Showing papers in "Journal of Applied Mechanics in 2009"

Added Mass Effects of Compressible and Incompressible Flows in Fluid-Structure Interaction

Abstract: The subiteration method which forms the basic iterative procedure for solving fluid structure-interaction problems is based on a partitioning of the fluid-structure system into a fluidic part and a structural part. In fluid-structure interaction, on short time scales the fluid appears as an added mass to the structural operator, and the stability and convergence properties of the subiteration process depend significantly on the ratio of this apparent added mass to the actual structural mass. In the present paper, we establish that the added-mass effects corresponding to compressible and incompressible flows are fundamentally different. For a model problem, we show that on increasingly small time intervals, the added mass of a compressible flow is proportional to the length of the time interval, whereas the added mass of an incompressible flow approaches a constant. We then consider the implications of this difference in proportionality for the stability and convergence properties of the subiteration process, and for the stability and accuracy of loosely-coupled staggered time-integration methods.

Dynamic Fracture of Shells Subjected to Impulsive Loads

Abstract: lation or in the vicinity of the crack tip 14. In related work, Armero and Ehrlich 15 used embedded discontinuity elements to model hinge lines in plates. The development of a fracture criterion that is computationally efficient and is easily applied in terms of available data poses a significant difficulty. Fracture criteria for quasibrittle materials, such as aluminum, are usually expressed in terms of the critical maximum principal tensile strain. However, in low order finite element models solved by explicit time integration, the maximum principal tensile strain tends to be quite noisy, so that crack paths computed by direct application of such a criterion tend to be erratic and do not conform to experimentally observed crack paths. Here, we propose a nonlocal form of a strain-based fracture criterion. The nonlocal form is obtained by a kernel-weighted average over a sector in front of the crack tip. In addition, we describe a combination of this kernel-weighted average with an angular component that can be used to indicate crack branching. The methodology is applied to the fracture of shell experiments performed by Chao and Shepherd 16. Although these experiments are very interesting, they do not provide enough experimental data for a validation of the methodology. Nevertheless, we show that the method is able to reproduce the change in failure mode that occurs for longer notches as compared with shorter notches and that the overall final configuration agrees reasonably well with that observed in the experiments.

Validation of Nonlinear Viscoelastic Contact Force Models for Low Speed Impact

Abstract: Compliant contact force modeling has become a popular approach for contact and impact dynamics simulation of multibody systems. In this area, the nonlinear viscoelastic contact force model developed by Hunt and Crossley (1975, “Coefficient of Restitution Interpreted as Damping in Vibroimpact,” ASME J. Appl. Mech., 42, pp. 440–445) over 2 decades ago has become a trademark with applications of the model ranging from intermittent dynamics of mechanisms to engagement dynamics of helicopter rotors and implementations in commercial multibody dynamics simulators. The distinguishing feature of this model is that it employs a nonlinear damping term to model the energy dissipation during contact, where the damping coefficient is related to the coefficient of restitution. Since its conception, the model prompted several investigations on how to evaluate the damping coefficient, in turn resulting in several variations on the original Hunt–Crossley model. In this paper, the authors aim to experimentally validate the Hunt–Crossley type of contact force models and furthermore to compare the experimental results to the model predictions obtained with different values of the damping coefficient. This paper reports our findings from the sphere to flat impact experiments, conducted for a range of initial impacting velocities using a pendulum test rig. The unique features of this investigation are that the impact forces are deduced from the acceleration measurements of the impacting body, and the experiments are conducted with specimens of different yield strengths. The experimental forces are compared with those predicted from the contact dynamics simulation of the experimental scenario. The experiments, in addition to generating novel impact measurements, provide a number of insights into both the study of impact and the impact response.

