On the dynamic mechanical properties of open-cell metal foams – A re-assessment of the ‘simple-shock theory’

Metal foams are increasingly used for energy absorption especially in lightweight structures and to resist blast and impact loads. This requires an understanding of the dynamic response of these materials for modelling purposes. As a supplement to Tan et al., 2005a, Tan et al., 2005b, hereinafter referred to as T–L for brevity, this paper provides experimental data for the dynamic mechanical properties of open-cell Duocel® foams having a three-dimensional (3D) distribution of cells. These confirm significant enhancement of the foam’s compressive strength, accompanied by changes in their deformation pattern in certain loading régimes, particularly what has come to be described as the ‘shock’ régime by Zheng et al. (2012). This paper examines experimentally, in a similar fashion as T–L, how the structural response of the individual cell walls is affected by cell-shape anisotropy at the cell (meso)-scale and how this, in turn, alters the pattern of cell crushing and the dynamic, mechanical properties. The distinctive role of cell microinertia and ‘shock’ formation are discussed in relation to the mechanical properties measured for these 3D cylindrical specimens. For consistency the same procedures described in T–L are used. The features identified are shown to be consistent with those observed in finite-element simulations of two-dimensional (2D) honeycombs as estimated by the one-dimensional (1D) steady-shock theory summarised in T–L. The different deformation patterns that develop in the various loading régimes are categorised according to the compression rate/impact speed. Critical values of impact velocity, corresponding to the transition from one pattern to the other, are quantified and predictive formulae for the compressive uniaxial strengths in the directions of two of the principal axes of the material in each loading régime are derived and discussed. The accuracy of the predictive formula in T–L is shown to critically depend on the ‘densification strain’ of the foam specimens. This parameter and the discussion that follows could assist the formulation and validation of alternative theoretical/computational models on the dynamic deformation of such materials.     

Amplitude dependence of filler-reinforced rubber: Experiments,constitutive modelling and FEM – Implementation

The focus of the present paper is the experimental investigation, the constitutive representation and the numerical simulation of the amplitude dependence of filler-reinforced elastomers. A standard way to investigate the dynamic properties of viscoelastic materials is via the dynamic modulus which is obtained from stress signals due to harmonic strain excitations. Based on comprehensive experimental data, an amplitude-dependent constitutive model of finite viscoelasticity is developed. The model is based on a modified Maxwell chain with process-dependent viscosities which depend on additional internal state variables. The evaluation of this thermodynamically consistent model is possible in both the time domain, via stress-time signals, and in the frequency domain, via the dynamic modulus. This property is very profitable for the parameter identification process. The implementation of the constitutive model into the commercial finite element code ANSYS with the user-programmable feature (UPF) USERMAT for large deformations in updated Lagrange formulation is presented. This implementation allows simulating the time-dependent behaviour of rubber components under arbitrary transient loading histories. Due to physical and geometrical nonlinearities, these simulations are not possible in the frequency domain. But, transient FEM computations of large loading histories are sometimes not possible in an acceptable time. In the context of the parameter identification the fundamental ideas are presented, how this problem has been solved. Transient FEM simulations of real rubber components are also shown to visualize the properties of the model in the context of the transient material behaviour.     

Finite deformation pseudo-elasticity of shape memory alloys – Constitutive modelling and finite element implementation

In this paper we suggest a new phenomenological material model for shape memory alloys. In contrast to many earlier concepts of this kind the present approach includes arbitrarily large deformations. The work is motivated by the requirement, also expressed by regulatory agencies, to carry out finite element simulations of NiTi stents. Depending on the quality of the numerical results it is possible to circumvent, at least partially, expensive experimental investigations. Stent structures are usually designed to significantly reduce their diameter during the insertion into a catheter. Thereby large rotations combined with moderate and large strains occur. In this process an agreement of numerical and experimental results is often hard to achieve. One of the reasons for this discrepancy is the use of unrealistic material models which mostly rely on the assumption of small strains. In the present paper we derive a new constitutive model which is no longer limited in this way. Further its efficient implementation into a finite element formulation is shown. One of the key issues in this regard is to fulfil “inelastic” incompressibility in each time increment. Here we suggest a new kind of exponential map where the exponential function is suitably computed by means of the spectral decomposition. A series expansion is completely avoided. Finite element simulations of stent structures show that the new concept is well appropriate to demanding finite element analyses as they occur in practically relevant problems.     

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.     

