Showing papers in "International Journal of Solids and Structures in 2007"
TL;DR: In this article, an experimental investigation of the rupture mechanisms in a mid-strength and a high-strength steel was conducted employing a novel test configuration using a double notched tube.
Abstract: An experimental investigation of the rupture mechanisms in a mid-strength and a high-strength steel were conducted employing a novel test configuration. The specimen used was a double notched tube ...
504 citations
TL;DR: In this article, a damage plasticity model for ductile fracture is proposed, which is established on the cylindrical coordinate system of principal stress space, and four simulations with emphasis on crack path prediction are presented.
Abstract: A damage plasticity model for ductile fracture is proposed. This model is established on the cylindrical coordinate system of principal stress space. Experimental results show that fracture initiation in uncracked ductile solids is sensitive to the hydrostatic pressure and dependent on the Lode angle. The joint effects of pressure and Lode angle define a fracture envelope in principal stress space. Plastic deformation induced damage is calculated by an integral of the damage rate measured at current loading and deformation status with respect to the fracture envelope. A power law damage rule is proposed to characterize the nonlinearity in damage accumulation. A damage-related weakening factor is adopted to describe the material deterioration. The material parameters are calibrated from standard laboratory tests. The proposed model is numerically implemented. Four simulations with emphasis on crack path prediction are presented.
434 citations
TL;DR: In this paper, the consistent equations of motion for the nonlocal Euler and Timoshenko beam models are provided, and some issues on the non-local beam theories are discussed.
Abstract: Investigations of wave and vibration properties of single- or multi-walled carbon nanotubes based on nonlocal beam models have been reported recently. However, there are numerous inconsistencies in the handling of the governing equations, applied forces, and boundary conditions based on some of the reported nonlocal beam models. In this paper, the consistent equations of motion for the nonlocal Euler and Timoshenko beam models are provided, and some issues on the nonlocal beam theories are discussed. The models are then applied to the studies of wave properties of single- and double-walled nanotubes. The wave and vibration properties of the nanotubes based on the presented nonlocal beam equations are studied, and scale effects are discussed.
354 citations
TL;DR: It is shown that the three-dimensional Mohr–Coulomb criterion can be cast as a set of conic constraints, thus facilitating efficient treatment by dedicated algorithms in conic programming.
Abstract: The application of conic programming to some traditionally difficult plasticity problems is considered. Convenient standard forms for conic programming of both limit and incremental elastoplastic analysis are given. The types of yield criteria that can be treated by conic programming is discussed and it is shown that the three-dimensional Mohr–Coulomb criterion can be cast as a set of conic constraints, thus facilitating efficient treatment by dedicated algorithms. Finally, the performance of a number of mixed finite elements is evaluated together with a state-of-the-art second-order cone programming algorithm.
281 citations
TL;DR: In this article, a micromechanics model based on the theoretical framework of plastic localization into a band introduced by Rice is developed, which consists of a planar band with a square array of equally sized cells, with a spherical void located in the centre of each cell.
Abstract: A micromechanics model based on the theoretical framework of plastic localization into a band introduced by Rice is developed. The model consists of a planar band with a square array of equally sized cells, with a spherical void located in the centre of each cell. The periodic arrangement of the cells allows the study of a single unit cell for which fully periodic boundary conditions are applied. The micromechanics model is applied to analyze failure by ductile rupture in experiments on double notched tube specimens subjected to combined tension and torsion carried out by the present authors. The stress state is characterized in terms of the stress triaxiality and the Lode parameter. Two rupture mechanisms can be identified, void coalescence by internal necking at high triaxiality and void coalescence by internal shearing at low triaxiality. For the internal necking mechanism, failure is assumed to occur when the deformation localizes into a planar band and is closely associated with extensive void growth until impingement of voids. For the internal shearing mechanism, a simple criterion based on the attainment of a critical value of shear deformation is utilized. The two failure criteria capture the transition between the two rupture mechanisms successfully and are in good agreement with the experimental result.
256 citations
TL;DR: In this paper, a confinement-sensitive plasticity constitutive model for concrete in triaxial compression is presented, aiming to describe the strength and deformational behaviour of both normal and high-strength concrete under multiaxial compression.
