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A constitutive equation accounting for strain rate, temperature and applied stress system dependencies of strain-induced martensitic transformation is given. A series of computational prediction of monotonic and cyclic deformation behavior including tension, compression and shearing of typical 304 austenitic stainless steel, have been performed under different environmental temperatures from 77 to 353 K . The effect of stress range, pre-strain, temperature and applied stress system on such responses of TRIP steels as the evolution of martensitic phase, the accumulated plastic strain, and the asymptotic nature of the stress–strain relation with an increase in the number of cycles is clarified. The predictability of the present constitutive model is checked against the experimental results. Furthermore, simulation of the cyclic deformation behavior of TRIP steel bars with ringed notch is performed.

A computational simulation method for three-dimensional trabecular surface remodeling was proposed, using voxel finite element models of cancellous bone, and was applied to the experimental data. In the simulation, the trabecular microstructure was modeled based on digital images, and its morphological changes due to surface movement at the trabecular level were directly expressed by removing/adding the voxel elements from/to the trabecular surface. A remodeling simulation at the single trabecular level under uniaxial compressive loading demonstrated smooth morphological changes even though the trabeculae were modeled with discrete voxel elements. Moreover, the trabecular axis rotated toward the loading direction with increasing stiffness, simulating functional adaptation to the applied load. In the remodeling simulation at the trabecular structural level, a cancellous bone cube was modeled using a digital image obtained by microcomputed tomography (μCT), and was uniaxially compressed. As a result, the apparent stiffness against the applied load increased by remodeling, in which the trabeculae reoriented to the loading direction. In addition, changes in the structural indices of the trabecular architecture coincided qualitatively with previously published experimental observations. Through these studies, it was demonstrated that the newly proposed voxel simulation technique enables us to simulate the trabecular surface remodeling and to compare the results obtained using this technique with the in vivo experimental data in the investigation of the adaptive bone remodeling phenomenon.

Under the influence of mechanical environment, bone structure is formed and maintained by adaptive remodeling that involves osteoclastic resorption and osteoblastic formation. In the mechanotransduction system in osteoblasts, it is believed that intracellular calcium plays a fundamental role and cytoskeletal actin filament is a crucial component for the signal transduction process. To clarify the role of actin filament in deformation-induced Ca2+ signaling, osteoblast-like cells (MC3T3-E1) with different actin filament densities controlled by cytochalasin D were subjected to tensile strain in vitro. The change in intracellular Ca2+ concentration labeled by fluo-3 was observed using a confocal laser-scanning microscope. As a result, the disruption of the actin filament was found to significantly suppress the deformation-induced Ca2+ response that was regulated according to the degree of actin filament organization. This result indicates that the actin filament is indispensable for the quantitative regulation of Ca2+ signaling in response to a mechanical stimulus in osteoblasts.

近年, 環境保護の観点から注目されている鉛フリーはんだバンプの実装設計において, 欠くことができないバンプの弾塑性クリープ構成則を同定するために, 走査型電子顕微鏡下で, バンプにせん断荷重を与え, 変形状態をその場観察した。その結果, 変位速度一定試験において, 試験温度の上昇に伴い, バンプにクラックが発生するまでの変位が増大することを提示した。次に, 有限要素法を用いたせん断試験のシミュレーションを行い, シンプレックス法を用いたシミュレーションによって得られた結果が実験によって得られた結果を再現できるように, 弾塑性クリープ構成則を同定する方法を提案した。そして, 同定した弾塑性クリープ構成則を異なる形状のバンプに適用し, そのせん断試験結果とシミュレーション結果を比較検討することにより, 提案した同定法は, 実装設計において有用であることを確認した。

The asymptotic homogenization method within the framework of the updated Lagrangian formulation is employed to derive a nonlocal constitutive equation for finitely deformed rate-independent materials with a periodic microstructure. Higher-order asymptotic terms naturally introduce strain gradient terms into constitutive equations for macroscopically homogeneous materials. Macroscopic properties, which are the ensemble average of their counterparts over a microscopic unit cell, are discussed. The variational principle of macroscopically homogeneous materials is then established and the complete boundary value problem is formulated.