The Through-Thickness Compressive Strength of a Composite Sandwich Panel With a Hierarchical Square Honeycomb Sandwich Core

Abstract: Sandwich panels with aluminum alloy face sheets and a hierarchical composite square honeycomb core have been manufactured and tested in out-of-plane compression. The prismatic direction of the square honeycomb is aligned with the normal of the overall sandwich panel. The cell walls of the honeycomb comprise sandwich plates made from glass fiber/epoxy composite faces and a polymethacrylimide foam core. Analytical models are presented for the compressive strength based on three possible collapse mechanisms: elastic buckling of the sandwich walls of the honeycomb, elastic wrinkling, and plastic microbuckling of the faces of the honeycomb. Finite element calculations confirm the validity of the analytical expressions for the perfect structure, but in order for the finite element simulations to achieve close agreement with the measured strengths it is necessary to include geometric imperfections in the simulations. Comparison of the compressive strength of the hierarchical honeycombs with that of monolithic composite cores shows a substantial increase in performance by using the hierarchical topology. DOI: 10.1115/1.3086436

Vector Extrapolation for Strong Coupling Fluid-Structure Interaction Solvers

Abstract: Fluid-structure interaction (FSI) solvers based on vector extrapolation methods are discussed. The FSI solver framework builds upon a Dirichlet-Neumann partitioning between general purpose fluid and structural solver. For strong coupling of the two fields vector extrapolation methods are employed to obtain a matrix free nonlinear solver. The emphasis of this presentation is on the embedding of well known vector extrapolation methods in a popular FSI solver framework and, in particular, the relation of these vector extrapolation methods to established fixed-point FSI schemes.

Analytical Modeling and Vibration Analysis of Partially Cracked Rectangular Plates With Different Boundary Conditions and Loading

Abstract: This study proposes an analytical model for vibrations in a cracked rectangular plate as one of the results from a program of research on vibration based damage detection in aircraft panel structures. This particular work considers an isotropic plate, typically made of aluminum, and containing a crack in the form of a continuous line with its center located at the center of the plate and parallel to one edge of the plate. The plate is subjected to a point load on its surface for three different possible boundary conditions, and one examined in detail. Galerkin's method is applied to reformulate the governing equation of the cracked plate into time dependent modal coordinates. Nonlinearity is introduced by appropriate formulations introduced by applying Berger's method. An approximate solution technique-the method of multiple scales-is applied to solve the nonlinear equation of the cracked plate. The results are presented in terms of natural frequency versus crack length and plate thickness, and the nonlinear amplitude response of the plate is calculated for one set of boundary conditions and three different load locations, over a practical range of external excitation frequencies.

Computation of Inviscid Supersonic Flows Around Cylinders and Spheres With the V-SGS Stabilization and YZβ Shock-Capturing

Abstract: The YZβ shock-capturing technique was introduced originally for use in combination with the streamline-upwind/Petrov-Galerkin (SUPG) formulation of compressible flows in conservation variables. It is a simple residual-based shock-capturing technique. Later it was also combined with the variable subgrid scale (V-SGS) formulation of compressible flows in conservation variables and tested on standard 2D test problems. The V-SGS method is based on an approximation of the class of SGS models derived from the Hughes variational multiscale method. In this paper, we carry out numerical experiments with inviscid supersonic flows around cylinders and spheres to evaluate the performance of the YZβ shock-capturing combined with the V-SGS method. The cylinder computations are carried out at Mach numbers 3 and 8, and the sphere computations are carried out at Mach number 3. The results compare well to those obtained with the YZβ shock-capturing combined with the SUPG formulation, which were shown earlier to compare very favorably to those obtained with the well established OVERFLOW code.