Abstract: In this paper, a confinement-sensitive plasticity constitutive model for concrete in triaxial compression is presented, aiming to describe the strength and deformational behaviour of both normal and high-strength concrete under multiaxial compression. It incorporates a three-parameter loading surface, uncoupled hardening and softening functions following the accumulation of plastic volumetric strain and a nonlinear Lode-angle dependent plastic potential function. The various model parameters are calibrated mainly on the basis of a large experimental database and are expressed in terms of only the uniaxial compressive concrete strength, leading to a single-parameter model, suitable for practical applications. The model’s performance is evaluated against experimental results and it is found that both the increased strength and deformation capacity of confined concrete are properly captured.
223 citations
TL;DR: In this article, a robust physically consistent three-dimensional constitutive model is developed to describe the finite mechanical response of amorphous polymers over a wide range of temperatures and strain rates, including the rubbery region and for impact loading rates.
Abstract: A robust physically consistent three-dimensional constitutive model is developed to describe the finite mechanical response of amorphous polymers over a wide range of temperatures and strain rates, including the rubbery region and for impact loading rates. This thermomechanical model is based on an elastic–viscoplastic rheological approach, wherein the effects of temperature, strain rate, and hydrostatic pressure are accounted for. Intramolecular, as well as intermolecular, interactions under large elastic–inelastic behavior are considered for the mechanisms of deformation and hardening. For a wide range of temperatures and strain rates, our simulated results for poly(methyl methacrylate) (PMMA) and polycarbonate (PC) are in good agreement with experimental observations.
212 citations
TL;DR: In this paper, a detailed variational formulation is provided for a simplified strain gradient elasticity theory by using the principle of minimum total potential energy, which leads to the simultaneous determination of the equilibrium equations and the complete boundary conditions of the theory for the first time.
Abstract: A detailed variational formulation is provided for a simplified strain gradient elasticity theory by using the principle of minimum total potential energy. This leads to the simultaneous determination of the equilibrium equations and the complete boundary conditions of the theory for the first time. To supplement the stress-based formulation, the coordinate-invariant displacement form of the simplified strain gradient elasticity theory is also derived anew. In view of the lack of a consistent and complete formulation, derivation details are included for the tutorial purpose. It is shown that both the stress and displacement forms of the simplified strain gradient elasticity theory obtained reduce to their counterparts in classical elasticity when the strain gradient effect (a measure of the underlying material microstructure) is not considered. As a direct application of the newly obtained displacement form of the theory, the problem of a pressurized thick-walled cylinder is analytically solved. The solution contains a material length scale parameter and can account for microstructural effects, which is qualitatively different from Lame’s solution in classical elasticity. In the absence of the strain gradient effect, this strain gradient elasticity solution reduces to Lame’s solution. The numerical results reveal that microstructural effects can be large and Lame’s solution may not be accurate for materials exhibiting significant microstructure dependence.
210 citations
TL;DR: In this article, an experimental method to determine the complete stress versus deformation relation for a thin adhesive layer loaded in shear is presented, based on a classical specimen geometry, i.e.
Abstract: An experimental method to determine the complete stress versus deformation relation for a thin adhesive layer loaded in shear is presented. The work is based on a classical specimen geometry, i.e. ...
207 citations
TL;DR: In this article, a mixed numerical-experimental method for the identification of the four in-plane orthotropic engineering constants of composite plate materials was presented, where two specimen geometries were used: one with a centered hole to increase the strain heterogeneity and one without a hole.
Abstract: This paper presents a mixed numerical–experimental method for the identification of the four in-plane orthotropic engineering constants of composite plate materials. A biaxial tensile test is performed on a cruciform test specimen. The heterogeneous displacement field is observed by a CCD camera and measured by a digital image correlation (DIC) technique. The measured displacement field and the subsequently computed strain field are compared with a finite element simulation of the same experiment. The four independent engineering constants are unknown parameters in the finite element model. Starting from an initial value, these parameters are updated till the computed strain field matches the experimental strain field. Two specimen geometries are used: one with a centered hole to increase the strain heterogeneity and one without a hole. It is found that the non-perforated specimen yields the most accurate results.