In order to estimate the accuracy of multiscale analysis for materials with microstructures based on the eigenstrain fields formulated by Nemat-Nasser and co-workers, we performed the computational simulation employed the piecewise approximation method, so called Subdivisions Method that discretizies inclusion region into the sub-domains where the eignenstrains are taken as constant. Through the numerical evaluation of the overall properties and microscopic deformation behavior of elastic solids that contain periodically distributed hard inclusions in soft matrix, we found that the results significantly depend on the way of discretization of inclusion into subregion. The results of Subdivisions Method with subregions that have the same volume show the excellent agreement with those due to Homogenization Method, whereas, those with the different volume were very poor. Therefore, it has been concluded that Subdivisions Method with the same volume of subregion provide efficient tool for the estimation of the macroscopic mechanical properties of the materials with periodic microstructures. The Subdivisions Method with the same volume of subregion is applied to investigate the overall complex properties and microstrain of unidirectional/short-fiber reinforced composite materials and the effect of the location of reinforcements under a constant volume fraction on its macroscopic mechanical properties are clarified.

To estimate the deformation behavior of rubber-blended glassy polymers, a computational method has been established with newly developed constitutive equation for glassy polymer and homogenization method. The parametric study has been performed through series of simulation of deformation behavior for the plane strain glassy polymer unit cell containing inclusion with different volume fraction, size, and different distribution pattern subjected to different directional loading. The effect of these parameters on the characteristic feature of the deformation resistance, the onset and propagation of shearband, the normal stress distribution on the interface of matrix and inclusion and the maximum mean stress inside the inclusions have been clarified. The results indicate that depending on these parameter, quite different types of shear bands appear and propogate. The decrease of the macroscopic yield stress is attributalbe to the onset of the shearband which connects the most neighboring particles. The macroscopic deformation behavior exhibits nearly isotropic for the case with different sized inclusions. The maximum normal stress appears at the position where the shear band arrived and it moves with the propagation of shear band. The maximum mean stress increases as the shearband is sharpened.

The purpose of the present article is to provide a perspective of constitutive equations for glassy polymers developed using the molecular chain network theory. The results of experimental observations of the deformation behavior of glassy polymers at macro- and microscale are indicated, and an accommodation of the characteristic feature of deformation behavior into the molecular chain network theories is discussed. The related computational simulations of neck formation and its propagation under plane strain and three-dimensional conditions are illustrated. The results clarified the three-dimensional characteristic feature of neck propagation behavior under isothermal condition and the effect of deformation-induced heat and pre-drawing on the plane strain neck propagation behavior.

Uniaxial tension tests were performed under a constant strain rate and various environmental temperatures from 77 to 373 K to identify the concrete form of the constitutive equation for TRIP steels. To elucidate the dependence of the martensitic transformation on the nonuniform deformation and to validate the proposed constitutive equation, the volume fraction of the martensite phase is predicted and measured using computational simulation and experimental procedures, respectively, for the uniaxial tension of bars with a ringed notch. The good correspondence between the local volume fraction of the martensite phase around the notch, obtained by both methods, verifies the validity of the proposed constitutive equation for the nonuniform deformation behavior. Subsequently, the computational simulations were performed to elucidate the deformation behavior of ringed-notched bars under compression and that of smooth/ringed-notched bars under cyclic loading.

In order to clarify the characteristic feature in the deformation behavior of particulate-reinforced composite materials, a homogenization method has been developed for the materials obeying the strain and strain-rate dependent constitutive equation that takes into account for the characteristic length scale by using the strain gradient theory and developed the corresponding finite element method. By means of the computational simulation under the plane-strain condition, a series of simulations with inhomogeneous deformation behavior of composite materials containing different volume fractions, size and distribution pattern of reinforcement subjected to different loading direction have been performed. As a result, it has been clarified that the resistance of composite material to deformation is substantially increased with the refinement of the particle size and significantly dependent on the loading direction under constant volume fraction of the reinforcement. This result indicates that the present simulation method has the capability of predicting the experimentally observed particle-size-dependent macroscopic characteristic feature of the composites. The main mechanism of the increase of the deformation resistance in the plastic range is attributable to the high strain gradient appearing in the matrix material, which increases with decreasing the distance between the particles. Therefore, the regularization of the distribution pattern that increases the value of the maximum strain gradient in the matrix contributes toward improving the resistance to macroscopic deformation behavior.

Recent advances in understanding of mechanical bone remodeling have been progressed by computational mechanics approach that allows analysis of structural and functional changes of bone with hierarchical structure under complicated mechanical environment. In this study, a simulation method of trabecular surface remodeling for cancellous bone was proposed using digital image-based finite element model in which mechanical environment at the trabecular level relating to cellular activities could be directly estimated. Morphological changes of trabeculae due to remodeling were simulated based on uniform stress hypothesis, that is, the resorption and formation were accomplished by removal and addition of the voxel elements on the trabecular surface driven by stress nonuniformity. Remodeling simulation of cancellous bone cube under compressive loading was conducted using a digital image-based model constructed based on μCT data from distal canine femur. Simulation results demonstrated that the changes in structural indices of cancellous bone qualitatively corresponded with experimental results, and the proposed simulation method has potential to predict the functional adaptation phenomena in cancellous bone.

