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Selecting a suitable constitutive equation which takes account of the precise strain rate sensitivity of the material is, in general, very important for dynamic-crash analyses. Tanimura-Mimura (T-M) model is one of a few constitutive equations which are able to describe the specific characteristics of many ferritic steels that the strain rate sensitivity in flow stress decreases with increasing plastic strain, however, it has not been examined well how the crash analyses are improved when this model is employed. In this paper, both experimental and numerical analyses of dynamic three-points bend test of thin steel sheet hollow column were conducted at the impact velocity of 4m/s in order to evaluate the effectiveness of T-M model. In the numerical analyses, Cowper-Symonds (C-S) model and strain rate insensitive (I-S) model as well as T-M model were employed, and their calculated results were compared with the experimental result. The calculated load-stroke relations by T-M model showed good agreement with the experimental ones over the whole stroke, on the contrary C-S model was in agreement only in the small stroke region. Shape profiles of the buckling portions of columns in the experiment were compared with the simulated results based on each model. The width of the buckling zone was getting smaller in the order of T-M model, I-S model and C-S model, and T-M model was found to give the best agreement with the experiment since its low strain hardening profiles in stress-strain relations at high strain rates promote the localization in the buckling zone. From these results, T-M model can be considered to improve accuracy of numerical simulation, especially in the case that significant strain localization such as buckling occurs.

In this research, the buckling behavior of long columns under dynamic load was investigated both experimentally and numerically, and an effective buckling criterion for dynamic load was derived from the results in terms of the impact velocity and the slenderness ratio. In the experiments, a free fall drop-weight type impact testing machine was employed. The dynamic buckling loads were measured by the load sensing block, and the displacements were measured by a high speed magnetic-resistance device. In the numerical analyses, dynamic FEM code 'MSC-Dytran' was used to simulate the typical experimental results, and the validity and the accuracy of the simulations were checked. The dynamic buckling loads at various impact velocities were then systematically investigated. From both experimental and simulated results, it was found that the dynamic to static buckling load ratios can be successfully described as a square function of the slenderness ratio of the columns, while they can be also described by a power law of the applied impact velocity.

This paper deals with the results of three dimensional compression tests carried out for high stiffness urethane foams (Penguin-foam, Sunstar Engineering Ltd.), and also deals with the constitutive modelling base on Shima-Oyane’s consolidation condition for the tested foamed urethane. Three kinds of urethane foams, relative densities of which were 0.1, 0.2 and 0.33, were employed in the experiments. Like metallic porous materials, the tested urethane foams show the strong plastic-compressibility. On the other hand, in modelling, unlike metallic porous materials, the identified material constants for different density foams do not take the same (or unified) values but take the different values when Shima-Oyane’s constitutive model is assumed. Furthermore, the experimentally derived stress-relative density curves could not be satisfactorily described by Shima-Oyane’s original constitutive model; the experimental stress-relative density curves show stronger work hardening as compared with the simulated ones especially in the large deformation stage. To avoid those inconvenience, in this paper, a modified Shima-Oyane type constitutive equation was also proposed, and it was shown that the proposed model could well express both the low work hardening area of the stress-relative density curves at the initial deformation stage and the strong work hardening area at the final deformation stage by supposing the stress restriction at initial deformation stage due to the buckling of cell walls of each foam, and the rapid stress increase at the large deformation stage caused by the successive contact and the friction between the bent cellular walls, respectively.

The high measurement accuracy in dynamic tension testing is required for designs and numerical simulations based on the accurate modeling of stress-strain relations at various strain-rates. The non-coaxial Hopkinson bar method (NCHBM) is one of the recently proposed methods for dynamic tension tests. In this study, the accuracy of the stress-strain relations obtained on the basis of NCHBM was investigated by the analysis based on FEM and by experiment. The FE models of NCHBM apparatus and plate-type specimens of various dimensions were made in detail. The target materials employed in this study were mild steel and SUS316 stainless steel. The effects of the rising, the dimensions of specimen, and the strain rate were examined systematically. The results calculated for the specimens of SUS316 were compared with those obtained by experiment. At last, the improving methods of the specimen fixation were proposed.