204 citations
TL;DR: In this paper, the authors investigated the ballistic perforation resistance of double-layered steel plates impacted by blunt and ogival projectiles both experimentally and numerically, and the main conclusion from both the experimental and numerical studies is that the overall protection level, i.e., the minimum ballistic limit velocity obtained independently of projectile nose shape, seems to increase significantly by double-layer the target.
Abstract: Civil and military ballistic protection systems often consist of thin, high-strength steel plates. Such plates may either be monolithic or layered with or without spacing. The idea of using layered plates instead of a monolithic one in order to increase the ballistic perforation resistance is not new, and the effect of using targets made up of several thinner plates has been investigated in the literature for a long time. However, results by various authors are contradicting and detailed experimental and numerical work is still required. In the present study, the ballistic perforation resistance of double-layered steel plates impacted by blunt and ogival projectiles was investigated both experimentally and numerically. In the tests, 12 mm thick (monolithic or layered) targets of Weldox 700 E were impacted using a gas-gun at sub-ordnance velocity, and the ballistic limit velocity of the different target combinations was obtained. In general, good agreement was obtained between the numerical simulations and the experimental results. It was found that in the case of blunt projectiles a large gain in the ballistic limit is offered by double-layered systems. These advantages seem to disappear when ogival projectiles are used. However, the main conclusion from both the experimental and numerical studies is that the overall protection level, i.e. the minimum ballistic limit velocity obtained independently of projectile nose shape, seems to increase significantly by double-layering the target.
TL;DR: In this article, a tensor-based finite element formulation with curvilinear coordinates and first-order shear deformation theory is used to develop the functionally graded shell finite element.
Abstract: A geometrically nonlinear analysis of functionally graded shells is presented. The two-constituent functionally graded shell consists of ceramic and metal that are graded through the thickness, from one surface of the shell to the other. A tensor-based finite element formulation with curvilinear coordinates and first-order shear deformation theory are used to develop the functionally graded shell finite element. The first-order shell theory consists of seven parameters and exact nonlinear deformations and under the framework of the Lagrangian description. High-order Lagrangian interpolation functions are used to approximate the field variables to avoid membrane, shear, and thickness locking. Numerical results obtained using the present shell element for typical benchmark problem geometries with functionally graded material compositions are presented.
TL;DR: In this article, a variational asymptotic method for unit cell homogenization (VAMUCH) is developed to predict the effective properties of periodically heterogeneous materials and recover the local fields.
Abstract: A new micromechanics model, namely, the variational asymptotic method for unit cell homogenization (VAMUCH), is developed to predict the effective properties of periodically heterogeneous materials and recover the local fields. Considering the periodicity as a small parameter, we can formulate a variational statement of the unit cell through an asymptotic expansion of the energy functional. It is shown that the governing differential equations and periodic boundary conditions of mathematical homogenization theories (MHT) can be reproduced from this variational statement. In comparison to other approaches, VAMUCH does not rely on ad hoc assumptions, has the same rigor as MHT, has a straightforward numerical implementation, and can calculate the complete set of properties simultaneously without using multiple loadings. This theory is implemented using the finite element method and an engineering program, VAMUCH, is developed for micromechanical analysis of unit cells. Many examples of binary composites, fiber reinforced composites, and particle reinforced composites are used to demonstrate the application, power, and accuracy of the theory and the code of VAMUCH.
TL;DR: In this article, the effect of interfaces on the overall properties of a composite with thin interface layers between inclusions and the matrix has been investigated, and explicit expressions constructed in the present work show that the overall elastic/conductive properties are affected mostly by the interface thickness (normalized to the size of the core particle) and are much less sensitive to the extent of the variation.
Abstract: For a composite with thin interface layers between inclusions and the matrix, the effective elastic properties and the effective conductivity (thermal or electric) are almost unaffected by the layers, provided (1) the layer thickness is much smaller than the inclusion sizes and (2) the contrast between the properties of the layers and either of the phases is not overly high. For composites with nanoparticles, the interface thickness may be comparable to the particle sizes. Therefore, the effect of interfaces on the overall properties may be substantial. The controlling parameters are (1) the ratio of the interface thickness to particle sizes and (2) variability of the properties across the interface thickness. Explicit expressions constructed in the present work show that the overall elastic/conductive properties are affected, mostly, by the interface thickness (normalized to the size of the core particle) and are much less sensitive to the extent of the variation and its exact character. Similarities and differences between the elasticity and the conductivity problems are discussed.
