Mechanical behavior of hexagonal honeycombs under low-velocity impact – theory and simulations

Based on the cells’ collapse mechanisms of the hexagonal honeycombs revealed from the numerical simulations under the low-velocity impact, an analytical model is established to deduce the crushing strength of the honeycomb and the stress at the supporting end both as functions of impact velocity, cell size, cell-wall angle, and the mechanical properties of the base material. The results show that the honeycomb’s crushing strength increases with the impact velocity, while the supporting stress decreases with the increase of the impact velocity. Combining with the dynamic predictions under the high-velocity impact in our previous work (Hu and Yu, 2010), the crushing strength of the honeycombs can be analytically predicted over wide range of crushing velocities. The analytical expression of the critical velocity is also obtained, which offers the boundary for the application of the functions of the honeycomb’s crushing strength under the low-velocity and the high-velocity impacts. All of the analytical predictions are in good agreement with the numerical simulation results.     

Eulerian–Lagrangian simulation of distinct clustering phenomena and RTDs in riser and downer

Numerical simulation of fully developed hydrodynamics of a riser and a downer was carried out using an Eulerian–Lagrangian model, where the particles are modeled by the discrete element method (DEM) and the gas by the Navier–Stokes equations. Periodic flow domain with two side walls was adopted to simulate the fully developed dynamics in a 2D channel of 10 cm in width. All the simulations were carried out under the same superficial gas velocity and solids holdup in the domain, starting with a homogenous state for both gas and solids, and followed by the evolution of the dynamics to the heterogeneous state with distinct clustering in the riser and the downer. In the riser, particle clusters move slowly, tending to suspend along the wall or to flow downwards, which causes wide residence time distribution of the particles. In the downer, clusters still exist, but they have faster velocities than the discrete particles. Loosely collected particles in the clusters move in the same direction as the bulk flow, resulting in plug flow in the downer. The residence time distribution (RTD) of solids was computed by tracking the displacements of all particles in the flow direction. The results show a rather wide RTD for the solids in the riser but a sharp peak RTD in the downer, much in agreement with the experimental findings in the literature. The ensemble average of transient dynamics also shows reasonable profiles of solids volume fraction and solids velocity, and their dependence on particle density.     

Mathematical models of shape memory alloy behavior for online and fast prediction of the hysteretic behavior

In this contribution, a new closed form of a mathematical model of Nickel–Titanium (NiTi) shape memory alloy (SMA) and its thermo-mechanical wire hysteresis behavior is developed. The approach is based on experimental data. The behavior of the heated and naturally cooled wire is modeled by mathematical expression. The cycle of heating and cooling is performed under a constant load. The prediction of the hysteretic behavior is realized through models adaptation, as predetermination, or real time determination of the models values, is developed and presented in detail. Simulations for position control using PID controller is shown for comparison purposes. The developed approach is incorporated in a feed forward control scheme. A comparison between the actual position and the predicted models position shows promising results.     

Characterization of mechanical properties by indentation tests and FE analysis – validation by application to a weld zone of DP590 steel

In this work, the mechanical properties of the metal active gas (MAG) weld zone and heat affected zone (HAZ) were characterized utilizing the continuous indentation method together with its finite element (FEM) analysis. To verify the measured properties, uni-axial tension and three point bending tests were performed for DP590 welded specimens. For numerical simulations, the isotropic hardening law was assumed along with the non-quadratic anisotropic yield function, Yld2000-2d. As for the failure criterion of the base material and weld zones particularly for the failure evaluation in the uni-axial tension test, Hill’s bifurcation theory and the M–K theory were applied to calculate the forming limit diagrams considering all measured properties including strain-rate sensitivity.     