In order to estimate the characteristic feature of the deformation behavior of materials with a length scale, the strain gradient plasticity theories, corresponding variational principle and a finite element method are given. Then the finite element method is applied to the estimation of the mechanical characteristics of the particle reinforced metal–matrix composites modeled under plane strain conditions. The effects of the volume fraction, size and distribution pattern of the reinforcement particles on the macroscopic mechanical property of the composite are discussed. It has been clarified that the deformation resistance of the composite is substantially increased with decreasing particle size under a constant volume fraction of the reinforcement material. The main cause of the increase of the deformation resistance in the plastic range is the high strain gradient appearing in the matrix material, which increases with the reduction of the distance between particles.

実装設計において問題となる層状半導体素子のクラック発生現象を解明するために, 走査型電子顕微鏡下で, 素子の層面に対して, 2方向から負荷を与える3点曲げ試験を行い, 発生する微小クラックをその場観察した。その結果, 負荷方向に依存して, 2種類のクラックが発生することを明らかにした。次に, モンテカルロ法と, 節点分離挙動をバネ要素で表現した有限要素モデルを用いて, 材料欠陥などの存在に依存した破壊強度の分布を考慮したクラック進展シミュレーション法を提案した。そして, 3点曲げ試験結果とシミュレーション結果を比較検討することにより, 提案したシミュレーション法は, 実装設計において有用であることを確認した。

Mouse monoclonal antibody FU-MK-1, raised against a human gastric adenocarcinoma, recognizes an antigen (termed MK-1 antigen) present on the majority of carcinomas. The present study aimed to identify the MK-1 molecule and to establish its relationship to other carcinoma antigens. Immunoprecipitation studies of human tumor cell lines revealed that FU-MK-1 recognizes a monomeric membrane glycoprotein with two forms, 40 kDa (major form) and 42 kDa (minor form), and with a molecular mass of 35 kDa following treatment with the N-glycosylation inhibitor tunicamycin. The partial amino acid sequence of a main fragment of the MK-1 molecule obtained by spontaneous cleavage under hypotonic conditions was examined, and the 17 contiguous NH 2-terminal amino acids were found to be identical with residues 81 –97 of the 314-residue GA733-2 protein [Szala et al.; Proc. Natl. Acad. Sci. USA, 87, 3542 –3546 (1990)]. Hence, the GA733-2 cDNA was cloned and the specificity of FU-MK-1 was confirmed using four recombinant forms of the GA733-2 antigen expressed in COS-1 cells. Immunoprecipitation with FU-MK-1 of the cell lysate transfected with the full-length GA733-2 cDNA revealed two bands corresponding to those obtained from the tumor cell lines. FU-MK-1 also precipitated three other recombinant proteins consisting of amino acids 1 – 265, 1–201, and 1–139 of the GA733-2 protein, respectively. Furthermore, immunoblotting analysis indicated that FU-MK-1 binds to a small fragment (6 kDa) generated from a tumor cell line under hypotonic conditions, suggesting that the FU-MK-1 epitope exists on the distal 6-kDa peptide of the extracellular domain of the GA733-2 molecule. We thus conclude that the MK-1 antigen is the GA733-2 antigen, which is currently being used as a target in clinical trials with monoclonal antibodies.

A simple optical technique is used to quantify creep crazing damage in a uniaxially stressed transparent glassy polymeric sheet of polymethyl methacrylate (PMMA) at room temperature. The areal craze densities are taken as a measure of the crazing damage. It is shown that the crazing damage increases with nominal applied stress and creep time. The crazing initiation time and the crazing damage evolution equation for PMMA is modeled from a mechanical viewpoint and the results are used to predict the nonlinear creep behavior of PMMA with growing damage. The predictions are in good agreement with the test results.