A Multiscale Finite Element Formulation With Discontinuity Capturing for Turbulence Models With Dominant Reactionlike Terms

Abstract: A stabilization technique targeting the Reynolds-averaged Navier-Stokes (RANS) equations is proposed to account for the multiscale nature of turbulence and high solution gradients The objective is effective stabilization in computations with the advection-diffusion reaction equations, which are typical of the class of turbulence scale-determining equations where reaction-dominated effects strongly influence the boundary layer prediction in the presence of nonequilibrium phenomena The stabilization technique, which is based on a variational multiscale method, includes a discontinuity-capturing term designed to be operative when the solution gradients are high and the reactionlike terms are dominant As test problems, we use a 2D model problem and 3D flow computation for a linear compressor cascade

Feasibility of Metallic Structural Heat Pipes as Sharp Leading Edges for Hypersonic Vehicles

Abstract: Hypersonic flight with hydrocarbon-fueled airbreathing propulsion requires sharp leading edges. This generates high temperatures at the leading edge surface, which cannot be sustained by most materials. By integrating a planar heat pipe into the structure of the leading edge, the heat can be conducted to large flat surfaces from which it can be radiated out to the environment, significantly reducing the temperatures at the leading edge and making metals feasible materials. This paper describes a method by which the leading edge thermal boundary conditions can be ascertained from standard hypersonic correlations, and then uses these boundary conditions along with a set of analytical approximations to predict the behavior of a planar leading edge heat pipe. The analytical predictions of the thermostructural performance are verified by finite element calculations. Given the results of the analysis, possible heat pipe fluid systems are assessed, and their applicability to the relevant conditions determined. The results indicate that the niobium alloy Cb-752, with lithium as the working fluid, is a feasible combination for Mach 6-8 flight with a 3 mm leading edge radius.

A Nonlinear Rubber Material Model Combining Fractional Order Viscoelasticity and Amplitude Dependent Effects

Abstract: A nonlinear rubber material model is presented, where influences of frequency and dynamic amplitude are taken into account through fractional order viscoelasticity and plasticity, respectively The problem of simultaneously modeling elastic, viscoelastic, and friction contributions is removed by additively splitting them Due to the fractional order representation mainly, the number of parameters of the model remains low, rendering an easy fitting of the values from tests on material samples The proposed model is implemented in a general-purpose finite element (FE) code Since commercial FE codes do not contain any suitable constitutive model that represents the full dynamic behavior of rubber compounds (including frequency and amplitude dependent effects), a simple approach is used based on the idea of adding stress contributions from simple constitutive models: a mesh overlay technique, whose basic idea is to create a different FE model for each material definition (fractional derivative viscoelastic and elastoplastic), all with identical meshes but with different material definition, and sharing the same nodes Fractional-derivative viscoelasticity is implemented through user routines and the algorithm for that purpose is described, while available von Mises' elastoplastic models are adopted to take rate-independent effects into account Satisfactory results are obtained when comparing the model results with tests carried out in two rubber bushings at a frequency range up to 500 Hz, showing the ability of the material model to accurately describe the complex dynamic behavior of carbon-black filled rubber compounds

Effective Properties of Carbon Nanotube and Piezoelectric Fiber Reinforced Hybrid Smart Composites

Abstract: We propose a new hybrid piezoelectric composite comprised of armchair single-walled carbon nanotubes and piezoelectric fibers as reinforcements embedded in a conventional polymer matrix. Effective piezoelectric and elastic properties of this composite have been determined by a micromechanical analysis. Values of the effective piezoelectric coefficient e31 of this composite that accounts for the in-plane actuation and of effective elastic properties are found to be significantly higher than those of the existing 1–3 piezoelectric composites without reinforced with carbon nanotubes.

The Energy Absorption Characteristics of Square Mild Steel Tubes With Multiple Induced Circular Hole Discontinuities—Part I: Experiments