Parameterization and modelling of large off-road tyres for ride analyses: Part 2 – Parameterization and validation of tyre models

Every mathematical model used in a simulation is an idealization and simplification of reality. Vehicle dynamic simulations that go beyond the fundamental investigations require complex multi-body simulation models. The tyre–road interaction presents one of the biggest challenges in creating an accurate vehicle model. Many tyre models have been proposed and developed but proper validation studies are less accessible. These models were mostly developed and validated for passenger car tyres for application on relatively smooth roads. The improvement of ride comfort, safety and structural integrity of large off-road vehicles, over rough terrain, has become more significant in the development process of heavy vehicles. This paper investigates whether existing tyre models can be used to accurately describe the vertical behaviour of large off road tyres while driving over uneven terrain. [1] Presented an extensive set of experimentally determined parameterization and validation data for a large off-road tyre. Both laboratory and field test are performed for various loads, inflation pressures and terrain inputs. The parameterization process of four tyre models or contact models are discussed in detail. The parameterized models are then validated against test results on various hard but rough off-road terrain and the results are discussed.     

Direct numerical simulation of flow over a forward-facing step – Flow structure and aeroacoustic source regions

A direct numerical simulation of the flow over a forward-facing step at a Reynolds number of 8000 based on the step height is presented. Calculations were performed using second-order finite volume discretisation in space on co-located meshes. A hybrid calculation approach based on Lighthill’s acoustic analogy is explained. Results of the simulation are intended to be used as a database for the validation of different discretisation schemes for the flow computation and simulation approaches for the calculation of sound radiation using a hybrid approach. Turbulent statistics are presented along with aeroacoustic source regions. Strong and weak forms of the aeroacoustic source term are presented and compared. For visualization purposes, the strong form is more suitable, whereas for the calculation of sound radiation both forms can be used. From the visualization of the aeroacoustic sources, it can be seen that they mainly concentrate on the region of the leading edge of the step and the shear layer close to the step.     

Void nucleation and growth in mineral-filled PVC – An experimental and numerical study

The nucleation and growth of voids in mineral-filled PVC have been investigated through experimental and numerical studies. Uniaxial tensile specimens were deformed in tension to different elongation levels and then unloaded. The macroscopic strain fields were recorded by use of digital image correlation. After the test, the microstructure of the deformed specimens was investigated in a scanning electron microscope. It was found that the observed volume strain on the macroscale is related to void growth on the microscale. In addition, finite element simulations were performed on unit cell models representing the microstructure of the material in a simplified manner. The numerical simulations demonstrate macroscopic dilation as a result of void growth. Moreover, the numerical simulations indicate that the experimentally observed stress-softening response of the PVC composite material may result from matrix-particle debonding.     

Modeling and simulation of severe slugging in air–water pipeline–riser systems

A mathematical model, numerical simulations and stability and flow regime maps corresponding to severe slugging in pipeline–riser systems, are presented. In the simulations air and water were used as flowing fluids. The mathematical model considers continuity equations for liquid and gas phases, with a simplified momentum equation for the mixture, neglecting inertia. A drift-flux model, evaluated for the local conditions in the riser, is used as a closure law. The developed model predicts the location of the liquid accumulation front in the pipeline and the liquid level in the riser, so it is possible to determine which type of severe slugging occurs in the system. The numerical procedure is convergent for different nodalizations. A comparison is made with experimental results corresponding to a catenary riser, showing very good results for slugging cycle and stability and flow regime maps.     

Anisotropic hardening – numerical application of a cubic yield theory and consideration of variable r-values for sheet metal

The first part of this paper contains a polynomial yield condition of third order connected with evolution equations for material tensors of higher orders. They are formulated by formal generalisation of an approach by Danilov. The second part presents a possibility of taking into account the rotation of the yield surface as a result of a variable planar anisotropy (r-value) in sheet metal. This is done by an extension of the evolution equations, based on a quadratic yield function. The corresponding deformation law and the set of evolution equations are numerically integrated for selected loading paths in the subspaces σ₁,σ₂ and σ,τ. Some of the experimentally observed effects, such as the increasing curvature of the yield locus curve in the loading direction or the specific rotation of the yield surface, are correctly reproduced.     

