Experimental Investigation on the Mechanical Properties of Polypropylene Hybrid Fiber-Reinforced Roller-Compacted Concrete Pavements

To explore the effect of multi-scale polypropylene fiber (PPF) hybridization on the mechanical properties of roller-compacted concrete (RCC), the early-age (3, 7, 14, 28 days) compressive strength, splitting tensile strength and uniaxial tensile test of RCC reinforced with micro-, macro- and hybrid polypropylene fibers were investigated. Then, the tensile stress–strain curve of polypropylene fiber-reinforced roller-compacted concrete (PFRCC) and the corresponding tensile parameters were obtained. The uniaxial tensile constitutive equation of PFRCC and fiber hybrid effect function was also proposed. Finally, the enhancement mechanism of fiber hybridization on mechanical properties of RCC was analyzed. The results indicated that the strength and toughness of PFRCC improved with the incorporation of PPF, showing obvious plastic failure characteristics of PFRCC. Before curing the concrete for 7 days, micro-PPF played a major role in strengthening RCC, while macro-PPF played a major role in reinforcing concrete after that. Moreover, the tensile strength and toughness indexes of multi-scale PFRCC performed the best, indicating the positive hybridization of three types of PPF. The proposed PFRCC uniaxial tensile constitutive equation and fiber hybrid effect function based on existing researches were also well matched with the experimental results.

Non-Isothermal Free-Surface Viscous Flow of Polymer Melts in Pipe Extrusion Using an Open-Source Interface Tracking Finite Volume Method

Polymer extrudate swelling is a rheological phenomenon that occurs after polymer melt flow emerges at the die exit of extrusion equipment due to molecular stress relaxations and flow redistributions. Specifically, with the growing demand for large scale and high productivity, polymer pipes have recently been produced by extrusion. This study reports the development of a new incompressible non-isothermal finite volume method, based on the Arbitrary Lagrangian–Eulerian (ALE) formulation, to compute the viscous flow of polymer melts obeying the Herschel–Bulkley constitutive equation. The Papanastasiou-regularized version of the constitutive equation is employed. The influence of the temperature on the rheological behavior of the material is controlled by the Williams–Landel–Ferry (WLF) function. The new method is validated by comparing the extrudate swell ratio obtained for Bingham and Herschel–Bulkley flows (shear-thinning and shear-thickening) with reference data found in the scientific literature. Additionally, the essential flow characteristics including yield-stress, inertia and non-isothermal effects were investigated.

Inverse parameter estimation to predict material parameters of the Cowper–Symonds constitutive equation in electrohydraulic forming process

The development of a reliable numerical simulation is essential for understanding high-speed forming processes such as electrohydraulic forming (EHF). This numerical model should be created based on the accurate material properties. However, dynamic material properties at strain rates exceeding 1000 s$$^{-1}$$ - 1 cannot be easily obtained through an experimental approach. Thus, this study predicted two material parameters in the Cowper–Symonds constitutive equation based on inverse parameter estimation, such that the parameters predicted using the numerical simulation corresponded well with those obtained from the experimental results. The target material was a 1-mm-thick Al 5052-H32 sheet. The comparison target included the final deformation shape of the sheet in the EHF-free bulging test at three input voltages of 6, 7, and 8 kV. For the inverse parameter estimation, the posterior distribution for the two parameters included a likelihood and a prior distribution. For the likelihood construction, a reduced-order surrogate model was developed in advance to substitute the numerical simulation based on ordinary Kriging and principal component analysis. Moreover, the error distribution of the bulge height between the experiment and reduced-order surrogate model was obtained. The prior distribution at 7 kV was defined as a uniform distribution, and the posterior distribution at 7 kV was employed as a prior distribution at 6, 7, and 8 kV. Furthermore, Markov chain Monte Carlo sampling was employed and the Metropolis–Hastings algorithm was adopted to obtain the samples following the posterior distribution. After the autocorrelation calculation for sample independence, the lag with an autocorrelation of $$\pm \,0.02$$ ± 0.02 interval was selected and every lag$$^{\mathrm {th}}$$ th sample was obtained. The total number of acquired samples was $$10^{5}$$ 10 5 , and the mean values were calculated from the obtained samples. Consequently, the numerical simulation with mean values displayed good agreement with the experimental results.

A Constitutive Equation of Turbulence

Even though applications of direct numerical simulations are on the rise, today the most usual method to solve turbulence problems is still to apply a closure scheme of a defined order. It is not the case that a rising order of a turbulence model is always related to a quality improvement. Even more, a conceptual advantage of applying a lowest order turbulence model is that it represents the analogous method to the procedure of introducing a constitutive equation which has brought success to many other areas of physics. First order turbulence models were developed in the 1920s and today seem to be outdated by newer and more sophisticated mathematical-physical closure schemes. However, with the new knowledge of fractal geometry and fractional dynamics, it is worthwhile to step back and reinvestigate these lowest order models. As a result of this and simultaneously introducing generalizations by multiscale analysis, the first order, nonlinear, nonlocal, and fractional Difference-Quotient Turbulence Model (DQTM) was developed. In this partial review article of work performed by the authors, by theoretical considerations and its applications to turbulent flow problems, evidence is given that the DQTM is the missing (apparent) constitutive equation of turbulent shear flows.

A Molecular Structure-Informed Viscoelastic Constitutive Model for Natural Rubber Materials

This paper presents a molecular structure-informed viscoelastic constitutive equation that adopts the Doi-Edward’s tube model with coarse-grained molecular dynamics (MD) simulation and primitive path analysis. Since this model contains polymer physics-related parameters directly obtained from molecular simulations, it can reflect molecular information in predictions of the viscoelastic behavior of elastomers, unlike other empirical models. The proposed incremental formulations and constitutive stiffness matrix were implemented into implicit finite element analysis (FEA) codes as a user-supplied material model and viscoelastic properties (storage, loss modulus, and tan⁡δ) were calculated from the constitutive equation. While obtaining polymer dynamics parameter of the molecular system, a relationship between self-diffusivity coefficient (D_c) and the polymerization degree of the polymer was confirmed. Furthermore, a series of parametric studies showed that increase of the primitive path length (L) and decrease of D_c have led to the strengthening of moduli and decrease of tan⁡δ peak. Moreover, under the same condition, the shift of tan⁡δ peak to low-frequency domain was observed, which implies a decline in free volume in the molecular system and an increase in the glass transition temperature.