Macroscopic deformation of a polymeric material is physically induced by collective evolution of orientation and alignment of its molecular chains. In the present work, we evaluate its deformation behavior from the molecular-level structure by the molecular dynamics simulations. Thermodynamic quantities such as free energy or entropy are key issues on considering the deformation of polymer because crystallization of the internal structure as deformation might produce entropy decrease. Therefore, we computationally calculate the thermodynamic values by the perturbation method within the MD scheme. First, the free energy difference on the structural change between the polyethylene (PE) and the syndiotactic polypropylene (st-PP) is examined. The results show the reasonable high energy barrier between them and the understandable entropy increase from PE to st-PP. Then, we apply it to amorphous polymer of PE constructed by the random walk method under the uniaxial tension. The entropy decrease due to decrease of the internal potential energy is obtained, which is one of the proper features of the polymer.

Residual stress and strain in living tissues have been investigated from the viewpoint of mechanical optimality maintained by adaptive remodeling. In this study, the residual stresses in the cortical-cancellous bone complex of bovine coccygeal vertebrae were examined. Biaxial strain gages were bonded onto the cortical surface, so that the gage axes were aligned in the cephalocaudal and circumferential directions. Strains induced by removal of the end-plate and the cancellous bone were recorded sequentially. The results revealed the existence of compressive residual stress in the cortical bone and tensile residual stress in the cancellous bone in both the cephalocaudal and the circumferential direction. The observed strains were examined on the basis of the uniform stress hypothesis using a three-bar model for the cephalocaudal direction and a three-layered cylinder model for the circumferential direction. In this model study, the magnitude of effective stresses, which is defined as the macroscopic stress divided by the area fraction of bone material, was found not to differ significantly between cephalocaudal and circumferential directions, although they were evaluated using independent models. These results demonstrate that the uniform stress state of the cortical-cancellous bone structure is consistent with results obtained in the cutting experiment when the existence of residual stress is taken into account.

The purpose of the present article is to provide a perspective for computational predictions related to plastic instabilities such as bulge, neck and shear band formation and their propagation in polymeric materials under a variety of deformation conditions. Constitutive models of polymeric materials are developed for glassy polymers and phenomenological models, which duplicate the experimentally observed characteristic behavior of polymeric materials, and physical models, which are developed by using the molecular chain network theory, are discussed. Since the instabilities propagate under almost steady state conditions without significant change in force, the special attention should be given to the computational simulations, which is briefly discussed. Instability behaviors such as the onset of bulge, neck and shear band and their propagation are presented with illustrative examples of computational simulations.

The purpose of the present article is to provide a perspective of constitutive equations for glassy polymers developed using the molecular chain network theory. The experimental observations of the deformation behavior of glassy polymers at macro- and micro-scale are indicated, and an accommodation of the characteristic feature of deformation behavior into the molecular chain network theories is discussed. The related computational simulations such as neck and shear band formation, and their propagations in plane strain conditions with thermomechanically coupled conditions are illustrated using examples.

Only a small number of glycoproteins has been reported to contain N-linked sugar chains with GalNAcbeta1-->4GlcNAc structure. Our previous studies showed that most glycoproteins from bovine milk fat globule membranes contain beta-N-acetylgalactosaminylated N-linked sugar chains [Sato et al., J. Biochem. 114 (1993) 890-900]. In order to study how widely this glycosylation occurs, lectin blot analysis of membrane glycoproteins from 12 bovine tissues was performed using Wistaria floribunda agglutinin (WFA), which interacts with oligosaccharides terminating with N-acetylgalactosamine. The WFA-positive bands were detected in samples from most tissues except for intestine although the number and reactivity of bands to lectin varied among the tissues. Upon pretreatment of blotted filters with Bacillus beta-N-acetylgalactosaminidase or N-glycanase, no lectin binding was observed. WFA-agarose column chromatography of oligosaccharides released by hydrazinolysis from membrane glycoproteins of bovine tissues except for intestine revealed that a few to 18% of the released oligosaccharides bind and are eluted from the column with 100 mM N-acetylgalactosamine. These results indicate that many glycoproteins from a variety of bovine tissues contain N-linked sugar chains with GalNAcbeta1-->4GlcNAc structure, suggesting a wider occurrence of this glycosylation in bovine tissues.

TRIP steel possesses favorable mechanical properties such as high strength, ductility and toughness and is frequently employed as structural material. To obtain the expected mechanical properties of TRIP steels through cold-working conditions, prediction and control of the material characteristics during the deformation processes are indispensable. Here, to evaluate such macroscopic characteristics as the stress-strain relationship and the average volume fraction of the overall specimen and such microscopic characteristics as shape, orientation and periodicity of the martensitic particles, uniaxial tension and compression tests, including SEM observation, for 304 austenitic stainless steels have been carried out under various environmental temperature conditions. On the basis of the experimental results, the deformation mode dependence of martensitic transformation and deformation behavior of TRIP steels are discussed. Finally, a deformation-mode-dependent transformation kinetics model is presented.

