Reference Configuration Research Articles

Stable Möbius Bands from Isometrically Deformed Circular Helicoids

We consider the problem of producing a ruled Möbius band by subjecting an unstretchable, homogeneous, isotropic, elastic material surface material surface in a circular helicoidal reference configuration to a deformation that is isometric and chirality preserving. We find that such a Möbius band is completely determined by the unit binormal of the Frenet frame of its midline, which must be a geodesic and must have uniform torsion inversely proportional to the pitch of the helicoidal reference configuration. Granted that the energy density of the material surface depends quadratically on the mean curvature of its deformed configuration, we show that the total energy stored in producing a ruled Möbius band as described reduces, in closed form and without approximation, to an integral over the midline of the Möbius band. We formulate and numerically solve a constrained variational problem for finding relative minima of the dimensionally reduced bending energy and construct corresponding stable Möbius bands. The only input parameter entering our variational problem is the number ν\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\ u $\\end{document} of turns in a helicoidal reference configuration. We only find solutions if ν\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\ u $\\end{document} exceeds a certain threshold, which we compute to machine precision. Above that threshold, an interplay between the operative constraints leads to a multiplicity of coexisting stable solutions with n≥3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$n\\ge 3$\\end{document} half twists. For each n≥3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$n\\ge 3$\\end{document}, we construct an energetically optimal Möbius band which exhibits n\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$n$\\end{document}-fold rotational symmetry. All other energy minima yield Möbius bands which lack symmetry. To our knowledge, this study contains the first examples of stable Möbius bands produced by isometrically deforming reference configurations that are not flat.

Thermo-elasticity displacement formulation for constrained articulated mechanical systems

This paper proposes an approach for thermal analysis of articulated systems subject to boundary and motion constraints (BMC). The solution framework is designed to capture large temperature fluctuations, significant change in geometry due to reference configuration and deformations, and geometric nonlinearity due to articulated mechanical systems (AMS) large displacements and spinning motion. Thermal-expansion displacements, which do not contribute to rigid-body translations, are determined from thermal stretch of position-gradient vectors using a new sweeping matrix technique designed to eliminate dependence on translational rigid-body modes. A new quadratic thermal-energy kinetic form is defined and used to formulate a dynamic force vector that accounts for thermal transient and inertia effects. Nodal thermal displacements are used in formulating AMS differential/algebraic equations (DAEs), and consequently, thermal stresses due to BMC equations are automatically accounted for based on integration of thermal analysis and Lagrange-D’Alembert principle, which is the foundation of computational multibody system (MBS) algorithms. The approach used in this study for large-displacement constrained and unconstrained thermal expansions is based on multiplicative decomposition of position-gradient matrix, instead of strain additive decomposition, for solution of thermo-elasticity problems. Four configurations are used to define continuum geometry and displacements: straight configuration, reference configuration, thermal-expansion configuration, and current configuration. The proposed approach allows applying thermal loads during constrained large displacements, does not impose restrictions on the choice of thermal coefficients, captures reference-configuration geometry and change in inertia forces due to temperature fluctuations, accounts for thermal displacement in formulating AMS nonlinear constraint equations, and allows for integration with MBS algorithms for the study of a wide range of thermo-elasticity problems.

The stress-free state of human erythrocytes: Data-driven inference of a transferable RBC model

The stress-free state (SFS) of red blood cells (RBCs) is a fundamental reference configuration for the calibration of computational models, yet it remains unknown. Current experimental methods cannot measure the SFS of cells without affecting their mechanical properties, whereas computational postulates are the subject of controversial discussions. Here, we introduce data-driven estimates of the SFS shape and the visco-elastic properties of RBCs. We employ data from single-cell experiments that include measurements of the equilibrium shape of stretched cells and relaxation times of initially stretched RBCs. A hierarchical Bayesian model accounts for these experimental and data heterogeneities. We quantify, for the first time, the SFS of RBCs and use it to introduce a transferable RBC (t-RBC) model. The effectiveness of the proposed model is shown on predictions of unseen experimental conditions during the inference, including the critical stress of transitions between tumbling and tank-treading cells in shear flow. Our findings demonstrate that the proposed t-RBC model provides predictions of blood flows with unprecedented accuracy and quantified uncertainties.

