Dynamic Constitutive Relation Research Articles

Biaxial experimental and analytical characterization of a dielectric elastomer

Electroactive polymers (EAPs) have emerged as a strong contender for use in low-cost efficient actuators in multiple applications especially related to biomimetic and mobile-assistive devices. Dielectric elastomers (DE), a subcategory of these smart materials, have been of particular interest due to their large achievable deformation and favourable mechanical and electro-mechanical properties. Previous work has been completed to understand the behaviour of these materials; however, their properties require further investigation to properly integrate them into real-world applications. In this study, a biaxial tensile experimental evaluation of 3M™ VHB 4905 and VHB 4910 is presented with the purpose of illustrating the elastomers’ transversely isotropic mechanical behaviours. These tests were applied to both tapes for equibiaxial stretch rates ranging between 0.025 and 0.300 s−1. Subsequently, a dynamic planar biaxial visco-hyperelastic constitutive relationship was derived from a Kelvin–Voigt rheological model and the general Hooke’s law for transversely isotropic materials. The model was then fitted to the experimental data to obtain three general material parameters for either tapes. The model’s ability to predict tensile stress response and internal energy dissipation, with respect to experimental data, is evaluated with good agreement. The model’s ability to predict variations in mechanical behaviour due to changes in kinematic variables is then illustrated for different conditions.

Experimental and Numerical Study on the Dynamic Compressive Properties of Concrete

Using electro-hydraulic servo-controlled testing system, the effects of strain rate on C30, C50 and C60 grade concrete are investigated in tests at the strain rates (10-5/s-10-1/s) in this paper. Based on the test results, the relationships between uniaxial compressive strength and strain rate are built, and the dynamic uniaxial compressive constitutive relationships of concrete are developed. Using the dynamic compressive constitutive relationship and Concrete damaged plasticity model in ABAQUS finite element program, the dynamic compressive properties of the three grades concrete are simulated, and the contrasts with test data are made.

Dynamic behavior of a woven glass-fiber-reinforced polymer composite at high strain rates and its dynamic constitutive relationship

ABSTRACTThe dynamic behavior of a woven glass-fiber-reinforced polymer composite at different strain rates was investigated. Regarded as a transversely isotropic material, dynamic compression tests of the composite in the normal and tangent directions were conducted by Split-Hopkinson pressure-bar devices. The experimental results show: (1) This composite is a viscoelastic material, and the dynamic compression-failure stress of the material indicates a distinct strain-rate hardening effect. The compression-failure stress in the normal direction increases by almost 30% when the strain rate changes from 900/s to 2000/s. The failure stress in the tangent direction is enhanced by 34% when the strain rate increases from 700/s to 2000/s. The failure stresses of the composite depend linearly on the strain rates, and the corresponding strain-rate hardening factors are 0.14 and 0.046 for the normal and tangent directions, respectively. (2) The dynamic compression-failure stresses and failure strains in the normal direction are significantly larger than the corresponding values in the tangent direction at different strain rates. Based on these results, the modified ZWT viscoelastic model was adopted, and the constitutive relationships of the composite in two directions are presented for characterizing their dynamic compression response.

A Study on High Temperature and High Strain Rate Dynamic Constitutive Relation of Q345 Steel

A Study on High Temperature and High Strain Rate Dynamic Constitutive Relation of Q345 Steel

Test on dynamic characteristics of subgrade of heavy-haul railway in cold regions

Dynamic characteristics of heavy-haul railway subgrade under vibratory loading in cold regions are investigated via low-temperature dynamic triaxial tests with multi-stage cyclic loading process. The relationship between dynamic shear stress and dynamic shear strain of frozen soil of subgrade under train loading and the influence of freezing temperatures on dynamic constitutive relation, dynamic shear modulus and damping ratio are observed in this study. Test results show that the dynamic constitutive relations of the frozen soils with different freezing temperatures comply with the hyperbolic model, in which model parameters a and b decrease with increasing freezing temperature. The dynamic shear modulus of the frozen soils decreases with increasing dynamic shear strains initially, followed by a relatively smooth attenuation tendency, whereas increases with decreasing freezing temperatures. The damping ratios decrease with decreasing freezing temperatures. Two linear functions are defined to express the linear relationships between dynamic shear modulus(damping ratio) and freezing temperature, respectively, in which corresponding linear coefficients are obtained through multiple regression analysis of test data.