With a view to examine the axial crushing behavior of thin-walled tubes, which form the parts of transports such as aircrafts and automobiles, under dynamic compressive loads, a series of numerical simulations for thin-walled circular tubes of various dimensions was carried out by using the explicit FEM code LS-DYNA. The energy absorption efficiency and the bifurcation conditions of the collapse modes of these tubes subjected to dynamic axial compression were primarily investigated. In order to confirm the validity of the simulations, first, some calculated results such as the load - displacement relation, the collapse behavior, the absorbed energy per unit volume, and so forth by using the axisymmetric FE model were compared with those obtained by way of experiment under the corresponding condition. Here, the absorbed energy per unit volume was formulated on the basis of Alexander's theory and the Johnson-Cook model, and the results obtained by this formulation were compared with the corresponding results obtained by the simulations and experiments for many tubes of various dimensions. Next, the effects of the initial imperfection and the inertial force on the bifurcation of the axial-collapse mode were examined by using the 3D-shell model. It was clarified that the mode of the dynamic progressive buckling was affected by the natural vibration mode.

The high measurement accuracy in dynamic tension testing is required for designs and numerical simulations based on the accurate modeling of stress-strain relations at various strain-rates. The non-coaxial Hopkinson bar method (NCHBM) is one of the recently proposed methods for dynamic tension tests. In this study, the accuracy of the stress-strain relations obtained on the basis of NCHBM is investigated by FEM. The finite element models of NCHBM apparatus and plate type specimens of various dimensions are made in detail. The target material employed in this study is mainly the mild steel that is proper for the investigation of measurement accuracy. On the other hand, SUS316 stainless steel and A7075 aluminum alloy are modeled as specimen materials for the comparison with the experiments. The effects of the bending, the constraint condition, the rising time, the size and geometry of specimen, and the strain rate are examined systematically.

For the improvement of car safety in collision, the development of high-speed processing technology, the refinement of practical constitutive equations for numerical simulation, and so forth, it is important to obtain accurate stress-strain relation of various materials in wide ranges of strain and strain rate. Through a series of numerical simulations of the specimen model of practical geometry by using the computer code LS-DYNA, some useful results in the determination of the geometry and dimensions of specimen suitable for dynamic tension test under the specified strain rate in the range 102-103 s-1, such as the effects of the rising time of input velocity and the lengths of grip and fillet on transient vibration, the relationship between the limits of gauge length and strain rate to give an adequate accuracy of dynamic stress-strain curves, and so forth, are obtained.

A new method of applying a dynamic load directly to a tensile specimen was developed. By combining the new method with the testing method based on a sensing block [1-5], we improved the testing method to obtain the entire tensile stress-strain curves for a wide range of strain rates on the order of 10 -3 ∼10 3 s -1 , with remarkable accuracy, especially for the high strain rates range. Based on numerical simulations and experiments, the accuracy of the measurement of the non-coaxial Hopkinson bar method [6,7] was discussed. By performing a series of numerical simulations, the relation between the gauge length of a specimen and the testing strain rate, necessary for obtaining an accurate dynamic stress-strain curves corresponding to a testing error of approximately 2% or 4%, was also obtained for a wide range of strain rates from 10s -1 to 10 4 s -1 .