Parameter Optimization of Foldable Flapping-Wing Mechanism for Maximum Lift

AbstractA lot of flapping-wing mechanisms have been proposed to mimic the flight characteristics of biological flyers. However, it is difficult to find studies that consider the unsteady aerodynamics in the design of the flapping-wing mechanisms. This paper presents a systematic approach to optimize the design parameters of a foldable flapping-wing mechanism (FFWM) with a proper aerodynamics model. For the kinematic model, the eight design parameters are defined to determine the reference configuration of the FFWM. The geometrical constraints of each design parameter are derived, and the kinematic analysis is conducted using the plane vector analysis method. The aerodynamic simulation using an unsteady vortex lattice method is performed to compute the aerodynamic loads induced by the flapping motion. An optimization problem is formulated to search for the optimal design parameters that maximize the average lift force considering the required power corresponding to the aerodynamic torques. The parameter optimization problem is solved for three different length ratios of the outer wing to the inner wing using a genetic algorithm. The optimization results show that increasing the outer wing length can cause a significant loss in the required power. The optimal design parameters found by the proposed approach allow the FFWM to generate maximum lift force with appropriate consideration of the required power.

Data-driven generation of 4D velocity profiles in the aneurysmal ascending aorta

Background and Objective: Numerical simulations of blood flow are a valuable tool to investigate the pathophysiology of ascending thoratic aortic aneurysms (ATAA). To accurately reproduce in vivo hemodynamics, computational fluid dynamics (CFD) models must employ realistic inflow boundary conditions (BCs). However, the limited availability of in vivo velocity measurements, still makes researchers resort to idealized BCs. The aim of this study was to generate and thoroughly characterize a large dataset of synthetic 4D aortic velocity profiles sampled on a 2D cross-section along the ascending aorta with features similar to clinical cohorts of patients with ATAA.Methods: Time-resolved 3D phase contrast magnetic resonance (4D flow MRI) scans of 30 subjects with ATAA were processed through in-house code to extract anatomically consistent cross-sectional planes along the ascending aorta, ensuring spatial alignment among all planes and interpolating all velocity fields to a reference configuration. Velocity profiles of the clinical cohort were extensively characterized by computing flow morphology descriptors of both spatial and temporal features. By exploiting principal component analysis (PCA), a statistical shape model (SSM) of 4D aortic velocity profiles was built and a dataset of 437 synthetic cases with realistic properties was generated.Results: Comparison between clinical and synthetic datasets showed that the synthetic data presented similar characteristics as the clinical population in terms of key morphological parameters. The average velocity profile qualitatively resembled a parabolic-shaped profile, but was quantitatively characterized by more complex flow patterns which an idealized profile would not replicate. Statistically significant correlations were found between PCA principal modes of variation and flow descriptors.Conclusions: We built a data-driven generative model of 4D aortic inlet velocity profiles, suitable to be used in computational studies of blood flow. The proposed software system also allows to map any of the generated velocity profiles to the inlet plane of any virtual subject given its coordinate set.

Improving the crashworthiness of CFRP structures by rubbery nanofibrous interlayers

Crashworthiness is the capability of a component to dissipate impact energy throughout its deformation and failure. Composite materials are used to produce crashworthy components to ensure vehicle safety, thanks to their ability to dissipate a high energy amount while maintaining a low weight. The present work investigates the integration of rubbery nanofibers within the laminate interlayers to enhance crush performance. Three different thicknesses (10, 20, and 40 µm) of nanofibrous mats made by nitrile butadiene rubber and polycaprolactone (NBR/PCL) blends were produced by single-needle electrospinning technique and integrated into the laminates during the hand-layup. Mechanical properties of the nano-modified laminates are compared to the reference configuration: the effect of the interlayers is evaluated by Double Cantilever Beam (DCB) and End-Notched Flexure (ENF) interlaminar fracture tests. At the same time, the specific crush energy absorption (SEA) is measured by the compression of self-supporting corrugated specimens. Results show that NBR/PCL nanofibers significantly increase the interlaminar fracture toughness (up to +254% for Mode I and +47% for Mode II), which ultimately helps to improve the total SEA up to +8.2%. The best SEA enhancement is achieved already with a 10 µm nanofibrous membrane while integrating the highest thickness mat has a detrimental effect.