Experimental Study on Dynamic Mechanical Properties of Galvanized Iron Wire under Seismic Strain Rate

This paper focuses on the mechanical properties of galvanized iron wire under various conditions of earthquake-type strain rate. The dynamic tensile test of galvanized iron wire was conducted on MTS New 810 electro-hydraulic servo-controlled testing system. The dynamic tensile constitutive relationship of galvanized iron wire was proposed under seismic strain rate. The accuracy of the proposed constitutive relationship of galvanized iron wire was verified by comparing with reinforcing steel.

Status Analysis of the Frozen Soil’s Dynamics Parameter Study

In this paper, the author points out several key problems needed to be solved about the dynamics of frozen soil by reviewing related literatures about hysteretic curve of frozen soil ,dynamic constitutive relation and dynamical parameter. The problems are the insufficient understanding on morphological characteristics of hysteretic curve and how to transform qualitative understanding into quantitative understanding about morphological characteristics of hysteretic curve. The problem is the rationality of selecting the dynamic constitutive model, namely how to establish the engineering applicable model which conforms to the actual soil mechanics performance.The problem is the rationality of the calculation method about dynamic elastic modulus and damping ratio, namely how to define dynamic modulus of elasticity of frozen soil correctly and the limitation of using the classical method to calculate the damping.

Dynamic Mechanical Properties and Constitutive Relation of an Aluminized Polymer Bonded Explosive at Low Temperatures

Polymer bonded explosives (PBXs) are widely used as energetic fillings in various warheads, which maybe are utilized under extreme environments, such as low or high temperatures. In this paper, the dynamic response of an aluminized polymer bonded explosive was tested at a range of temperatures from −55°C to −2°C and a fixed loading strain rate (~700 s−1) with the split Hopkinson pressure bar (SHPB). The PBX tested is aluminized, which contains 76 wt% RDX, 20 wt% aluminum powder, and 4 wt% polymer binder, respectively. The results show that the effect of temperature on the strength of the PBX is obvious at the tested strain rates. Based on the experimental results and prophase studies, a constitutive model was obtained, in which the effect of temperature and strain rate were considered. The modeling curves fit well with the experimental results, not only at low temperature under 0°C, but also at room temperature (20°C). The model may be used to predict the dynamic performances of the PBXs in various environments.

Mechanical properties of a silty clay subjected to freezing–thawing

The structure of soil will change a lot after freezing and thawing. The mechanical properties and the microstructures are quite different from those of the undisturbed soil. Based on the static triaxial tests and dynamic triaxial tests, this paper studied the mechanical characteristics of a silty clay and quantitatively analyzed the scanning electron microscopy (SEM) images of the silty clay before and after freezing and thawing. According to the static triaxial test and the disturbed state concept (DSC), the constitutive relationship of the thawing soil was investigated. The dynamic triaxial tests were conducted to study the dynamic constitutive relationship of the thawing soil and the mechanical parameters were compared with those of the undisturbed soil. The parameters of the microstructures of silty clay were extracted to analyze the influences of the freezing and thawing on silty soil.

Research on stamp charging car coal box pressure through field test

Coal box pressure has great significance in stamp charging car design. Because of the complexity of the dynamic constitutive relation of the coal powder, the pressure is usually considered in the design as a linear load, which presents neither the instantaneous maximum impact nor the variation during the stamping process, and therefore lacks accuracy. In this research, to obtain a more accurate box pressure, a series of field tests have been conducted, which included side wall tests, bottom plate tests and proof tests. The side wall and bottom plate pressures have been investigated through separating the pressure as ‘impulse pressure’ and ‘coal pressure’, which decouples the pressure curves from the side wall and bottom plate tests. As a consequence, a method to calculate box pressure at any time during the stamping has been derived through the analysis of statistic test results. To verify the method, a finite element method (FEM) model has been built and applied with pressures from the method. The FEM results fit well with the proof test result, which indicates that the method is capable of being used for stamp charging car design. In addition, the paper presents some statistic conclusions, such as stamping effect depth, which is useful for further researches.