Strength evaluation for the wire is very important to avoid crack generation at the selection of materials and the structural design of semiconductor packages. This paper describes the strength evaluation for a wire with the copper-cored semiconductor package. A simplified FEM model targeting issues at the package structural design was developed and its validity was checked against a more elaborated FEM model. From the FEM analysis of thermal stress induced by the difference of thermal expansion coefficients of the composite materials and the detection of crack generation during the thermal cyclic test, it has been clarified that the point location where the maximum thermal stress appears coincides with the one where the crack occurs. Through a series of FEM analysis, it has been proved that the cause of a crack is strongly related to the gap between the lid and the copper core and the suitable length of the gap to prevent crack has been obtained. A new semiconductor package based on the proposed strength evaluation method is working well without cracking. Thus, the capability and validity of the proposed evaluation method has been proved.

Neck propagation of polymeric materials under tension is a characteristic feature which can be physically explained by the deformation induced evolution of molecular chain structure. In this study, atomic force microscope is applied to glassy polymer with tensile deformation to observe the hierarchical structures at successive molecular to macrolevels, and to clarify the quantitative relation between micro- and macroscopic deformation behaviors. First, hierarchical structure of fibrillar morphology on drawn amorphous polycarbonate film were observed : microfibril structure with a diameter between 5 and 7μm ; that with a diameter between 1 and 2.5 μm ; nanofibrils with a diameter of around 100 nm ; and regular chain pattern corresponding to the crystalline packing. Second, microscopic lattice pattern marked on surface of the specimen was employed to investigate the relation between micro- and macroscopic deformation behaviors. Macroscopic deformation and orientation of microfibril structure were quantitatively measured around the neck, which revealed that the rotation of the aligned microfibril structures were behind to that of the principal direction of plastic stretch due to shear strain by necking.

In order to determine the characteristic feature in the deformation behavior of particulatereinforced composite material, a constitutive equation that takes into account the characteristic length scale has been developed using the strain gradient theory. By means of the plane-strain finite element method with the proposed constitutive equation, a series of simulations of inhomogeneous deformation behavior of composite materials with different volume fractions of reinforcement, particle size and distribution pattern of reinforcement have been performed. As a result, it has been determined that the resistance of composite material to deformation is substantially increased with the refinement of the particle size under constant volume fraction of reinforcement. Furthermore, the regulaization of the distribution pattern which increases the value of the maximum strain gradient in the matrix contributes toward improving the resistance to deformation.

A nonaffine molecular chain network model of glassy polymers in which the number of entangled points of molecular chains may change according to the local distortion caused by the deformation and the temperature increase has been developed. A simple evolution equation which correlates the number of entangled points to the distortion and the change of the temperature has been proposed. Subsequently, the corresponding three-dimensional thermo-elasto-viscoplastic constitutive equation is developed. The finite element simulations with the proposed constitutive equation has been carried out for the glassy polymer blocks under plane strain tension and simple shearing. It is clarified that the neck and shear band propagate under low deformation rate, whereas they stay at their initial location due to the excessive softening caused by the temperature increase as compared with the orientation hardening. In simple shearing, the high temperature area corresponds to the significantly distorted area, while, in tension, they are different. Thus, the contributions of temperature and distortion on the reduction of the number of entangled points are different depending on the deformation modes.

We have developed three types of piezoelectric bimorph structure actuators. The first actuator has a displacement of over 3 mm at 100 Vpk and high reliability by resonance effect of the displacement magnifying part. The second one has a displacement of over 1 mm at 100 Vpk and high stability for change in driving frequency by combined two resonances. The third one has a linearity of displacement until 85% of fracture point and low temperature characteristics by a direct bonding technique that bonds piezoelectric single crystals without using adhesive.

The purpose of the present article is to provide a perspective for a network model for glassy polymers and computational predictions of mechanical behavior related to plastic instabilities, such as neck and shear band formation, and their propagation. The constitutive equations developed using the molecular chain network theory are discussed. The computational strategy for the simulation, and neck and shear band propagations in plane strain and under 3D conditions with and without thermomechanically coupled conditions are presented with illustrative examples.