TL;DR: In this paper, different electromagnetic boundary conditions on the crack-faces in magnetoelectroelastic materials, which possess coupled piezoelectric, piezomagnetic and magnetelectric effects, are discussed.
Abstract: This paper discusses the different electromagnetic boundary conditions on the crack-faces in magnetoelectroelastic materials, which possess coupled piezoelectric, piezomagnetic and magnetoelectric effects. A notch of finite thickness in these materials containing air (or vacuum) is also addressed. Four ideal crack-face electromagnetic boundary condition assumptions, that is, (a) electrically and magnetically impermeable crack, (b) electrically impermeable and magnetically permeable crack, (c) electrically permeable and magnetically impermeable crack and (d) electrically and magnetically permeable crack, are investigated separately. The influence of notch thickness on the field intensity factors at notch tips and the electromagnetic field inside the notch are obtained in closed-form. The results are compared with the ideal crack solutions. Applicability of crack-face electromagnetic boundary condition assumptions is discussed.
TL;DR: In this paper, an analytical treatment is presented for the propagation of harmonic waves in magneto-electro-elastic multilayered plates, where the general anisotropic and three-phase coupled constitutive equations are used.
Abstract: An analytical treatment is presented for the propagation of harmonic waves in magneto-electro-elastic multilayered plates, where the general anisotropic and three-phase coupled constitutive equations are used. The state-vector approach is employed to derive the propagator matrix which connects the field variables at the upper interface to those at the lower interface of each layer. The global propagator matrix is obtained by propagating the solution in each layer from the bottom of the layered plate to the top using the continuity conditions of the field variables across the interfaces. From the global propagator matrix, we finally obtain the dispersion relation by imposing the traction-free boundary condition on the top and bottom surfaces of the layered plate. Dispersion curves, modal shapes, and natural frequencies are presented for layered plates made of orthotropic elastic (graphite–epoxy), transversely isotropic PZT-5A, piezoelectric BaTiO3 and magnetostrictive CoFe2O4 materials. While the numerical results show clearly the influence of different stacking sequences as well as material properties on the field response, the general methodology presented in the paper could be useful to the analysis and design of layered composites made of smart piezoelectric and piezomagnetic materials.
TL;DR: In this article, the Gurtin-Murdoch surface/interface elasticity model is applied to take into account the surface and interface stress effects by using the complex variable technique of Muskhelishvili.
Abstract: In traditional continuum mechanics, the effect of surface energy is ignored as it is small compared to the bulk energy For nanoscale materials and structures, however, the surface effects become significant due to the high surface/volume ratio In this paper, two-dimensional elastic field of a nanoscale elliptical inhomogeneity embedded in an infinite matrix under arbitrary remote loading and a uniform eigenstrain in the inhomogeneity is investigated The Gurtin–Murdoch surface/interface elasticity model is applied to take into account the surface/interface stress effects By using the complex variable technique of Muskhelishvili, the analytic potential functions are obtained in the form of an infinite series Selected numerical results are presented to study the size-dependency of the elastic field and the effects of surface elastic moduli and residual surface stress It is found that the elastic field of an elliptic inhomogeneity under uniform eigenstrain is no longer uniform when the interfacial stress effects are taken into account
TL;DR: In this paper, the authors used the finite element method to simulate the co-evolution of debonding along the interface and necking in a thin metal laminate, and they showed that necking of the film is accommodated mainly by interfacial sliding, rather than interfacial opening.
Abstract: When a laminate of a thin metal film on a tough polymer substrate is stretched, the metal film may rupture at strains ranging from a few percent to a few tens of percent. This variation in the ductility of the metal film is modulated by the adhesion of the metal/polymer interface. To study this modulation, here we use the finite element method to simulate the co-evolution of two processes: debonding along the interface and necking in the metal film. We model the interface as an array of nonlinear springs, and model the metal and the polymer as elastic–plastic solids. The simulation shows that necking of the film is accommodated mainly by interfacial sliding, rather than interfacial opening. Depending on the resistance of the interface to sliding, the metal film can exhibit three types of tensile behavior: the film slides and ruptures at a small strain by forming a single neck, the film slides and deforms to a large strain by forming multiple necks, and the film deforms uniformly to a very large strain without sliding and necking. 2006 Elsevier Ltd. All rights reserved.