MODELING FLUID FLOWS IN DISTENSIBLE TUBES FOR APPLICATIONS IN HEMODYNAMICS

We present a lattice Boltzmann (LB) model for the simulation of hemodynamic flows in the presence of compliant walls. The new scheme is based on the use of a continuous bounce-back boundary condition, as combined with a dynamic constitutive relation between the flow pressure at the wall and the resulting wall deformation. The method is demonstrated for the case of two-dimensional (axisymmetric) pulsatile flows, showing clear evidence of elastic wave propagation of the wall perturbation in response to the fluid pressure. The extension of the present two-dimensional axisymmetric formulation to more general three-dimensional geometries is currently under investigation.

Dynamic Constitutive Relation and Fracture Model of Q235A Steel

Strength and ductility data for Q235A steel from 20 oC to 950 oC was obtained from a series of experimental tests. The stress rate sensitivity was studied by conducting Split-Hopkinson Tension Bar (SHTB) test and uniaxial tension test on smooth cylindrical specimens while the influence of stress triaxiality on ductility was revealed by conducting upsetting tests, tension tests on pre-notched cylinder specimens and torsion tests on SASs. Slightly modified versions of the two Johnson–Cook (J–C) models describing flow stress and fracture strain are presented to characterize the properties of Q235A steel as function of strain rate, temperature and stress triaxiality. Corresponding model parameters were calibrated based on the test data and with the help of finite element calculation. It was found that the modified Johnson–Cook (MJC) models give more close predictive results compared with the original J–C models.

Effective Dynamic Constitutive Relations for 3-D Periodic Elastic Composites

ABSTRACTCentral to the idea of metamaterials is the concept of dynamic homogenization which seeks to define frequency dependent effective properties for Bloch wave propagation. Recent advances in the theory of dynamic homogenization have established the coupled form of the constitutive relation (Willis constitutive relation). This coupled form of the constitutive relation naturally emerges from ensemble averaging of the dynamic fields and automatically satisfies the dispersion relation in the case of periodic composites. Its importance is also notable due to its invariance under transformational acoustics. Here we discuss the explicit form of the effective dynamic constitutive equations. We elaborate upon the existence and emergence of coupling in the dynamic constitutive relation and further symmetries of the effective tensors.

A Dynamic Constitutive Model of Saturated Remolded Loess

A series of dynamic triaxial tests were performed to study a dynamic constitutive relationship of saturated remolded loess under cyclic loading. A new dynamic rational function constitutive model based on damping ratio was proposed. The model assumed the calculated damping ratio equaled to the measured damping ratio and the hysteresis curve was consisted by two curves accorded with rational function. This not only ensured that the theoretical hysteresis curve reflected the real energy dissipation of remolded loess but also retained the high calculated efficiency of this model. The hysteresis curve equation under constant amplitude symmetric loading was deduced and results of this model were verified by the tests.

A New Method for Dynamic p-y Curves of Pile-Cap Structure in Layered Soil

Lateral dynamic response of pile foundation in liquefiable soil has been one of the focal problems of the geotechnical engineering field and varieties of test methods are put forward by experts and scholars. In the dissertation, a shaking table test is based on and a new calculation method is involved too. It’s the first time that using Fiber Prague Grating (FBG) technology in the method of study on lateral dynamic response of pile foundation in liquefiable soil. Experimental results indicate that calculation by method of FBG is more accurate than that by acceleration integral method. Data processing shows that p-y curve of pile foundation in liquefiable soil can be better to indicate the actual dynamic constitutive relation, and it establishes the theoretical basis of experimental study and engineer application of pile foundation in liquefiable soil