Abstract: This two-part article reports the results of experimental and numerical works conducted on the energy absorption characteristics of thin-walled square tubes with multiple circular hole discontinuities. Part I presents the experimental tests in which dynamic and quasistatic axial crushings are performed. The mild steel tubes are 350 mm in length, 50 mm wide, and 1.5 mm thick. Circular hole discontinuities, 17 mm in diameter, are laterally drilled on two or all four opposing walls of the tube to form opposing hole pairs. The total number of holes varies from 2 to 10. The results indicate that the introduction of holes decreases the initial peak force but an increase in the number of holes beyond 2 holes per side does not further significantly decrease the initial peak force. The findings show that strategic positioning of holes triggers progressive collapse hence improving energy absorption. The results also indicate that the presence of holes may at times disrupt the formation of lobes thus compromising the energy absorption capacity of the tube. In Part II, the finite element package ABAQUS /EXPLICIT version 6.4–6 is used to model the dynamic axial crushing of the tubes and to investigate the action of the holes during dynamic loading at an impact velocity of 8 m/s.

Preconditioning Techniques for Nonsymmetric Linear Systems in the Computation of Incompressible Flows

Abstract: In this paper we present effective preconditioning techniques for solving the nonsymmetric systems that arise from the discretization of the Navier-Stokes equations. These linear systems are solved using either Krylov subspace methods or the Richardson scheme. We demonstrate the effectiveness of our techniques in handling time-accurate as well as steady-state solutions. We also compare our solvers with those published previously.

Energy Dissipation in Normal Elastoplastic Impact Between Two Spheres

Abstract: Elastoplastic deformation occurs widely in engineering impact. Although many empirical solutions of elastoplastic impact between two spheres have been obtained, the analytical solution, verified by means of other methods, to the impact model has not been put forward. This paper proposes a dynamic pattern of elastoplastic impact for two spheres with low relative velocity, in which three stages are introduced and elastic and plastic regions are both considered. Finite element analyses with various parameters are carried out to validate the above model. The numerical results prove to agree with the theoretical predictions very well. Based on this model, the dissipation nature of elastoplastic impact are then analyzed, and the conclusion can be drawn that materials with lower yield strength, higher elastic modulus, and higher mass density have better attenuation and dissipation effects. The study provides a basis to predict the particle impact damping containing plastic deformation and to model the impact damped vibration system enrolling microparticles as a damping agent.

Flow of a Biomagnetic Visco-Elastic Fluid in a Channel With Stretching Walls

Abstract: The flow of a visco-elastic fluid in a channel with stretching walls under the action of an externally applied magnetic field generated by a magnetic dipole was studied in this paper. As per an experimental report, the variation in magnetization M of the fluid with temperature T was approximated as a linear equation of state M = K 1 T, where K 1 is a constant called the pyromagnetic coefficient. In this investigation the model used is that of Walter's liquid B fluid, which includes the effect of fluid visco-elasticity. By introducing appropriate nondimensional variables, the problem is reduced to solving a coupled nonlinear system of ordinary differential equations subject to a set of boundary conditions. The problem is solved by developing a suitable numerical technique based on finite difference approach. Computational results concerning the variation in the velocity, pressure and temperature fields, skin friction and the rate of heat transfer with magnetic field strength, Prandtl number, and blood visco-elasticity are presented graphically. The results presented reveal that the velocity of blood in the normal physiological state can be lowered by applying a magnetic field of sufficient intensity. The study bears the promise of important applications in controlling the flow of blood during surgery and also during treatment of cancer by therapeutic means when it involves magnetic drug targeting (hyperthemia).

Slip Effects on the Peristaltic Flow of a Third Grade Fluid in a Circular Cylindrical Tube

Abstract: Peristaltic flow of a third grade fluid in a circular cylindrical tube is undertaken when the no-slip condition at the tube wall is no longer valid. The governing nonlinear equation together with nonlinear boundary conditions is solved analytically by means of the perturbation method for small values of the non-Newtonian parameter, the Debroah number. A numerical solution is also obtained for which no restriction is imposed on the non-Newtonian parameter involved in the governing equation and the boundary conditions. A comparison of the series solution and the numerical solution is presented. Furthermore, the effects of slip and non-Newtonian parameters on the axial velocity and stream function are discussed in detail. The salient features of pumping and trapping are discussed with particular focus on the effects of slip and non-Newtonian parameters. It is observed that an increase in the slip parameter decreases the peristaltic pumping rate for a given pressure rise. On the contrary, the peristaltic pumping rate increases with an increase in the slip parameter for a given pressure drop (copumping). The size of the trapped bolus decreases and finally vanishes for large values of the slip parameter.