TL;DR: In this article, a distributed parameter model is used to study the pull-in instability of cantilever type nanomechanical switches subjected to intermolecular and electrostatic forces.
Abstract: In this paper, a distributed parameter model is used to study the pull-in instability of cantilever type nanomechanical switches subjected to intermolecular and electrostatic forces. In modeling of the electrostatic force, the fringing field effect is taken into account. The model is nonlinear due to the inherent nonlinearity of the intermolecular and electrostatic forces. The nonlinear differential equation of the model is transformed into the integral form by using the Green’s function of the cantilever beam. Closed-form solutions are obtained by assuming an appropriate shape function for the beam deflection to evaluate the integrals. The pull-in parameters of the switch are computed under the combined effects of electrostatic and intermolecular forces. Electrostatic microactuators and freestanding nanoactuators are considered as special cases of our study. The detachment length and the minimum initial gap of freestanding nano-cantilevers, which are the basic design parameters for NEMS switches, are determined. The results of the distributed parameter model are compared with the lumped parameter model.
TL;DR: In this paper, a user-developed continuum damage model implemented in the finite element code ABAQUS® is employed in the simulation of damage initiation and material stiffness degradation, in order to correctly predict the buckling loads of tow-steered panels under compression.
Abstract: The past developments on tow-placement technology led to the production of machines capable of controlling fibre tows individually and placing them onto the surface of a laminate with curvilinear topology. Due to the variation of properties along their surface, such structures are termed variable-stiffness composite panels.
In previous experimental research tow-steered panels have shown increased buckling load capacity as compared with traditional straight-fibre laminates. Also, numerical analyses by the authors showed that first-ply failure occurs at a significant higher load level. The focus of this paper is to extend those analyses into the postbuckling progressive damage behaviour and final structural failure due to accumulation of fibre and matrix damage. A user-developed continuum damage model implemented in the finite element code ABAQUS® is employed in the simulation of damage initiation and material stiffness degradation.
In order to correctly predict the buckling loads of tow-steered panels under compression, it is of crucial importance to take into account the residual thermal stresses resulting from the curing process. Final failure of tow-steered panels in postbuckling is predicted to within 10% difference of the experimental results. Curvilinear-fibre panels have up to 56% higher strength than straight-fibre laminates and damage initiation is also remarkably postponed. Tow-steered designs also show more tolerance to central holes than traditional laminates.
TL;DR: In this paper, an improved simple third-order shear deformation theory for the analysis of shear flexible plates is presented, which is composed of three parts: the simple thirdorder kinematics of displacements reduced from the higher-order displacement field derived previously by the author; a system of 10th-order differential equilibrium equations in terms of the three generalized displacements of bending plates; five boundary conditions at each edge of plate boundaries.
Abstract: An improved simple third-order shear deformation theory for the analysis of shear flexible plates is presented in this paper. This new plate theory is composed of three parts: the simple third-order kinematics of displacements reduced from the higher-order displacement field derived previously by the author; a system of 10th-order differential equilibrium equations in terms of the three generalized displacements of bending plates; five boundary conditions at each edge of plate boundaries. Although the resulting displacement field is the same as that proposed by Murthy, the variational consistent governing equations and the associated proper boundary conditions are derived and identified in this work for the first time in the literature. The applications and accuracy of the present shear deformation theory of plates are demonstrated by analytically solving the differential governing equations of a twisting plate, a bending beam and two bending plates to which the 3-D elasticity solutions are available, and excellent agreements are achieved even for the torsion of a plate with square cross-section as well the local effects of stresses at plate boundaries can be characterized accurately. These analytical solutions clearly show that the simple third-order shear deformation theory developed in this work indeed gives better results than the first-order shear deformation theories and other simple higher-order shear deformation theories, since the present third-order shear flexible theory is based on a more rigorous kinematics of displacements and consists of not only a system of variational consistent differential equations, but also a group of consistent boundary conditions associated with the differential equations. The present simple third-order shear deformation theory can easily be applied to the static and dynamic finite element analysis of laminated plates just like the applications of other popular shear flexible plate theories, and improved results could be obtained from the present simple third-order shear deformable theories of plates.