Elastic–plastic behavior of steel sheets under in-plane cyclic tension–compression at large strain

Elastic–plastic behavior of two types of steel sheets for press-forming (an aluminum-killed mild steel and a dual-phase high strength steel of 590 MPa ultimate tensile strength) under in-plane cyclic tension–compression at large strain (up to 25% strain for mild steel and 13% for high strength steel) have been investigated. From the experiments, it was found that the cyclic hardening is strongly influenced by cyclic strain range and mean strain. Transient softening and workhardening stagnation due to the Bauschinger effect, as well as the decrease in Young's moduli with increasing prestrain, were also observed during stress reversals. Some important points in constitutive modeling for such large-strain cyclic elasto-plasticity are discussed by comparing the stress–strain responses calculated by typical constitutive models of mixed isotropic–kinematic hardening with the corresponding experimental observations.     

The phenomena of shock wave reflection — a review of unsolved problems and future research needs

Although the phenomenon of shock wave reflection was discovered more than a hundred years ago, active research related to this phenomenon still goes on in many countries in the world (e.g., Australia, Canada, China, Germany, Israel, Japan, Poland, Russia and United States of America). As a matter of fact the research activity increased so drastically in the past decade and a half that a special scientific meeting dedicated to better understanding the reflection phenomena of shock waves, namely The International Mach Reflection Symposium was initiated in 1981 and was held since then in the major research centers actively involved in the research of shock wave reflections. In the present paper the status of the research of the phenomenon of shock wave reflection will be discussed in general, and unresolved problems and future research needs will be pointed out.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

A thermodynamic approach to the rheology of highly interactive filler-polymer mixtures: Part I – Theory

The rheological behavior of highly interactive filler-polymer mixtures is simulated utilizing a double network created by the entangled polymer matrix and the adsorbed polymer. Both networks are represented by a nonlinear viscoelastic constitutive equation. The dependence of rheological properties on filler concentration is taken into account through the bridging density resulting from polymer-filler interactions and a hydrodynamic reinforcement. The relative contribution of both networks is computed through the energy balance consistent with the thermodynamics of the polymer-filler chemical interactions and fluid mechanics. This self-consistent approach allows one to calculate the strain dependence of dynamic properties under oscillatory flow and shear rate dependence of stresses under steady simple shear flow and upon start up and cessation of shear flow. Received: 11 May 2000 Accepted: 8 March 2001     

Surface rheology of sorbitan tristearate and β-lactoglobulin: Shear and dilatational behavior

Proteins and surfactants behave very differently under shear and dilatational deformation. In this work, we compare specifically their surface properties by evaluating their rheological response. Oil-soluble surfactant, sorbitan tristearate (Span 65), and globular protein, β-lactoglobulin, were spread and adsorbed onto the surface, respectively. A 2D searle-type measuring geometry with a biconical bob was used for measuring the surface shear rheology, and a pendant drop film balance was used for measuring the dilatational rheology. Both equipments provided the viscoelastic properties (surface shear and dilatational complex moduli) of interfacial layers. Also, the linear and non-linear rheology of these systems was studied by increasing the amplitude of the oscillation. Linear rheology showed that dilatational deformation is mostly affected by the nature of the molecular structure at the interface, whereas shear deformation is affected by the strength of the surface film due to the intermolecular interactions. Furthermore, large-amplitude oscillatory shear rheology indicated that the non-linearity increases with the surface concentration, and is higher for insoluble Span 65 spread films than for soluble protein adsorbed layers. Dilatational and shear deformation provide complementary information about interfacial layers that can be optimized so as to fully characterize the surface depending of the type of film (spread or adsorbed) and the technique used (shear or dilatational rheology under linear or non-linear regimes). This information is useful to correlate the structure and the mechanical properties of interfacial systems.     

Next-generation NATO reference mobility model complex terramechanics – Part 2: Requirements and prototype

In part 2 of this paper, the Complex Terramechanics (CT) software tools requirements recommended by the NATO research task group RTG-248 are presented along with example simulations from a CT prototype software tool which attempts to satisfy the requirements.     