The great Hanshin–Awaji earthquake, which occurred in Japan in 1995, caused fracture and destruction of a large number of structures. One of the examples, whose mechanism is not clear, is the fracture of a bridge bearing part of the Nielsen bridge type that does not occur under ordinary static or dynamic loading. The fracture probably resulted from a very high stress due to an unexpected dynamic mechanism or an impact. In this paper, the three dimensional dynamic behaviour of a bridge of the Nielsen bridge type was analysed, for a collision/impact between the upper and the lower bridge bearings, which might have occurred in the great Hanshin–Awaji earthquake. The numerical results show that an impact due to a relative velocity of 5–6 m/s between the upper and the lower bridge bearings generates a stress sufficient to lead to the fracture in the upper bridge bearing. The location and the direction of the maximum principal stress determined numerically in the upper bridge bearing coincide fairly well with the observed features of the actual fracture plane.

It is desired to obtain the material properties in a wide range of strain rates and strain to be used for numerical simulations of car crushing, high speed forming and others. To conduct dynamic material testing, adapting suitable specimen size and shape for each testing strain rate is important to obtain the results with good accuracy and interchangeability for a wide range of strain rates. Any standard for the specimen size and shape, however, is not yet established except quasistatic testing. In this study, the upper limit of the gauge length of the test piece, to keep the testing error under a few percent, for the dynamic tensile testing in the strain-rate range from 102 to 104 s-1 were obtained through a series of numerical simulations.

In recent years, an increasing interest has been paid to the accurate measurement of stress-strain relations of materials for wide range of strain rates which are needed to formulate the constitutive equations of rate-sensitive materials precisely. The Hopkinson Pressure Bar system is widely used for this purpose. However, the device should be long enough to prevent the immediate reflection of stress waves from the ends of the input and output bars. The newly developed Sensing Block (SB) system, which consists of a small sensing projection and a relatively large mass block, is expected to be used widely for many materials. In this paper, the bounds of application of the SB method for measuring dynamic load was examined numerically. The relation between the size of sensing projection and the rising time of applied load was cleared to satisfy some criterions on the accuracy for each model. The results ensure the sufficient accuracy for measuring dynamic load under the obtained conditions.

Initial transient behavior of a tall-building-model due to a strong near-source earthquake has been studied based on the numerical simulation using the code MSC. Dytran. It was found that stresses occurred in the initial transient stage exceeded the yield stress of material in many columns, in the case of elastic-plastic building model, and that those exceeded the tensile strength of material in many columns, in the case of elastic building model. Through discussing on the dynamic properties of the structural material with the rate dependency of strain hardening rate of the material, the possibility to be occurred the brittle fracture of column even at strain rate in the range of 0.1∼1 s-1 was pointed out. These results show very possibility that a high stress sufficient to lead the initiation of damage such as local fracture and crack can be reached in some parts of the tall-building-model due to a strong near-source earthquake.

This paper presents a practical viscoplastic constitutive model covering a wide range of strain rates, large deformation, and applicable to various grouped metals. The essential new feature of the constitutive model is employment of a specific function between quasistatic yield strengths and strain rate sensitivities of grouped metals in the strain rate range where thermally activation for dislocation motion is the dominant mechanism of the material strain rate sensitivity. This new feature enables us to use unified or common material constants to describe the dynamic behavior of grouped materials in the strain rate range mentioned above. In the model, formulations for the strain rate sensitivity at higher strain rates of up to 104-105s-1, and for the temperature dependence of flow stress are also made so that the strain rate sensitivity in the wide range of strain rates, and at various temperatures are successfully described. In order to verify the validity of the proposed constitutive model, simulations of stress-strain curves at an elevated strain rate and variations of stress with the logarithm of strain rate at various temperatures are compared with the corresponding experimental results. It is found that the simulations based on the proposed constitutive model are in fairly good agreement with experimental results.

In 1995, the great Hanshin-Awaji earthquake caused a large amount of destruction and structural failures. One example, whose mechanism is not fully clear, is the fracture of a bridge bearing of a Nielsen type bridge that does not occur under the ordinary static or dynamic loading conditions. The fracture probably resulted from very high stress due to an unexpected dynamic mechanism. In this paper, the 3-dimensional dynamic behavior of a Nielsen type bridge was analyzed by assuming a collision between the upper and the lower parts of the bearing, which might have occurred in the great Hanshin-Awaji earthquake. The numerical results show that an impact due to a relative velocity of 5∼6m/s between the upper and the lower parts of the bearing generates a stress sufficient to cause a fracture in the upper bearing. The observed features of the actual fracture surface was also simulated fairly closely.