TL;DR: In this paper, several approaches available in the literature for identifying the constitutive parameters of linear elastic materials from full-field measurements are presented and their sensitivity to a white noise added to the data is compared.
Abstract: In this paper, several approaches available in the literature for identifying the constitutive parameters of linear elastic materials from full-field measurements are presented and their sensitivity to a white noise added to the data is compared. The first investigated approach is the virtual fields method (VFM). It is shown that the uncertainty of the parameters identified with the VFM when a white noise is added to the data depends on the choice of a relevant set of virtual fields. Optimal virtual fields exist, thus minimizing the uncertainty and providing the “maximum likelihood solution”. The other approaches investigated in this paper are based on finite element model updating (FEMU). It is proved that FEMU approaches actually yield equations similar to the ones derived from the VFM, but with nonoptimal sets of virtual fields. Therefore, the FEMU approaches do not provide the “maximum likelihood solution”. However, the uncertainty of FEMU approaches varies dramatically with the cost function to minimize. On one hand, the FEMU approach based on the “displacement gap” minimization yields equations which are very close to the ones of the VFM approach and therefore, its uncertainty is almost the same as the VFM one. On the other hand, it is shown that other approaches based on the “constitutive equation gap” minimization or the “equilibrium gap” minimization provide biased solutions. For all the approaches, very fast algorithms, converging in only two iterations, have been devised. They are finally applied to real experimental data obtained on an orthotropic composite material. Results confirm the success of two methods: the VFM approach which provides the “maximum likelihood solution” and the FEMU approach based on the “displacement gap” minimization.
TL;DR: In this article, the elastic and inelastic properties of balsa wood have been characterized using scanning electron microscopy, and the microstructure and its deformation modes under compression were characterized using the Argon-Budiansky kinking model.
Abstract: Balsa wood is a natural cellular material with excellent stiffness-to-weight and strength-to-weight ratios as well as superior energy absorption characteristics. These properties are derived from the microstructure, which consists of long slender cells (tracheids) with approximately hexagonal crosssections that are arranged axially. Parenchyma are a second type of cells that are radially arranged in groups that periodically penetrate the tracheids (rays). Under compression in the axial direction the material exhibits a linearly elastic regime that terminates by the initiation of failure in the form of localized kinking. Subsequently, under displacement-controlled compression, a stress plateau is traced associated with the gradual spreading of crushing of the cells through the material. The material is less stiff and weaker in the tangential and radial directions. Compression in these directions crushes the tracheids laterally but results in a monotonically increasing response typical of lateral crushing of elastic honeycombs. The elastic and inelastic properties in the three directions have been established experimentally as a function of the wood density. The microstructure and its deformation modes under compression have been characterized using scanning electron microscopy. In the axial direction it was observed that in the majority of the tests, failure initiated by kinking in the axial–tangential plane. The local misalignment of tracheids in zones penetrated by rays ranged from 4° to 10° and axial compression results in shear in these zones. Measurement of the shear response and the shear strength in the planes of interest enabled estimation of the kinking stress using the Argon–Budiansky kinking model. The material strength predicted in this manner has been found to provide a bounding estimate of the axial strength for a broad range of wood densities. The energy absorption characteristics of the wood have also been measured and the specific energy absorption was found to be comparable to that of metallic honeycombs of the same relative density.
TL;DR: In this paper, the effect of projectile nose shape, impact velocity and plate thickness on the deformation of the target plates was studied and a finite element analysis of the problem was carried out using ABAQUS finite element code.