Light Activated Shape Memory Polymer Characterization

Abstract: Since their development, shape memory polymers (SMPs) have been of increasing interest in active materials and structures design. In particular, there has been a growing interest in SMPs for use in adaptive structures because of their ability to switch between low and high stiffness moduli in a relatively short temperature range. However, because a thermal stimulus is inappropriate for many morphing applications, a new light activated shape memory polymer (LASMP) is under development. Among the challenges associated with the development of a new class of material is establishing viable characterization methods. For the case of LASMP both the sample response to light stimulus and the stimulus itself vary in both space and time. Typical laser light is both periodic and Gaussian in nature. Furthermore, LASMP response to the light stimulus is dependent on the intensity of the incident light and the time varying through the thickness penetration of the light as the transition progresses. Therefore both in-plane and through-thickness stimulation of the LASMP are nonuniform and time dependent. Thus, the development of a standardized method that accommodates spatial and temporal variations associated with mechanical property transition under a light stimulus is required. First generation thick film formulations are found to have a transition time on the order of 60 min. The characterization method proposed addresses optical stimulus irregularities. A chemical kinetic model is also presented capable of predicting the through-thickness evolution of Young's modulus of the polymer. This work discusses in situ characterization strategies currently being implemented as well as the current and projected performance of LASMPs.

Scattering by a Cavity in an Exponentially Graded Half-Space

Abstract: An inhomogeneous half-space containing a cavity is bonded to a homogeneous half-space. Waves are incident on the interface and the problem is to calculate the scattered waves. For a circular cavity in an exponentially graded half-space, it is shown how to solve the problem by constructing an appropriate set of multipole functions. These functions are singular on the axis of the cavity, they satisfy the governing differential equation in each half-space, and they satisfy the continuity conditions across the interface between the two half-spaces. Seven recent publications are criticized: They do not take proper account of the interface between the two half-spaces.

Vibration and Snap-Through of Bent Elastica Strips Subjected to End Rotations

Abstract: A flexible strip is rotated at its ends until it forms a deep circular arc above its ends. Then the ends are kept immovable and are rotated downward until the arch suddenly snaps into an inverted configuration. The strip is analyzed as an inextensible elastica. Two-dimensional equilibrium shapes, vibration modes and frequencies, and critical rotations for snap-through are determined using a shooting method. Experiments are also conducted and results are compared with those from the analysis. The agreement is good. In addition, a microelectromechanical systems (MEMS) example is analyzed, in which an electrostatic force below a buckled strip causes the strip to snap downward, and the critical force is obtained as a function of the vertical gap.

Time-Derivative Preconditioning Methods for Multicomponent Flows—Part I: Riemann Problems

Abstract: A time-derivative preconditioned system of equations suitable for the numerical simulation of inviscid multicomponent and multiphase flows at all speeds is described. The system is shown to be hyperbolic in time and remains well conditioned in the incompressible limit, allowing time marching numerical methods to remain an efficient solution strategy. It is well known that the application of conservative numerical methods to multicomponent flows containing sharp fluid interfaces will generate nonphysical pressure and velocity oscillations across the component interface. These oscillations may lead to stability problems when the interface separates fluids with large density ratio, such as water and air. The effect of which may lead to the requirement of small physical time steps and slow subiteration convergence for implicit time marching numerical methods. At low speeds the use of nonconservative methods may be considered. In this paper a characteristic-based preconditioned nonconservative method is described. This method preserves pressure and velocity equilibrium across fluid interfaces, obtains density ratio independent stability and convergence, and remains well conditioned in the incompressible limit of the equations. To extend the method to transonic and supersonic flows containing shocks, a hybrid formulation is described, which combines a conservative preconditioned Roe method with the nonconservative preconditioned characteristic-based method. The hybrid method retains the pressure and velocity equilibrium at component interfaces and converges to the physically correct weak solution. To demonstrate the effectiveness of the nonconservative and hybrid approaches, a series of one-dimensional multicomponent Riemann problems is solved with each of the methods. The solutions are compared with the exact solution to the Riemann problem, and stability of the numerical methods are discussed.