The main aim of this paper is to give important information for understanding the mechanism of the axial crushing of thin-walled structures under dynamic loading, from the safety point of view in car crushing. For this, the axial crushing experiments of circular tube specimens were conducted by using the dynamic-loading device with the load sensing block to evaluate the properties of dynamic progressive buckling of two types of materials. The thin-walled circular tube specimens of steel and aluminum alloy were chosen, stressing mainly on the behavior of steel specimens. The effect of impact velocity on the magnitude of axial stress corresponding to the first buckling of the dynamic progressive buckling, and the effect of the differences between those material properties on the behavior of the dynamic progressive buckling were clarified. The absorbed energy per unit volume of the steel specimen was also examined. It was found that the ratio of the thickness to the diameter of the specimen affects greatly the absorbed energy per unit volume and the deformation mode of dynamic progressive buckling.

To examine axial crushing properties of aluminum alloys under high strain rate deformations, the axial crushing tests of thin-walled circular tube specimens were conducted. Particularly, we introduced a new apparatus, load sensing block, with a special technique based on the theory of stress wave propagation for the dynamically-loaded axial crushing test. It enables us to get stable outputs to illustrate stress-strain curves for a wide strain range even in the case of the specimens with long length in the axial direction or low impedance. In accordance with the split-Hopkinson bar method, the size of device must be extended considerably in those cases. In order to evaluate the energy absorption abilities of those specimens, we paid attention to the absorbed energy density per unit length. The comparison among the modes of dynamic progressive buckling shows that the concertina buckling mode has the largest absorption ability among those modes. The conditions governing those buckling modes are also discussed.

Spall damage analyses are conducted in the framework of continuum damage mechanics with special emphasis on the 3-dimensionality and the effect of void volume fraction on the spall process. The evolution equation of a scalar damage variable taking account of the nucleation and growth of spherical voids, and the elastic-viscoplastic constitutive equations extended to damaged materials are incorporated into the commercial hydrocode MANJUSRI-3D. The axisymmetric two-dimensional analyses of the plate-impact tests on OFHC copper plates are performed to examine the effect of the ratio of the target radius to its thickness and that of the volumetric strain related to the void development on the relation between volumetric strain and hydrostatic pressure.

This paper is concerned with the elaborate modeling of ductile spall damage due to void nucleation and growth in viscoplastic materials by means of continuum damage mechanics. The evolution equation of a scalar damage variable is developed by taking account of nucleation and growth of spherical voids in a unit cell; it is expressed in terms of the rates of the void nucleation and its radius growth. The resulting damage evolution equation and elastic-viscoplastic constitutive equations of the damaged material are incorporated into the commercial hydrocode MANJUSRI-3D, and the axisymmetric two-dimensional analyses of the plate-impact tests are performed. The results of the numerical analyses are compared with those of the one-dimensional analyses, axisymmetric analysis without explicit modeling of void growth, and the corresponding experiments.

Elaboration of the preceding one-dimensional analysis of ductile spall damage based on damage mechanics was discussed by performing axisymmetric two-dimensional analyses. The effects of surface energy due to cavity nucleation and elastic-viscoplastic-damage coupling were incorporated into the energy conservation law. Then, the application of the commercial finite-difference program MANJUSRI-3D for nonlinear dynamic analysis to the axisymmetric two-dimensional problem was discussed. Finally, a plate impact of OFHC copper discs was analyzed by the present method, and the effects of the radial stress wave and surface nucleation energy on the spall damage process were elucidated. The results of analysis were compared with those of one-dimensional analysis and experiments.