Macro-performance evaluation of friction stir welded automotive tailor-welded blank sheets: Part I – Material properties

In order to evaluate the macroscopic performance of friction stir welded automotive tailor-welded blank (TWB) sheets, the hardening behavior, anisotropic yielding properties and forming limit diagram were characterized both for base (material) and weld zones. In order to describe the Bauschinger and transient hardening behaviors as well as permanent softening during reverse loading, the modified Chaboche type combined isotropic–kinematic hardening law was applied. As for anisotropic yielding, the non-quadratic anisotropic yield function, Yld2000-2d, was utilized for base material zones, while isotropy was assumed for weld zones for simplicity. As for weld zones, hardening properties were obtained using the rule of mixture and selectively by direct measurement using sub-sized specimens. Forming limit diagrams were measured for base materials but calculated for weld zones based on Hill’s bifurcation and M–K theories. In this work, four automotive sheets were considered: aluminum alloy 6111-T4, 5083-H18, 5083-O and dual-phase steel DP590 sheets, each having one or two thicknesses. Base sheets with the same and different thicknesses were friction-stir welded for tailor-welded blank (TWB) samples.     

Bifurcation and chaotic behavior of a discrete-time Ricardo–Malthus model

The dynamics of a discrete-time Ricardo–Malthus model obtained by numerical discretization is investigated, where the step size δ is regarded as a bifurcation parameter. It is shown that the system undergoes flip bifurcation and Neimark–Sacker bifurcation in the interior of $R^{2}_{+}$ by using the theory of center manifold and normal form. Numerical simulations are presented not only to illustrate our theoretical results, but also to exhibit the system’s complex dynamical behavior, such as the cascade of period-doubling bifurcation in orbits of period 2, 4, 8 16, period-11, 22, 28 orbits, quasiperiodic orbits, and the chaotic sets. These results reveal far richer dynamics of the discrete model compared with the continuous model. The Lyapunov exponents are numerically computed to confirm further the complexity of the dynamical behaviors.     

Modeling and waveform optimization of stick–slip micro-drives using the method of dimensionality reduction

In this paper, the dynamics of piezo-actuated stick–slip micro-drives are studied experimentally and theoretically. First, the stick–slip-based force-generating test stand is introduced, and experimental results are presented. Then, a numerical model is formulated which explicitly includes the dynamics of normal and tangential properties of the contact areas in the frictional driving elements of the drive. The contact forces are simulated using the method of dimensionality reduction. We show that the experimentally observed behavior can be described without using any fitting parameters or assuming any generalized laws of friction if the explicit contact mechanics of the frictional contacts is taken into account. Furthermore, an even simpler model of the drive is developed to get a qualitative understanding of the system. It is employed to gain a new actuation method, which reduces the vibrations of the drive’s runner and therefore enhances its performance.     

Renewal of basic laws and principles for polar continuum theories (Ⅺ)—consistency problems

Some consistency problems existing in continuum field theories are briefly reviewed.Three arts of consistency problems are clarified based on the renewed basic laws for polar continua.The first art discusses the consistency problems between the basic laws for polar continua.The second art discusses the consistency problems between the basic laws for polar continua and for other nonpolar continua.The third art discusses the consistency problems between the basic laws for micropolar continuum theories and the dynamical equations for rigid body.The results presented here can help us to get a deeper understanding the structure of the basic laws for various continuum theories and the interrelations between them.In the meantime,these results obtained show clearly that the consistency problems could not be solved in the framework of traditional basic laws for continuum field theories.     

Next-generation NATO reference mobility model complex terramechanics – Part 1: Definition and literature review

The US army along with NATO member and partner nations’ militaries need an accurate software tool for predicting ground vehicle mobility (such as speed-made-good and fuel-consumption) on world-wide terrains where military vehicles may be required to operate. Currently, the NATO Reference Mobility Model (NRMM) is the only NATO recognized tool for assessing ground vehicle mobility. NRMM was developed from the 1960s to the 1980s and relies on steady-state empirical formulas which may not be accurate for new military ground vehicles. A NATO research task group (RTG-248) was established from 2016 to 2018 to develop the NG-NRMM (next-generation NRMM) software tool requirements and an NG-NRMM prototype which uses high-fidelity “simple” or “complex” terramechanics models for the terrain/soil along with modern 3D multibody dynamics software tools for modeling the vehicle. NG-NRMM Complex Terramechanics (CT) models are those that utilize full 3D soil models capable of predicting the 3D soil reaction forces on the vehicle surfaces (including tires, tracks, legs, and under body) and the 3D flow and deformation of the soil including both elastic and plastic deformation under any 3D loading condition. In Part 1 of this paper, an overview of the full spectrum of terramechanics models from the highest fidelity to the lowest fidelity is presented along with a literature review of CT ground vehicle mobility models.     