Computational Modeling of Damage Development in Composite Laminates Subjected to Transverse Dynamic Loading

Abstract: This paper presents a robust computational model for the response of composite laminates to high intensity transverse dynamic loading emanating from local impact by a projectile and distributed pressure pulse due to a blast. Delaminations are modeled using a cohesive type tie-break interface introduced between sublaminates while intralaminar damage mechanisms within the sublaminates are captured in a smeared manner using a strain-softening plastic-damage model. In the latter case, a nonlocal regularization scheme is used to address the spurious mesh dependency and mesh-orientation problems that occur with all local strain-softening type constitutive models. The results for the predicted damage patterns using the nonlocal approach are encouraging and qualitatively agree with the experimental observations. The predictive performance of the proposed numerical model is assessed through comparisons with available instrumented impact test results on a class of carbon-fiber reinforced polymer (CFRP) composite laminates. Force-time histories and other derived cross-plots such as the force versus projectile displacement and progression of projectile energy loss as a function of time are compared with available experimental results to demonstrate the efficacy of the model in capturing the details of the dynamic response. Another case study involving the blast loading of CFRP composite laminates is used to further highlight the capability of the proposed model in simulating the global structural response of composite laminates subjected to distributed pressure pulses.

In- and Out-of-plane Vibrations of a Rotating Plate with Frictional Contact: Investigations on Squeal Phenomena

Abstract: Rotating plates are used as a main component in various applications. Their vibrations are mainly unwanted and interfere with the functioning of the complete system. The present paper investigates the coupling of disk (in-plane) and plate (out-of-plane) vibrations of a rotating annular Kirchhoff plate in the presence of a distributed frictional loading on its surface. The boundary value problem is derived from the basics of the theory of elasticity using Kirchhoff’s assumptions. This results in precise information about the coupling between the disk and the plate vibrations under the action of frictional forces. At the same time we obtain a new model, which is efficient for analytical treatment. Approximations to the stability boundaries of the system are calculated using a perturbation approach. In the last part of the paper nonlinearities are introduced leading to limit cycles due to self-excited vibrations.

Time-Derivative Preconditioning Methods for Multicomponent Flows-Part II: Two-Dimensional Applications

Abstract: A time-derivative preconditioned system of equations suitable for the numerical simulation of multicomponent/multiphase inviscid flows at all speeds was described in Part I of this paper. The system was shown to be hyperbolic in time and remain well conditioned in the incompressible limit, allowing time marching numerical methods to remain an efficient solution strategy. Application of conservative numerical methods to multicomponent flows containing sharp fluid interfaces was shown to generate nonphysical pressure and velocity oscillations across the contact surface, which separates the fluid components. It was demonstrated using the one-dimensional Riemann problem that these oscillations may lead to stability problems when the interface separates fluids with large density ratios, such as water and air. The effect of which leads to the requirement of small physical time steps and slow subiteration convergence for the implicit time marching numerical method. Alternatively, the nonconservative and hybrid formulations developed by the present authors were shown to eliminate this nonphysical behavior. While the nonconservative method did not converge to the correct weak solution for flow containing shocks, the hybrid method was able to capture the physically correct entropy solution and converge to the exact solution of the Riemann problem as the grid is refined. In Part II of this paper, the conservative, nonconservative, and hybrid formulations described in Part I are implemented within a two-dimensional structured body-fitted overset grid solver, and a study of two unsteady flow applications is reported. In the first application, a multiphase cavitating flow around a NACA0015 hydrofoil contained in a channel is solved, and sensitivity to the cavitation number and the spatial order of accuracy of the discretization are discussed. Next, the interaction of a shock moving in air with a cylindrical bubble of another fluid is analyzed. In the first case, the cylindrical bubble is filled with helium gas, and both the conservative and hybrid approaches perform similarly. In the second case, the bubble is filled with water and the conservative method fails to maintain numerical stability. The performance of the hybrid method is shown to be unchanged when the gas is replaced with a liquid, demonstrating the robustness and accuracy of the hybrid approach.