Accounting for stray capacitances in impedance measuring cells — A mandatory step in the investigation of solid ion conductors

The determination of the dielectric response properties is essential to the investigation of solid ion conductors. The stray capacitance contributions of the measuring cell must be systematically determined and subtracted from the acquired data. Hereby, we report and discuss a general method that can be used for the accurate determination of stray capacitance in impedance measuring cells. Our method can be applied to all commercial or custom-made impedance cells or sample holders used for variable temperature conductivity measurements of fast ion conductors. After the description of the method, we present the experimental calibration done for a 2032-type coin cell sample holder. The 2032-type coin cell is a highly reliable sample holder for impedance measurements of air sensitive materials. We tested the method on a known sample and we validated it by comparing with the results obtained in a simple reference configuration. Our simple, efficient and robust method for the determination of parasitic capacitive contributions may serve as an example of good practice in the field of solid electrolytes, solid state batteries and dielectric materials investigations.

A Linear Isotropic Cosserat Shell Model Including Terms up to $O(h^{5})$. Existence and Uniqueness

In this paper we derive the linear elastic Cosserat shell model incorporating in the variational problem effects up to order $O(h^{5})$ in the shell thickness $h$ as a particular case of the recently introduced geometrically nonlinear elastic Cosserat shell model. The existence and uniqueness of the solution is proven in suitable admissible sets. To this end, inequalities of Korn-type for shells are established which allow to show coercivity in the Lax-Milgram theorem. We are also showing an existence and uniqueness result for a truncated $O(h^{3})$ model. Main issue is the suitable treatment of the curved reference configuration of the shell. Some connections to the classical Koiter membrane-bending model are highlighted.

Coarse-Graining of a Discrete Model for Edge Dislocations in the Regular Triangular Lattice

We consider a discrete model of planar elasticity where the particles, in the reference configuration, sit on a regular triangular lattice and interact through nearest neighbor pairwise potentials, with bonds modeled as linearized elastic springs. Within this framework we introduce plastic slip fields, whose discrete circulation around each triangle detects the possible presence of an edge dislocation. We provide a $\Gamma$-convergence analysis, as the lattice spacing tends to zero, of the elastic energy induced by edge dislocations in the energy regime corresponding to a finite number of geometrically necessary dislocations.

Bending and Stretching in a Narrow Ribbon of Nematic Polymer Networks

AbstractWe study the spontaneous out-of-plane bending of a planar untwisted ribbon composed of nematic polymer networks activated by a change in temperature. Our theory accounts for both stretching and bending energies, which compete to establish equilibrium. We show that when equilibrium is attained these energy components obey acomplementarityrelation: one is maximum where the other is minimum. Moreover, we identify ableachingregime: for sufficiently large values of an activation parameter (which measures the mismatch between the degrees of order in polymer organization in the reference and current configurations), the ribbon’s deformation is essentially independent of its thickness.