Abstract: The present study deals with the experimental and numerical investigations of aluminum target plates impacted by blunt, ogive and hemispherical nosed steel projectiles. The projectiles were normally impacted on the target plates of 0.5, 0.71, 1, 1.5, 2, 2.5 and 3 mm thicknesses at different velocities with the help of a pneumatic gun. Effect of projectile nose shape, impact velocity and plate thickness on the deformation of the target plates was studied. Hemispherical nosed projectile caused highest global deformation (dishing) of the target plates. Ogive nosed projectiles were found to be the most efficient penetrator for the case of plates of thicknesses 0.5, 0.71, 1.0 and 1.5 mm. For the case of plates of thicknesses 2.0, 2.5 and 3.0 mm however, blunt nosed projectiles required least energy to perforate the target plates. The ballistic limit velocity of hemispherical nosed projectiles was found to be highest as compared to the other two projectiles. Finite element analysis of the problem was carried out using ABAQUS finite element code. Results of the numerical analysis were compared with the experiments and good correlation between the two was found.
TL;DR: In this paper, the influence of heat conduction in both structural and material designs in two dimensions is studied, where the former attempts to find the optimal structures with the maximum stiffness and minimum resistance to heat dissipation and the latter tries to tailor composite materials with effective thermal conductivity and bulk modulus attaining their upper limits like Hashin-Shtrikman and Lurie-Cherkaev bounds.
Abstract: This paper studies the influence of heat conduction in both structural and material designs in two dimensions. The former attempts to find the optimal structures with the maximum stiffness and minimum resistance to heat dissipation and the latter to tailor composite materials with effective thermal conductivity and bulk modulus attaining their upper limits like Hashin–Shtrikman and Lurie–Cherkaev bounds. In the part of structural topology optimization of this paper solid material and void are considered respectively. While in the part of material design, two-phase ill-ordered base materials (i.e. one has a higher Young’s modulus, but lower thermal conductivity while another has a lower Young’s modulus but higher conductivity) are assumed in order to observe competition in the phase distribution defined by stiffness and conduction. The effective properties are derived from the homogenization method with periodic boundary conditions within a representative element (base cell). All the issues are transformed to the minimization problems subject to volume and symmetry constraints mathematically and solved by the method of moving asymptote (MMA), which is guided by the sensitivities with respect to the design variables. To regularize the problem the SIMP model is explored with the nonlinear diffusion techniques to create edge-preserving and checkerboard-free results. The illustrative examples show how to generate Pareto fronts by means of linear weighting functions, which provide an in-depth understanding how these objectives compete in the topologies.
TL;DR: In this paper, the basic governing equations for isotropic and homogeneous generalized thermoelastic half-space under hydrostatic initial stress are formulated in the context of the Green and Naghdi theory of types II and III.
Abstract: In this paper, the basic governing equations for isotropic and homogeneous generalized thermoelastic half-space under hydrostatic initial stress are formulated in the context of the Green and Naghdi theory of types II and III These governing equations are solved analytically to obtain the dimensional velocities in an xy-plane It is shown that there exist three plane waves, namely a thermal wave, a P-wave and an SV-wave The reflection from an insulated and isothermal stress-free surface is studied to obtain the reflection amplitude ratios of the reflected waves for the incidence of P- and SV-waves Numerical computations are carried out and comparisons made with the results predicted in the presence and absence of hydrostatic initial stress Also the effect of the thermoelastic coupling parameter and the thermal condition on amplitude ratios are shown graphically
TL;DR: In this paper, the authors present a complete theory for metal plasticity that includes directional distortional hardening, supplemented by the classical kinematic and isotropic hardenings.
Abstract: This paper presents a complete theory for metal plasticity that includes directional distortional hardening, supplemented by the classical kinematic and isotropic hardenings. Starting from an isotropic yield surface, the distortional hardening will be modeled either by fourth-order tensor-valued internal variable multiplied by a scalar, a scalar-valued internal variable in conjunction with the back stress, or a second-order tensor-valued internal variable. These models are unique because the rate equations for all internal variables, including the fourth order tensor, are derived strictly on the basis of sufficient conditions for the satisfaction of the second law of thermodynamics for positive dissipation, in conjunction with a few simple and plausible assumptions about free energy storage and release in the material. The models are shown to fit experimentally found yield surfaces rather well, in particular the model with the fourth-order tensor. Furthermore, this model is shown to simulate stress controlled biaxial ratchetting better than the same model without distortion of the yield surface.
TL;DR: In this paper, a second gradient Biot model for porous materials is proposed to describe the local dilatant behavior of a porous material induced by pore opening elastic and capillary interaction phenomena among neighbouring pores and related micro-filtration phenomena by means of a continuum microstructured model.
