Dynamic Constitutive Equations Research Articles

Inversion of image-only intrinsic parameters for steel fibre concrete under combined rate-temperature conditions: An adaptively enhanced machine learning approach

Concrete not only bears quasi-static loads during the service of engineering structures, but also bears impact or explosion due to accidental accidents, so more and more attention has been paid to the study of concrete deformation characteristics and stress distribution. Obtaining the correct constitutive parameters is crucial for the study of the mechanical behavior of concrete, and the determination of constitutive parameters is essentially an inverse process, which is very challenging. In this paper, third-order Bessel curves are used to construct dynamic constitutive equations for steel-fibre concrete under rate-temperature union conditions, and to establish a database of the constitutive parameters corresponding to the factors influencing the mechanical behaviour of concrete. In order to select highly accurate and adaptive intelligent inversion models, Firstly, the black-winged kite optimisation algorithm (BKA) has been improved by improving the black-winged kite leader condition and integrating the optimal perturbation strategy of Morlet wavelet factor, which proves the superiority of the MBKA algorithm by comparing it with the BKA, Dung Beetle Optimisation Algorithm (DBO), Grey Wolf Optimisation Algorithm (GWO), and Harris Hawk Algorithm (HHO) in searching for the optimal results. Secondly, based on the database, the MBKA-LSSVR model, MBKA-LSSVR-Adaboost model, CNN-GRU model and CNN-LSTM model were built sequentially, respectively. The final results show that the MBKA-LSSVR-Adaboost model has the highest accuracy and the best performance for the parameter Pi (i = 0,1,2,3), and the inverted stress-strain curve proves that the proposed method is effective and accurate in determining the proposed constitutive parameters.

Dynamic behaviour of adobe bricks in compression: The role of fibres and water content at various loading rates

This paper presents the results of an experimental research aimed at assessing the material performance of adobe bricks in compression for a wide range of induced strain rates, from statics to high velocity impact. Adobe connotes a traditional masonry whose bricks are made of sundried soil mixtures possibly reinforced with natural fibres and joined together using mud mortar. The inclusion of fibre and the presence of water in the mixture have a dominant effect on the mechanical performance of adobe bricks and masonry. Their influence on the dynamic behaviour of this material is quantified and interpreted in this study at high strain rates also with data produced through Hopkinson bar testing. Appropriate dynamic increase factors and constitutive equations for adobe materials in dynamics are also investigated. The paper presents the experimental campaign, shows the main results and offers qualitative and quantitative interpretations for the principal damage patterns observed.

The mechanical behaviour of polyvinyl butyral at intermediate strain rates and different temperatures

Polyvinyl butyral (PVB) is often used in laminated glass and windscreen for its high ductility and good adhesion with glass. Previous studies have shown that the mechanical properties of PVB are both rate-dependent and temperature-dependent. To investigate mechanical properties of PVB material under different strain rates and different temperatures, a series of tensile tests on 1.52 mm-thick PVB specimens are carried out, covering designed engineering strain rates from 0.1/s to 300/s and temperatures from −30 °C to 40 °C, using an Instron high-speed servo-hydraulic testing machine and temperature box. Corresponding true stress-true strain curves are obtained. The testing results are then analyzed and empirical formulae are derived for key mechanical property parameters. Finally, based on G’Sell model, dynamic constitutive equations are given at different temperatures for PVB.

Dynamic Mechanical Properties of Typical CFRP Laminate Under High-impact Compressive Loads

Because of its outstanding mechanical properties, carbon fiber reinforced plastic (CFRP) is widely used in structures bearing high-impact loads. In this study, based on the bridging model, the dynamic constitutive equations and yield criteria concerning the strain rate effect of composite material are used to analyze the optimal design and compressive strength of a CFRP laminate under high-impact compressive loads. The mechanical properties of laminates under different strain rates were calculated and compared with experimental results to verify the viability of improving the bridging model, where our theoretical results agreed with them. Structural design schemes based on this were analyzed and a ply scheme satisfying our requirements selected. Using this scheme, samples were manufactured and subjected to quasi-static and medium strain rate compressive tests, and the results agreed with theoretical calculations. This study can help design optimal CFRP structures for penetrator case under high-impact compressive loads and predict their properties.