Markov Model for Dynamic Analysis of Rock-Soil Structure

Dynamic analysis of structure of rock-soil material is a difficulty in structure analysis of rock-soil material. Dynamic analysis referred here is equivalent to plasticity analysis in classical elasticity/plasticity theory. But, for the structure of rock-soil material, the granules form a structure in the form of network, which makes dynamic analysis especially complex. We attempt to simplify granular form in this study, and construct a Markov model of structural evolution of system according to finite connection modalities between granules. Connection modality distributions for each structural state are obtained using recursion technique. Next, depending on connection modality distribution, we obtain the mechanical and geometric parameters of the system, thus stiffness-strength-displacement relation can be established. This relation serves as the basis for building dynamic constitutive relationship for rock-soil material. Literature on relevant subjects has been rarely found so far, and our discussion is only a tentative exploration.

Fracture Model of the Failure Wave in the Shocked Brittle Materials

A new failure model was developed to describe the failure wave formation and propagation in shocked glass. The progressive percolation of microcracks into the stressed body gives rise to the failure wave phenomenon which could be regarded as a diffusion process. The propagation of failure front is governed by a nonlinear diffusion equation. The dynamic damage constitutive relation is built up to compute the stress state in the material through the failure process. Numerical results are presented and compared to lateral stress gauge measurements in shocked glasses. It is shown that the proposed model can capture the essence of the failure wave phenomenon.

Fracture Model of the Failure Wave in the Shocked Brittle Materials

A new failure model was developed to describe the failure wave formation and propagation in shocked glass. The progressive percolation of microcracks into the stressed body gives rise to the failure wave phenomenon which could be regarded as a diffusion process. The propagation of failure front is governed by a nonlinear diffusion equation. The dynamic damage constitutive relation is built up to compute the stress state in the material through the failure process. Numerical results are presented and compared to lateral stress gauge measurements in shocked glasses. It is shown that the proposed model can capture the essence of the failure wave phenomenon.

Study on Stochastic Damage Constitutive Relation for HSHPC Material Subjected to Uniaxial Tension Stress

Based on the kind of damage constitutive models, such as spring friction block model and spring model, which are proposed for ordinary concrete by domestic and foreign scholars, and taking the differences which are caused by different failure mechanisms in mechanical properties of HSHPC and ordinary concrete into consideration, this paper presents the spring-friction block model which is suitable for revealing the stochastic damage constitutive relation of HSHPC material subjected to uniaxial tension stress. By introducing the failure strain stochastic field of concrete material subjected to uniaxial compressive stress, and according to the principle of energy conservation during the process of damage failure, the stochastic damage constitutive equation of HSHPC material subjected to uniaxial tension stress is derived. The theoretical results agree well with the experimental conclusions, and it shown that the proposed stochastic damage constitutive relation can objectively reflect the failure mechanism of HSHPC material. The research achievements will provide a basic research method for establishing the dynamic damage constitutive relation of HSHPC material.

Overall dynamic properties of three-dimensional periodic elastic composites

This article presents a method for the homogenization of three-dimensional periodic elastic composites. It allows for the evaluation of the averaged overall frequency-dependent dynamic material constitutive tensors relating the averaged dynamic field variable tensors of velocity, strain, stress and linear momentum. Although the form of the dynamic constitutive relation for three-dimensional elastodynamic wave propagation has been known, this is the first time that explicit calculations of the effective parameters (for three dimensions) are presented. We show that for three-dimensional periodic composites, the overall compliance (stiffness) tensor, as produced directly by our formulation, is Hermitian, regardless of whether the corresponding unit cell is geometrically or materially symmetric. Overall, mass density is shown to be a tensor and, like the overall compliance tensor, always Hermitian. The average strain and linear momentum tensors are, however, coupled, and the coupling tensors are shown to be each others' Hermitian transpose. Finally, we present a numerical example of a three-dimensional periodic composite composed of elastic cubes periodically distributed in an elastic matrix. The presented results corroborate the predictions of the theoretical treatment illustrating the frequency dependence of the constitutive parameters. We also show that the effective properties calculated in this paper satisfy the dispersion relation of the composite.