Local Damage Evolution of Double Cantilever Beam Specimens During Crack Initiation Process: A Natural Boundary Condition Based Method

Abstract: Cohesive zone models are being increasingly used to simulate fracture and debonding processes in metallic, polymeric, and ceramic materials and their composites. The crack initiation process as well as its actual stress and damage distribution beyond crack tip are important for understanding fracture of materials and debonding of adhesively bonded joints. In the current model, a natural boundary condition based method is proposed, and thus the concept of extended crack length (characteristic length l) is no longer required and more realistic and natural local deformation beyond crack tip can be obtained. The new analytical approach, which can consider both crack initiation and propagation as well as local deformation and interfacial stress distribution, can be explicitly obtained as a function of the remote peel load P with the given bilinear cohesive laws. An intrinsic geometric constraint condition is then used to solve the remote peel load P. The nonlinear response in both the ascending and descending stages of loading is accurately predicted by the current model, as evidenced by a comparison with both experimental results and finite element analysis results. It is found that the local deformation and interfacial stress beyond crack tip are relatively stable during crack propagation. It is also found that, when the cohesive strength is low, it has a significant effect on the critical peel load and loadline deflection. In principle, the approach developed in the current study can be extended to multilinear cohesive laws, although only bilinear cohesive law is presented in this work as an example.

The Energy Absorption Characteristics of Square Mild Steel Tubes With Multiple Induced Circular Hole Discontinuities—Part II: Numerical Simulations

Abstract: This paper is Part II of a two-part article and presents the results of numerical simulations conducted to investigate the energy absorption characteristics of square tubes subjected to dynamic axial loading. Part I reports the experimental results of both quasistatic and dynamic tests. The validated model is used to study the crushing characteristics of tubes with multiple induced circular hole discontinuities using the finite element package ABAQUS/EXPLICIT version 6.4-6. Holes of diameter 17 mm are used as crush initiators, which are laterally drilled into the tube wall to form opposing hole pairs. Holes of diameters 12.5 mm and 25 mm are also used to assess the effects of hole diameter on energy absorption. Two hole spacing configurations are investigated, one in which the hole pairs are placed at regular intervals of 50 mm along the tube wall and another in which the hole pairs are spaced symmetrically along the tube length. Holes are also drilled on either two or all four opposing tube walls. The number of holes is varied from 2 to 10. The results indicate that the introduction of the holes decreases the initial peak force. However, an increase in the number of holes, beyond two holes, does not further significantly decrease the initial peak force. A study of the crushing history of the tubes reveals that crushing is initiated at the location of the holes. The results also indicate that the type of hole spacing determines how crushing is initiated at the hole locations. The model satisfactorily predicts the resultant collapse shapes but overpredicts the crushed distance.