Reissner stationary variational principle for nonlocal strain gradient theory of elasticity

Abstract The general form of Reissner stationary variational principle is established in the framework of the nonlocal strain gradient theory of elasticity. Including two size-dependent characteristic parameters, the nonlocal strain gradient elasticity theory can demonstrate the significance of the strain gradient as well as the nonlocal elastic stress field. Based on the Reissner functional, the governing differential and boundary conditions of dynamic equilibrium and differential constitutive equations of the classical and first-order nonlocal stress tensor are derived in the most general form. Additionally, the boundary congruence conditions are formulated and discussed for the nonlocal strain gradient theory. To exhibit the application value of Reissner variational principle, it is employed to examine the nonlinear vibrations of size-dependent Bernoulli-Euler and Timoshenko beams. In the case of immovable boundary conditions, employing the weighted residual Galerkin method, the homotopy analysis method is also utilized to determine the closed form analytical solutions of the geometrically nonlinear vibration equations. Consequently, the analytical expressions for the nonlinear natural frequencies of Bernoulli-Euler and Timoshenko nonlocal strain gradient beams are derived.

A new approach for studying the transient response of thin-walled beams of open profile with Cosserat-type micro-structure

In the present paper, the dynamic response of a three-layered thin-walled spatially curved beam of open profile is investigated. As a result of the homogenization of heterogeneous rheological parameters of such a beam, its behaviour could be described by the dynamic constitutive Cosserat equations characterizing a general isotropic, linear micropolar material. Under the action of nonstationary excitations on the beam, plane transient waves (surfaces of discontinuity) are generated in the beam. By the help of the generalized Hadamard–Thomas conditions of compatibility, the velocities of four types of transient waves are found from the set of dynamic Cosserat equations, and the recurrent equations have been obtained which allow one to determine the discontinuities in the desired values and discontinuities in the arbitrary order time-derivatives of these values on each of four waves. This procedure enables one to construct the desired values in terms of the ray series behind the wave fronts up to the boundary where the waves have been generated. The superposition of the ray series for four types of waves allows one to define completely each of the values to be found within the entire disturbed domain. As an example illustrating the proposed procedure for solving boundary-value dynamics problems for beams subjected to transient loading, the problem of the normal impact of a long elastic rod with a rounded end upon a lateral surface of a three-layered thin-walled beam of open profile is considered.

Dynamic mechanical properties and constitutive equations of 2519A aluminum alloy

To analyze the effects of strain rate and temperature on the flow stress of 2519A aluminum alloy, the dynamic mechanical properties of 2519A aluminum alloy were measured by dynamic impact tests and quasi-static tensile tests. The effects of strain rate and temperature on the microstructure evolution were investigated by optical microscopy (OM) and transmission electron microscopy (TEM). The experimental results indicate that 2519A aluminum alloy exhibits strain-rate dependence and temperature susceptibility under dynamic impact. The constitutive constants for Johnson–Cook material model were determined by the quasi-static tests and Hopkinson bar experiments using the methods of variable separation and nonlinear fitting. The constitutive equation seems to be consistent with the experimental results, which provides reference for mechanical characteristics and numerical simulation of ballistic performance.

The Dynamic Performance of Copper under Impact Loading

The incident wave and transmission wave varying with the time have been obtained by SHPB experiment. The relationship curve for stress and strain of material copper has also been obtained. The whole process has been numerical simulated by LSDYNA procedure. The results between the experiment and numerical simulation are accordance .It indicates that the dynamic constitutive equations can be researched by SHPB experiment with enough precision. With the primary gas gun, the dynamic properties of copper have been studied under high pressure. Hugoniot curve of metal materials have been obtained, which can be used to study the high- pressure equation of state. The parameters of the state equation have been obtained. The copper is often used to the dynamic test as the standard materials, so the dynamic performance of the copper self is so important.