Abstract: Second gradient theories have been developed in mechanics for treating different phenomena as capillarity in fluids, plasticity and friction in granular materials or shear band deformations. Here, there is an attempt of formulating a second gradient Biot like model for porous materials. In particular the interest is focused in describing the local dilatant behaviour of a porous material induced by pore opening elastic and capillary interaction phenomena among neighbouring pores and related micro-filtration phenomena by means of a continuum microstructured model. The main idea is to extend the classical macroscopic Biot model by including in the description second gradient effects. This is done by assuming that the surface contribution to the external work rate functional depends on the normal derivative of the velocity or equivalently assuming that the strain work rate functional depends on the porosity and strain gradients. According to classical thermodynamics suitable restrictions for stresses and second gradient internal actions (hyperstresses) are recovered, so as to determine a suitable extended form of the constitutive relation and Darcy's law. Finally a numerical application of the envisaged model to one-dimensional consolidation is developed; the obtained results generalize those by Terzaghi; in particular interesting phenomena occurring close to the consolidation external surface and the impermeable wall can be described, which were not accounted for previously.
TL;DR: In this paper, the Voronoi tessellation technique and the finite element (FE) method were used to study the dynamic crushing responses of honeycomb structures having irregular cell shapes and non-uniform cell wall thickness.
Abstract: Dynamic crushing responses of honeycomb structures having irregular cell shapes and non-uniform cell wall thickness are studied using the Voronoi tessellation technique and the finite element (FE) method. FE models are constructed for such honeycomb structures based on Voronoi diagrams with different degrees of cell shape irregularity and cell wall thickness non-uniformity. The plateau stress, the densification strain energy and the initiation strain are determined using the FE models. Simulation results reveal that the “X” and “V” shaped deformation modes evident in a perfectly ordered honeycomb at low or moderate impact velocities are disrupted as cell shapes become irregular and/or cell wall thickness gets non-uniform. The “I” shaped deformation mode is clearly seen in all honeycomb structures at high impact velocities. Both the plateau stress and the densification strain energy are found to decrease as the degree of cell shape irregularity or the degree of cell wall thickness non-uniformity increases, with the weakening effect induced by the presence of non-uniform cell wall thickness being more significant. When the two types of imperfections co-exist in a honeycomb structure, the interaction between them is seen to exhibit a complicated pattern and to have a nonlinear effect on both the plateau stress and the densification strain energy. It is also found that stress waves propagate faster in a honeycomb structure having irregular cell shapes and slower in a honeycomb structure having non-uniform cell wall thickness than in a perfectly ordered honeycomb. Finally, the strain hardening of the cell wall material is seen to have a strengthening effect on the plateau stress, which is more significant for perfectly ordered honeycombs than for imperfect honeycomb structures.
TL;DR: In this article, the effective mechanical behavior of an elasto-plastic matrix reinforced with a random and homogeneous distribution of aligned elastic ellipsoids was obtained by the finite element simulation of a representative volume element (RVE) of the microstructure and by homogenization methods.
Abstract: The effective mechanical behavior of an elasto-plastic matrix reinforced with a random and homogeneous distribution of aligned elastic ellipsoids was obtained by the finite element simulation of a representative volume element (RVE) of the microstructure and by homogenization methods. In the latter, the composite behavior was modeled by linearization of the local behavior through the use of the tangent or secant stiffness tensors of the phases. "Quasi-exact" results for the tensile deformation were attained by averaging of the stress-strain curves coming from the numerical simulation of RVEs containing a few dozens of ellipsoids. These results were used as benchmarks to assess the accuracy of the homogenization models. The best approximations to the reference numerical results were provided by the incremental and the second-order secant methods, while the classical or first-order secant approach overestimated the composite flow stress, particularly when the composite was deformed in the longitudinal direction. The discrepancies among the homogenization models and the numerical results were assessed from the analysis of the stress and strain microfields provided by the numerical simulations, which demonstrated the dominant effect of the localization of the plastic strain in the matrix on the accuracy of the homogenization models. (C) 2007 Elsevier Ltd. All rights reserved.