Finite element modelling of Al/SiCp metal matrix composites with particles aligned in stripes—a 2D–3D comparison

3D Finite element calculations comparing to axisymmetric calculations have been performed to predict quantitatively the tensile behaviour of composites reinforced with ceramic particles aligned in stripes. The analyses are based on a unit cell model, which assumes the periodic arrangement of reinforcements. The results are presented in such a manner that can be directly compared for all possible aspect ratios and inclusion volume fractions. It is indicated that varying the distance between the stripes when particle volume fraction is kept constant significantly influences the overall mechanical behaviour of composites. Whereas during elastic deformation 3D and axisymmetric formulations predict quantitatively similar results, the mechanical behaviour perpendicular to the stripe direction predicted by 3D and axisymmetric models may differ depending on the inclusion volume fraction. Nevertheless an appreciable strengthening in the stripe direction independent on the model and deformation stage is predicted.     

The shearing edge of tracked vehicle – Soil interactions in path clearing applications utilizing Multi-Body Dynamics modeling & simulation

Tracked vehicle – soil interactions were modeled and analyzed to compare the mobility of two notional path clearing implements pushed by a tracked vehicle. This exploration assesses the capabilities and limitations of the state-of-the-art in tracked vehicle dynamics modeling and simulation over soft-soil terrain. Unique modeling and simulation methods to stretch the capability of the current state-of-the-art contribute to the overall discussion. One path clearing implement was a roller and rake combination. The other was a quickly rotating flail system that cleared a definitive path by impacting and flinging the soil away. Geotechnical forcing functions implemented Coulomb’s lateral earth pressure theory and Terzaghi passive soil failure models to compute the forces at the soft-soil – implement interfaces. Coulomb theory was reimagined to account for anomalies present when modeling the flail, mainly its arced motion and non-semi-infinite soil resistance zone. The path-clearing implements were simulated over discrete events and compared by means of load and acceleration time histories. The discrete events include side-slopes, grades, half-rounds, potholes, cross country terrain, and ‘V’ shaped ditches (V-ditch). Overall, the flail system experienced lower peak loads at the interface brackets and lower peak accelerations at the vehicle’s center of gravity than the roller-rake system.     

Flow fields and packing states in the discharge flow of noncircular particles—A SIPHPM simulation

Although the discharge flow of spherical materials has been extensively explored, the effect of particle shape on discharge is still poorly understood. The present work explores the two-dimensional discharge flow fields of noncircular particles using the soft-sphere-imbedded pseudo-hard particle model method. Rectangular particles having different aspect ratios (R_a = 1, 1.5, 2–5) and regular polygonal particles having different numbers of sides (N_s = 3–8, 10) are discharged through hopper beds having different orifice widths (D_i = 40, 70.77, 99.13, 125.74, 151.13 mm). The discharge rates of differently shaped particles in different beds are consistent with Beverloo’s relation. Moreover, the flow fields are computed and evaluated to study the effects of R_a, N_s, and D_i on particle discharge. The characteristics of particle–particle connections in the discharge process are evaluated according to the temporal evolution and spatial distribution of the contact points. Additionally, the effect of the initial packing on the discharge profile is investigated. The findings help clarify the discharge of noncircular particles.     

Chaos in a tethered satellite system induced by atmospheric drag and Earth’s oblateness

Nonlinear Dynamics - This paper describes the chaos behavior of an in-plane tethered satellite system induced by atmospheric drag and the Earth’s oblateness. A commonly used model, the...     

Crack tortuousity in the nacreous layer – Topological dependence and biomimetic design guideline

The nacreous layer in seashells is known for two phenomenal aspects: light-weightiness and superior fracture toughness. Of a multitude of toughening mechanisms, the highly meandering nature of the crack path through its staggered architecture has been reported to contribute approximately a third of its overall toughness. In the current article, we are trying to establish the scientific rationale associated with the influence of overlap length on the crack-tip driving force from a local perspective via development of a simplified analytical model. Characteristic overlap lengths computed showed reasonable agreement with the values reported in the nacreous layer and previously published experimental data. Biomimetic design guideline obtained from the current investigation would thereby lead to development of synthetic staggered architecture materials with improved stiffness, load-transfer and toughness.     