Finite strain poro-hyperelasticity: an asymptotic multi-scale ALE-FSI approach supported by ANNs

This contribution introduces and discusses a formulation of poro-hyperelasticity at finite strains. The prediction of the time-dependent response of such media requires consideration of their characteristic multi-scale and multi-physics parameters. In the present work this is achieved by formulating a non-dimensionalised fluid–solid interaction problem (FSI) at the pore level using an arbitrary Lagrange–Euler description (ALE). The resulting coupled systems of PDEs on the reference configuration are expanded and analysed using the asymptotic homogenisation technique. This approach yields three partially novel systems of PDEs: the macroscopic/effective problem and two supplementary microscale problems (fluid and solid). The latter two provide the microscopic response fields whose average value is required in real-time/online form to determine the macroscale response (a concurrent multi-scale approach). In order to overcome the computational challenges related to the above multi-scale closure, this work introduces a surrogate approach for replacing the direct numerical simulation with an artificial neural network. This methodology allows for solving finite strain (multi-scale) porohyperelastic problems accurately using direct automated differentiation through the strain energy. Optimal and reliable training data sets are produced from direct numerical simulations of the fully-resolved problem by including a simple real-time output density check for adaptive sampling step refinement. The data-driven approach is complemented by a sensitivity analysis of the RVE response. The significance of the presented approach for finite strain poro-elasticity/poro-hyperelasticity is shown in the numerical benchmark of a multi-scale confined consolidation problem. Finally, to show the robustness of the method, the system response is dimensionalised using characteristic values of soil and brain mechanics scenarios.

Refined MagSail thrust model for preliminary mission design and trajectory optimization

A magnetic sail is an advanced propellantless propulsion system concept for deep space missions, proposed by Dana Andrews and Robert Zubrin about 30 years ago. The thrust is generated by the electromagnetic interaction between the solar wind charged particles and an artificial magnetic field obtained through a large current-carrying coil made of superconducting material. This paper discusses an up-to-date single-loop magnetic sail thrust model based on the numerical and experimental results obtained in the last decade. In particular, a particle model is initially used to evaluate the performance of a reference configuration in terms of thrust components in a body reference frame. Then, some scaling relationships are used to estimate the magnetic sail performance as a function of the design parameters. The proposed thrust model is used to analyze the minimum-time transfer problem between two circular and coplanar heliocentric orbits. Minimum flight times necessary to complete ephemeris-free Earth-Venus and Earth-Mars transfers are calculated as a function of the magnetic sail characteristic size in a parametric way.

Implicit Integration Algorithm for Solving Evolution of Microstructural Vectors Based on Eulerian Formulation in Plane Stress Condition

Abstract This paper presents a mathematical formulation and implicit numerical algorithm for solving the integral of a three-dimensional momentum balance based on the inelastic evolution of microstructural vectors for thin plates in Eulerian formulation. A recent theoretical discussion (Lee and Rubin, 2020, “Modeling Anisotropic Inelastic Effects in Sheet Metal Forming Using Microstructural Vectors—Part I: Theory,” Int. J. Plast., 134, p. 102783. 10.1016/j.ijplas.2020.102783) showed that Eulerian constitutive equation based on microstructural vectors for thin plates has the advantage of capturing the anisotropic behavior of the material axis with insensitivity to the randomness of the reference configuration. However, all the discussions were theoretically conducted only at a local material point in homogeneous deformation conditions, which do not require consideration of the momentum balance with flexible velocity gradients in a three-dimensional volume. For usability, numerical algorithms are needed to solve evolution of the microstructural vectors in the three-dimensional space. This paper presents the first numerical algorithm to solve the inelastic evolution of microstructural vectors in the Eulerian formulation. A generalized material coordinated system is matched to the microstructural vectors in a three-dimensional space by considering the Eulerian constitutive equations insensitive to the superposed rigid body motions (SRBM). Numerical algorithms were then introduced to implicitly solve the nonlinear momentum balance, evolution of the microstructural vectors, and tangent modulus. The formula and numerical algorithms were validated by predicting the tension tests when the principal loading angle varied from the reference axis. The results show that the proposed numerical algorithm can describe the evolution of the microstructure based on the Eulerian formulation.