Local Minimizers and Quasiconvexity – the Impact of Topology

The aim of this paper is to discuss the question of existence and multiplicity of strong local minimizers for a relatively large class of functionals : from a purely topological point of view. The basic assumptions on are sequential lower semicontinuity with respect to W^1,p-weak convergence and W^1,p-weak coercivity, and the target is a multiplicity bound on the number of such minimizers in terms of convenient topological invariants of the manifolds and .In the first part of the paper, we focus on the case where is non-contractible and proceed by establishing a link between the latter problem and the question of enumeration of homotopy classes of continuous maps from various skeleta of into . As this in turn can be tackled by the so-called obstruction method, it is evident that our results in this direction are of a cohomological nature.The second part is devoted to the case where =^N and is a bounded smooth domain. In particular we consider integralswhere the above assumptions on can be verified when the integrand F is quasiconvex and pointwise p-coercive with respect to the gradient argument. We introduce and exploit the notion of a topologically non-trivial domain and under this establish the first existence and multiplicity result for strong local minimizers of that in turn settles a longstanding open problem in the multi-dimensional calculus of variations as described in [6].     

Modeling of the Front of Melting and Destruction of a Melt Film During Gas‐Laser Cutting of Metals

The products of laser cutting of metals on an automated laser setup are investigated. Results of model experiments are presented, where soft wax was used instead of metal transforming into the melt; soft wax filled a narrow flat slot between two glass plates and was removed by a heated air stream. The physical processes of melting of the liquidwax film, its destruction, and entrainment by the gas jet being assumed to be analogous to the processes of metalmelt spraying inside the cut in fullscale experiments, the characteristic size of drops formed thereby is evaluated. The modeling results are in qualitative agreement with the results of fullscale experiments. It is shown that the quality of laser cutting of metals directly depends on the character of spraying of the liquid melt and the process of its removal.     

Renewal of basic laws and principles for polar continuum theories （XI）——consistency problems

Some consistency problems existing in continuum field theories are briefly reviewed. Three arts of consistency problems are clarified based on the renewed basic laws for polar continua. The first art discusses the consistency problems between the basic laws for polar continua. The second art discusses the consistency problems between the basic laws for polar continua and for other nonpolar continua. The third art discusses the consistency problems between the basic laws for micropolar continuum theories and the dynamical equations for rigid body. The results presented here can help us to get a deeper understanding the structure of the basic laws for various continuum theories and the interrelations between them. In the meantime, these results obtained show clearly that the consistency problems could not be solved in the framework of traditional basic laws for continuum field theories.     

Collaborative optimization of screening efficiency and screen surface load — Part I: Modeling and evaluation

The screen surface load (SSL) caused by granular materials is an important factor affecting the structural performance of vibrating screen. Based on virtual experiment, a multi-objective collaborative optimization method is proposed to control the SSL under high screening efficiency (SE) in this work. Firstly, a DEM model was established to study the influence of process parameters on SE and SSL. Secondly, the NSGA-II (Non-dominated Sorting Genetic Algorithm) was employed to optimize the screening parameters with both SE and SSL as targets. The optimization method proves to be effective implementing on a linear vibrating screening. With SE equals to 98.5%, the SSL optimizable range is 39.2%. While compromising the SE to 88.7%, the SSL optimizable range improves to 48.6%. The result shows that the collaborative optimization could effectively control the SSL while maintaining a high SE, which is of great significance to improve the service life of screen surface and screen body.