By the duplex effect produced by two kinds of phases of austenite and martensite, the transformation-induced plasticity (TRIP) steel is improved in ductility and fracture toughness. The strain-induced martensitic phase transformation could be associated with the strain localization behavior. Accordingly, the measurement of the amount of local transformation is necessary in order to construct a more physical evolution model in the constitutive equation. In this study, a new measurement system using a micro-hardness tester is proposed to obtain a volume fraction map of the martensitic phase expanding in the neighbor of strain localization. Then the system is applied to investigate the inhomogenous transformation behavior around the notch root of SUS 304 stainless steel bar under uniaxial tension.

In order to develop a constitutive equation for polymeric materials covering a wide class of deformation processes a three-dimensional nonaffine model has been developed by adopting the non-Gaussian network theory with the generalized Argon double-kink model of intermolecular resistance. A phenomenological relation between the non-Gaussian molecular chain network structure and entanglement of chains is formulated and a simple evolutional equation of the number of entanglements of chains during the deformation process is developed. The validity of the proposed constitutive equation has been proven through comparison between the predicted results and experimental results. Furthermore, its application to the deformation analysis of circular polymeric bars under tension has been discussed

The transformation-induced plasticity (TRIP) steel possesses such favorable mechanical properties as high work-hardening characteristics, tenacity and strength. The strain-induced martensitic transformation, however, strongly depends on the temperature and strain rate imposed, and an appropriate improvement of mechanical properties is realized under quite restricted circumstances. To obtain the required mechanical properties, a constitutive model which can suitably predict the deformation behavior including transformation under a wide range of deformation rate and temperature has been developed by employing Olson and Cohen's model for strain-induced martensitic transformation kinetics. Then, the deformation behavior of a SUS304 (18-8) cylinder has been simulated under different environmental temperature with different strain rates by the thermocoupled finite-element method accounting for the latent heat induced by martensitic transformation. The possibility of the improvement of such mechanical properties of the material as strength, ductility and toughness has been individually discussed.

The relation between the non-Gaussian molecular chain network structure and entanglement of chains and a simple evolution equation of the number of entanglement of chains during the deformation process are developed to cover a wide class of deformation processes of polymeric materials which manifest remarkable anisotropy according to the orientation of molecular chains. With the generalized Argon double-kink model of the intermolecular resistance, a three-dimensional constitutive equation is developed and the validity of the proposed constitutive equation has been examined through the comparison between the predicted results and experimentally obtained results. Application of the proposed constitutive equation to the prediction of deformation behavior of tension of polymeric materials is discussed.

Plane-strain dynamic flow localization in tension blocks under a wide range of deformation rates has been investigated numerically. The material is characterized by a thermo-elasto-viscoplastic constitutive equation with strain-gradient-dependent flow stress. The mixed type variational principle for the corresponding materials is developed to satisfy this continuity requirement of the higher-order derivative of velocity. In this variational principle, the velocity and representative strain rate are regarded as independent variables. The finite element method developed using the variational principle has been employed to explore the effects of deformation rate applied, and shape and size of the blocks on the flow localization behavior.

The purpose of the present article is provide a perspective for computational predictions related to such plastic instabilities as buckling, necking and flow localization including shear–banding under a wide range of deformation rates for a variety of materials, including single– and polycrystals. Computational bifurcation analyses for general cases, axisymmetric to nonaxisymmetric deformation, very thin–walled bodies, and specific materials with nonstandard constitutive equations are given. The postbifurcation analyses and regularization schemes to remedy the problems associated with spurious mesh sensitivity and incorrect convergence in finite element prediction of flow localization behavior are discussed. The instability behavior of thick circular tubes deformed under pressure and combined loading of internal/external pressure and axial force, neck and bulge propagations in polymeric materials, wrinkling of thin plates and shells under sheet metal forming processes, flow localization of thermo–elasto–viscoplastic materials under a wide range of deformation rates including adiabatic shear banding, and flow localization behavior of mono– and polycrystalline solids are reviewed with illustrative examples.

Plane-strain dynamic flow localization in tension and compression of thermo-elasto-viscoplastic blocks under a wide range of deformation rates and different boundary conditions has been investigated numerically. The material is characterized by incorporating the strain, strain-rate, and temperature sensitivities through J2-type generalization of the expression relating uniaxial stress, strain, strain rate and temperature. Strain-rate-history dependence of the flow stress under abruptly changing strain rate is also considered for specific materials. By means of plane-strain explicit finite-element analysis, we explored the effects of deformation rate, inertial effect, strain-rate and temperature sensitivities of materials, strain-rate-history dependence of the how stress, and shape and size of blocks on the flow localization behaviour.