Finite Element Analysis of Plugging Failure in Steel Plates Struck by Blunt Projectiles

Abstract: In this paper, the influence of mesh sensitivity on the fracture predictions during penetration and perforation of hardened blunt-nose cylindrical steel projectiles in plates of Weldox 460E, Weldox 700E, and Weldox 900E steel has been studied The main objective is to try to describe the experimentally obtained trend of a decrease in ballistic limit velocity with increased target strength when the plates are impacted by blunt projectiles This behavior is due to the occurrence of highly localized shear bands as the target strength increases The impact tests are analyzed using the explicit solver of a nonlinear finite element code A thermoelastic-thermoviscoplastic constitutive model with coupled or uncoupled ductile damage was used in the simulations It was found that the residual velocity continuously increases when the element size is decreased from 125 μm to 15 μm in the shear zone, and that this increase is significantly stronger for impact velocities close to the ballistic limit The ballistic limit decreases by up to 25% when the size of the element is decreased from 125 μm to 30 μm; the decrease being somewhat greater for the two steels with the highest strength Even with the finest mesh, the experimental trend of a decreasing ballistic limit with increasing target strength was not predicted in the simulations, neither with coupled nor uncoupled damage Nonlocal simulations based on smoothing of the damage and temperature fields, which are the two variables causing the softening, were carried out for the Weldox steels and a mesh size of 30 μm These simulations indicate a reduction in the mesh sensitivity for both the coupled and uncoupled damage approaches when nonlocal averaging is employed

Pointwise Identification of Elastic Properties in Nonlinear Hyperelastic Membranes—Part II: Experimental Validation

Abstract: Following the theoretical and computational developments of the pointwise membrane identification method reported in the first part of this paper, we perform a finite inflation test on a rubber balloon to validate the method. The balloon is inflated using a series of pressurized configurations, and a surface mesh that corresponds through all the deformed states is derived using a camera-based three dimensional reconstruction technique. In each configuration, the wall tension is computed by the finite element inverse elastostatic method, and the in-plane stretch relative to a slightly pressurized configuration is computed with the aid of finite element interpolation. Based on the stress-strain characteristics, the Ogden model is employed to describe the material behavior. The elastic parameters at every Gauss point in a selected region are identified simultaneously. To verify the predictive capability of the identified material model, the deformation under a prescribed pressure is predicted using the finite element method and is compared with the physical measurement. The experiment shows that the method can effectively delineate the distributive elastic properties in the balloon wall.

Energy and Momentum Transfer in Air Shocks

Abstract: A series of one-dimensional studies is presented to reveal basic aspects of momentum and energy transfer to plates in air blasts. Intense air waves are initiated as either an isolated propagating wave or by the sudden release of a highly compressed air layer. Wave momentum is determined in terms of the energy characterizing the compressed layer. The interaction of intense waves with freestanding plates is computed with emphasis on the momentum and/or energy transferred to the plate. A simple conjecture, backed by numerical simulations, is put forward related to the momentum transmitted to massive plates. The role of the standoff distance between the compressed air layer and the plate is elucidated. Throughout, dimensionless parameters are selected to highlight the most important groups of parameters and to reduce parametric dependencies to the extent possible.

Three-Dimensional Elasticity Solution for Sandwich Plates With Orthotropic Phases : The Positive Discriminant Case

Abstract: A three-dimensional elasticity solution for rectangular sandwich plates exists only under restrictive assumptions on the orthotropic material constants of the constitutive phases (i.e., face sheets and core). In particular, only for negative or zero discriminant of the cubic characteristic equation, which is formed from these constants (case of three real roots). The purpose of the present paper is to present the corresponding solution for the more challenging case of positive discriminant, in which two of the roots are complex conjugates.

Pointwise Identification of Elastic Properties in Nonlinear Hyperelastic Membranes―Part I: Theoretical and Computational Developments

Abstract: We present an innovative method for characterizing the distributive elastic properties in nonlinear membranes. The method hinges on an inverse elastostatic approach of stress analysis that can compute the wall stress in a deformed convex membrane structure using assumed elastic models without knowing the realistic material parameters. This approach of stress analysis enables us to obtain the wall stress data independently of the material in question. The stress and strain data collected during a finite inflation motion are used to delineate the elastic property distribution in selected regions. In this paper, we discuss the theoretical and computational underpinnings of the method and demonstrate its feasibility using numerical simulations involving a saclike structure of known material property.