Experimental study and modeling of water transport through short-side-chain perfluorosulfonic acid membranes

Perfluorosulfonic acid polymer membranes are state-of-the-art electrolytes in PEMFCs and PEMWEs, and their degradation represents still one of the limiting factor to increase lifetime of electrochemical devices. Due to significant role of water in stressing degradation mechanisms, this work, through an experimental and theoretical analysis, deepens comprehension of materials and constructive properties of short-side-chain (SSC) membranes on dynamic water transport. A systematic analysis is carried out by analysing samples with different membrane thickness and EW, coupled with different gas diffusion layers. A model was adopted to analyse both steady-state and transient water transport tests, evaluating individual contributions to the total water mass transfer. Particular attention was given to swelling/shrinking mechanism, highlighting its strong impact on water sorption and membrane hydration. Membrane diffusion and interfacial mass transfer were independently investigated, identifying their interconnections with material-bulk and superficial properties. Results highlight that membrane with low EW (790 g mol−1), coupled with hydrophilic gas diffusion layers that oppose negligible interfacial resistances to water transport, allows to reduce total resistance by approximately 39% compared to reference configuration (980 g mol−1, hydrophobic).

Nonlinear and Linearized Models in Thermoviscoelasticity

We consider a quasistatic nonlinear model in thermoviscoelasticity at a finite-strain setting in the Kelvin–Voigt rheology, where both the elastic and viscous stress tensors comply with the principle of frame indifference under rotations. The force balance is formulated in the reference configuration by resorting to the concept of nonsimple materials, whereas the heat transfer equation is governed by the Fourier law in the deformed configurations. Weak solutions are obtained by means of a staggered in-time discretization where the deformation and the temperature are updated alternatingly. Our result refines a recent work by Mielke and Roubíček (Arch Ration Mech Anal 238:1–45, 2020) since our approximation does not require any regularization of the viscosity term. Afterwards, we focus on the case of deformations near the identity and small temperatures, and we show by a rigorous linearization procedure that weak solutions of the nonlinear system converge in a suitable sense to solutions of a system in linearized thermoviscoelasticity. The same property holds for time-discrete approximations and we provide a corresponding commutativity result.

The Sobolev Jordan-Schönflies problem

We consider the planar unit disk D as the reference configuration and a Jordan domain Y as the deformed configuration, and study the problem of extending a given boundary homeomorphism φ:∂D→onto∂Y as a Sobolev homeomorphism of the complex plane. Investigating such a Sobolev variant of the classical Jordan-Schönflies theorem is motivated by the well-posedness of the related pure displacement variational questions in the theory of Nonlinear Elasticity (NE) and Geometric Function Theory (GFT). Clearly, the necessary condition for the boundary mapping φ to admit a W1,p-Sobolev homeomorphic extension is that it first admits a continuous W1,p-Sobolev extension. For an arbitrary target domain Y this, however, is not sufficient. Indeed, first for each p<∞ we construct a Jordan domain Y and a homeomorphism φ:∂D→onto∂Y which admits a continuous W1,p-extension but does not even admit a W1,1-homeomorphic extension. Second, for a quasidisk target Y and the whole range of p, we prove that a boundary homeomorphism φ:∂D→onto∂Y admits a Wloc1,p-homeomorphic extension to C if and only if it admits a W1,p-extension to the unit disk. Quasidisks have been a subject of intensive study in GFT. They do not allow for singularities on the boundary such as cusps. Third, for any power-type cusp target there is a boundary homeomorphism from the unit circle whose harmonic extension has finite Dirichlet energy but does not have a homeomorphic extension in W1,2(D,C). Surprisingly, the Dirichlet integral (p=2) plays a unique role for the Sobolev Jordan-Schönflies Problem in the case of cusp targets. Even more, fourth we prove that if the target Y has piecewise smooth boundary, p≠2 and φ:∂D→onto∂Y has a W1,p-Sobolev extension to D, then it admits a homeomorphic extension to C in Wloc1,p(C,C). Fifth, if in addition Y is quasiconvex, then the one-sided Sobolev Jordan-Schönflies problem has a solution when p=2. Indeed, we show that the harmonic extension of φ:∂D→onto∂Y has a finite Dirichlet integral if and only if φ admits a homeomorphic extension h:D‾→ontoY‾ with finite Dirichlet energy.

