistence image, a pattern that characterizes the dependence of the fiber trajectory on the flow kinematics and the suspension concentration. Such a pattern could be used for classification and modeling purposes, in rheology or during processing monitoring.