Particle–wall interaction in entrained-flow slagging coal gasifiers: Granular flow simulation and experiments in a cold flow model reactor

Entrained-flow slagging coal gasifiers display large conversion efficiencies and small levels of unconverted carbon at the exhaust. Both features are apparently at odds with the fairly small “space-time” of the particle-laden gas feeding, as compared with the time scale of heterogeneous gasification of carbon. This apparent inconsistency can be explained by considering that fuel residence times are longer than the “space-time” due to segregation of fuel particles in the near-wall region of the gasifier. Segregation is promoted by swirl flow, by particle–wall interaction as the wall is covered by a molten layer of slag and by the establishment of a dense-dispersed flow of granular solids in the proximity of the wall.This study presents results of granular flow simulations of the interaction of a dense-dispersed particle flow with the confining wall. Simulations consider that both the particles and the wall may be either “sticky” or “non sticky”, based on the prevailing elastic vs plastic behaviour upon collision. The effect of drag forces exerted on particles by swirled gas flow is simulated in a simplified manner. Particle–particle collisions are modelled with a Hertzian approach that includes torque and cohesion. The extent and time scale of segregation of a lump of particles loaded into a cylindrical vessel are assessed. Results clearly indicate the different structure of the layer of particles establishing at the wall surface in the different interaction regimes.Results of simulations are qualitatively compared with results of an experimental campaign performed in a reactor representing a cold flow model of the entrained-flow gasifier, where solid, molten or semi-molten particles have been simulated by atomized wax as surrogate material. Altogether, the results confirm the importance of the particle–particle and particle–wall micromechanical interactions for a correct prevision of the segregation of fuel particles in entrained-flow slagging gasifiers.     

Cavitation in brittle metallic glasses – Effects of stress state and distributed weak zones

Experimental studies and atomistic simulations have shown that brittle metallic glasses fail by a cavitation mechanism whose origin has been traced to the presence of intrinsic atomic density fluctuations which give rise to weak zones with reduced yield strength. It has been shown recently through continuum analysis that the presence of these zones can lower the cavitation stress considerably under equibiaxial loading. The objective of the present work is to study the effect of the applied stress state on the cavitation behavior of such a heterogeneous plastic solid with distributed weak zones. To this end, 2D plane strain finite element simulations are performed by subjecting a unit cell containing a weak zone to different (biaxiality) stress ratios. The volume fraction and yield strength of the weak zone are varied over a wide range. The results show that unlike in a homogeneous plastic solid, the cavitation stress of the heterogeneous aggregate does not reduce appreciably as the stress ratio decreases from unity when the yield strength of the weak zone is low. It is found that a non-dimensional parameter characterizing the stress state prevailing in the weak zone and its yield properties uniquely control the cavitation stress. The nature of cavitation bifurcation may change from unstable bifurcation to the left at sufficiently low stress ratio to one involving snap cavitation at high stress ratio.     

Fluid–solid interaction simulation of flow and stress pattern in thoracoabdominal aneurysms: A patient-specific study

Thoracoabdominal aneurysm (TA) is a pathology that involves the enlargement of the aortic diameter in the inferior descending thoracic aorta and has risk factors including aortic dissection, aortitis or connective tissue disorders. Abnormal flow patterns and haemodynamic stress on the diseased aortic wall are thought to play an important role in the development of this pathology and the internal wall stress has proved to be more reliable as a predictor of rupture than the maximum diameter for abdominal aortic aneurysms; but this assumption has not been validated yet for aneurysms involving the thoracic aorta. In the present study, three patients with TAs of different maximum diameters were scanned using magnetic resonance imaging (MRI) techniques. Realistic models of the aneurysms were reconstructed from the in vivo MRI data acquired from the patients, and subject-specific flow conditions were applied as boundary conditions. The wall and thrombus were modelled as hyperelastic materials and their properties were derived from the literature. A normal descending aorta was also simulated to provide data for comparison. Fully coupled fluid–solid interaction (FSI) simulations as well as solid static simulations were performed using ADINA 8.2. The results show that the wall stress distribution and its magnitude are strongly dependent on the 3-D shape of the aneurysm and the distribution of thrombus. Maximum wall stresses in all TA models are higher than in the normal aorta, and values of maximum wall stress are not directly related to the maximum aneurysm diameter. Comparisons between the FSI and solid static simulation results showed no significant difference in maximum wall stress, supporting those previous studies which found that FSI simulations were not necessary for wall stress prediction.     

Thickness Effect of Pulse Shaper on Dynamic Stress Equilibrium and Dynamic Deformation Behavior in the Polycarbonate Using SHPB Technique

0Introduction Thehighstrainratestress strainresponsesofpolymersandpolymericcompositematerialshave receivedincreasedscientificandindustrialattentioninrecentyears.Polymericmaterialsaresubjected todynamicloadingandhighstrainratedeformationinavarietyofimporta…