Yoshiaki Okui

An improved hyperelasticity relation in modeling viscoelasticity response of natural and high damping rubbers in compression: experiments, parameter identification and numerical verification

The rate-dependent behavior of natural and high damping rubbers is investigated in the compression regime. The experimental results demonstrate the prominence of the rate-dependent high initial stiffness feature in high damping rubber at low stretch level. A modified hyperelastic model is proposed to represent the rate-independent elastic responses including the high initial stiffness feature. A comparative evaluation is carried out to display the better performance of the proposed hyperelastic model than conventional ones over the strain range in representing the equilibrium and the instantaneous responses. The hyperelastic model is incorporated in a finite deformation rate-dependent model structure. A parameter identification scheme is proposed to identify the parameters for the equilibrium and instantaneous responses from the experimental data. The difficulties of direct application of infinitely fast or slow loading rate to such highly viscous materials to obtain these responses and thereby to identify the nonlinear elastic parameters are overcome. The proposed scheme is applied to three types of specimens including natural rubber and high damping rubber. Finally, numerical results obtained from the finite deformation rate-dependent model are compared with the test results to verify the adequacy and robustness of the proposed parameter identification scheme.

Micromechanics-based prediction of creep failure of hard rock for long-term safety of high-level radioactive waste disposal system

A high-level radioactive waste disposal project is under way in Japan. Isolation of the radioactive waste in a rock formation at great depth is considered as one of the promising disposal methods. Before proceeding with the disposal project, however, assessment of the long-term stability of rock mass surrounding waste packages is necessary. This paper presents a micromechanics-based model for predicting the creep failure of hard rock under compression. The subcritical crack growth due to stress corrosion cracking and interaction effects between cracks are considered as the main mechanisms of creep failure. An evolution problem of two interacting cracks is formulated and creep failure following tertiary creep is represented as unstable extension of the interacting cracks in the present model. The time to failure is calculated for different values of axial stress, confining pressure, and environmental conditions such as temperature and presence of water. The effects of water, temperature, and stress states on the long-term behavior are also included in the proposed model.

Stress and time-dependent failure of brittle rocks under compression: A theoretical prediction

A micromechanics-based continuum theory called interaction field theory (IFT) can reproduce localization phenomena such as shear faulting and axial splitting of rock under compression. The validity of IFT is examined by comparing its predictions of short-term strength and creep behavior of hard rock with reported experimental data. The theory is formulated through an averaging scheme for an elastic solid containing many microcracks. The growth of the microcracks is assumed to occur through two mechanisms: stress-induced crack growth and stress corrosion. Failure of rock under compression is known to be governed by the interactive behavior of microcracks. Yet in many earlier analyses the information on interaction is lost through conventional averaging schemes. IFT introduces a new field quantity which represents the interaction effect and the associated governing integral equation. IFT reproduces not only inelastic deformation of rock but also eventual macroscopic failure due to localization of microcracking. In the numerical analysis of short-term behavior, macroscopic failure is reproduced as a bifurcation from a homogeneous state of deformation into a localized one. The strengths are obtained as a result of numerical analysis with material constants of an intact matrix and the quantities related to initial defects. The strengths of Westerly granite obtained as a function of the confining pressure are compared with published experimental data. For time-dependent behavior of hard rock, creep tests of granite are analyzed. Comparisons are made between experimental failure times and numerical results for different confining pressures and environmental conditions.

A continuum theory for solids containing microdefects

Abstract The conventional continuum theory is based on the constitutive equations that prescribe relations between the average stress and strain, valid when the local deformation is more or less uniform. However, when the deformation is localized, the effects of interaction among microdefects become important, and must be included in the formulation of any effective continuum theory. One promising way of establishing a continuum theory that can capture localization phenomena, is to use micromechanics. In this study, we establish a micromechanics-based continuum theory (named interaction field theory) which can model localization phenomena, such as shear failure in rocks or shear band formation in sands under compression. A new field variable (interaction field) that characterizes the effects of interaction among microdefects is introduced, and its governing integral equation is formulated. Although the technique is applicable to any material with any microstructure, for an illustration the theory is formulated and used to study the behavior of rocks under compression. Numerical results are given that illustrate the difference between the proposed theory and the conventional continuum damage mechanics. It is confirmed that the proposed theory can describe the localization process by microcracking in shear failure and axial splitting of rocks under compression.

Measurement of Lateral Deformation in Natural and High Damping Rubbers in Large Deformation Uniaxial Tests

In testing the mechanical behavior of rubbers, the incompressibility assumption is used to predict the deformed cross section under loading and thereby to calculate the true stress. There are, however, cases where rubbers can undergo considerable volumetric deformation in large strain experiments. Microstructural investigation through a scanning electron microscope was carried out on a void-filled natural rubber specimen to clarify the effect of voids on the compressibility feature. The microstructure of the natural rubber was observed qualitatively and quantitatively in uniaxial tension and compared to the microstructure in the underformed condition. The existence of the compressibility feature in the void-filled rubber was confirmed from a microstructural viewpoint. The findings indicate the necessity of accurate measurement of the deformed cross section in mechanical tests to obtain the true stress. To this end, an experimental setup capable of measuring the deformed cross section of the rubber specimens subjected to large uniaxial compression is proposed. To do this, the accuracy of laser beams is used for measurement of distance and a mechanical jig is developed to synchronize the movement of the laser transducer with the vertical crosshead of the load cell of a computer-controlled servohydraulic testing machine. Thus the constraints associated with conventional strain gages in measuring large strains are overcome. Finally, two natural rubber specimens and one high damping rubber specimen were tested in the proposed setup to display the adequacy of the developed device in measuring lateral deformation of rubber-like highly deformable solids in large strain uniaxial testing.

Seismic Performance of a Highway Bridge with Different Modeling Techniques for Laminated Rubber Bearings at a Low Temperature

The current study is devoted towards evaluating the effectiveness of modeling of natural rubber bearings (RBs) and lead rubber bearings (LRBs) on seismic responses of a highway bridge by conducting nonlinear dynamic analysis for six distinct ground motions of level-2 earthquake applied in the longitudinal direction. Three analytical models of isolation bearings are considered for comparison: the conventional design models including the equivalent linear model and the bilinear model, a rate-dependent rheology model, and a proposed simplified model. The novelty of the proposed simplified model is to reproduce the nonlinear elasto-plastic behavior along with strain hardening at high strain levels. Model parameters for the isolation bearings are evaluated from experimental results at low temperature (-20°C). A numerical algorithm for solving the first order governing differential equation of the rheology model has been developed to implement into nonlinear dynamic analysis software. The dynamic responses of the isolation bearings and the rotation responses of the plastic hinge in concrete piers are compared for different modeling. The effect of modeling the isolation bearings at low temperature is significantly observed in the responses indicating that a careful selection of isolation bearings model is imperative for seismic design of an isolated bridge system.