Large eddy simulation study of the impact of an obstacle on cooling properties of a multiperforated liner

Large eddy simulations are performed to investigate the impact of a solid obstacle on the flow around a multiperforated plate typical of aeronautical combustion chambers. The reference configuration is a perforated plate with approximately 200 holes immersed between a cold vein and hot vein at a typical operating point of helicopter combustors. The micro-jet Reynolds number is of the order of 4000, while the blowing and momentum ratios are close to 4 and 8, respectively. A variant configuration is considered that features an additional cylindrical obstacle located in the cold vein and mimicking a spark plug. The study reveals that, downstream of the obstacle, the cooling effectiveness of the plate is reduced by approximately 40 % compared with the reference case, mainly due to the absence of perforation at the obstacle location. The mass flow rate within the holes in the wake produced by the obstacle is reduced by 7 %, which is likely to locally influence the plate cooling. The reduction is attributed to the wake's pressure loss and its impact on the discharge coefficient. Additionally, the cooling effectiveness outside the wake shows a 5 % increase that can be linked to the mass flow rate increase within corresponding holes.

Experimental and numerical investigation of solid-solid phase change material assisted heat sink with integrated heat pipe for electronic cooling

Advancements in phase change materials (PCM) technology offer adaptable solutions for challenging high heat dissipation problems in electronic devices. In this work, the influence of Neopentyl Glycol (NPG) as PCM having solid-solid phase transition on the functioning of heat pipe assisted heat sink is studied. Experimental and numerical investigation was performed on the transient thermal performance of heat pipe integrated PCM-assisted heat sink application with forced air cooling. The heat pipe's evaporator section is in contact with PCM- assisted heat sink, while condenser section is exposed to the ambient. Investigations were carried out at power levels of 9–13 W, corresponding to an equivalent heat flux range of 2.5–3.5 kW/m2 and with PCM filling of 33, 66 and 99 % of the heat sink volume where without integration of PCM and heat pipe in heat sink as the reference configuration. PCM-assisted heat sink and heat pipe configurations outperformed other configurations based on charging period for all experimental parameters with a maximum enhancement ratio of 3.29. Heat sink assembly comprising 99 % PCM with heat pipe gives the most significant results on comparison with all other configurations, whereas the assembly without heat pipe showed the best results for 66 %.

A Fast Aerodynamic Model for Aircraft Multidisciplinary Design and Optimization Process

A multidisciplinary design analysis and optimization process is developed at ONERA for the design of tube and wing and blended wing–body aircraft configurations. This process is composed of different disciplinary modules (geometry, propulsion, aerodynamics, structure, handling qualities and flight mission), and the overall process considers different fidelity levels for these modules at each step of the design process. This article describes the low-fidelity aerodynamic module used during the preliminary design optimization process. Analytical formulations retained for lift and drag components are presented in the first part. Then, the performances estimated by the aerodynamic module on some reference configurations are compared with both numerical and experimental data, showing a quite good agreement for both tube and wing and blended wing–body configurations not only for global performance but also for individual drag components.

Mean Value Ensemble Hubbard-U Correction for Spin-Crossover Molecules.

High-throughput searches for spin-crossover molecules require Hubbard-U corrections to common density functional exchange-correlation (XC) approximations. However, the Ueff values obtained from linear response or based on previous studies overcorrect the spin-crossover energies. We demonstrate that employing a linearly mixed ensemble average spin state as the reference configuration for the linear response calculation of Ueff resolves this issue. Validation on a commonly used set of spin-crossover complexes shows that these ensemble Ueff values consistently are smaller than those calculated directly on a pure spin state, irrespective of whether that be low- or high-spin. Adiabatic crossover energies using this methodology for a generalized gradient approximation XC functional are closer to the expected target energy range than with conventional Ueff values. Based on the observation that the Ueff correction is similar for different complexes that share transition metals with the same oxidation state, we devise a set of recommended averaged Ueff values for high-throughput calculations.