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.

Dynamic tensile constitutive equations and fracture of metallic neodymium and lanthanum

Based on tensile tests, static on MTS and dynamic on the first tensile loading in optimized tensile split Hopkinson bar (TSHB) tests for neodymium (Nd) and lanthanum (La) sheet specimens, this study determined tensile constitutive equations of Nd and La. It was found that the Nd and La sheet specimens were fractured during the first tensile loading in TSHB tests. The transmitted and reflected pulses of TSHB tests for Nd and La sheet specimens computed with the determined tensile constitutive equations and the strain rate dependent fracture strain criterion could be consistent with the experimental data. The relation between the dynamic failure strength and the strain rate was discussed. The fractured Nd and La sheets of tensile tests were investigated by using scanning electron microscope. It was found that a transition from random to deterministic damage evolution patterns was notable as the strain rates increase for La sheet specimens while the transition unobserved for Nd sheet specimens.

Determination of Dynamic Constitutive Equations Based on an Information Criterion by the Elasto-Plastic Waves Propagation Analysis.

Previously, we presented the determination method of a dynamic constitutive equation with strain- rate sensitivity from the results of an uniaxial longitudinal impact compression test. The proposed method could derive an appropriate strain-rate sensitive dynamic constitutive equation as a polynomial without consideration based on underlying material physics. However, the method needs a lot of test results over a wide strain-rate range. This paper presents the determination method of a dynamic constitutive equation from a few impact test results. The proposed method determines unknown coefficients involved in a polynomial that appears dynamic constitutive relations of a material by nonlinear least squares method. Furthermore, the proposed method determines the optimum degree of a polynomial constitutive equation by AIC (Akaike information criterion). This paper, further, presents the split Hopkinson pressure bar method using a stepped striker bar. The proposed method can obtain the relations between the dynamic stresses and strain-rates in a wide range from a single impact test.

Dynamic constitutive equation of GFRP obtained by Lagrange experiment

The note presents a method of constructing dynamic constitutive equations of material by means of Lagrange experiment and analysis. Tests were carried out by a light gas gun and the stress history profiles were recorded on multiple Lagrange positions. The dynamic constitutive equations were deduced from the regression of a series of data which was obtained by Lagrange analysis based upon recorded multiple stress histories. Here constitutive equations of glass fibre reinforced phenolic resin composite(GFRP) in uniaxil strain state under dynamic loading are given. The proposed equations of the material agree well with experimental results.

Ｍａｌｖｅｒｎ型構成方程式を用いた金属粉末の動的圧粉解析

In powder Metallurgy process, some dynamic powder compaction methods have been proposed because they have advantages of giving uniform density distribution even for high-aspect-ratio parts and breaking surface oxides of powders, comparing with static powder compaction methods.Constitutive equations considering strain-rate effect are usually used to analyze the dynamic deformation of solid materials. One-dimensional dynamic analyses using static stress-strain relations were carried out so far. However, in case of powder materials, constitutive equation considering the strain-rate effect has not been applied.In this paper a Malvern-Type constitutive equation, Ee=σ+K(σ-f(e)) for powder materials is employed to analyze dynamic behavior of powder materials. A constant, K, in the equation is obtained by comparing the experimental and analytical results in terms of plastic strain distribution at longitudinal in a container. In the case of rapidly solidified Al-Li powder, K=2×105 is obtained.This method can widely be applicable to get dynamic constitutive equations for powders.

Determination Method for Dynamic Constitutive Equations Based on an Information Criterion.

This paper presents an easy determination method for the dynamic constitutive equations of materials with strain-rate sensitivity. The proposed method will easily determine a simple constitutive equation from the results of ordinary impact tests. Previously, the determination of dynamic constitutive equations is usually attempted from a metallographical or physical standpoint. Such attempts often need detailed consideration, and most of the derived equations become complex. Furthermore, the estimation of the involved unknown parameters in the equations is also difficult. If simple dynamic constitutive equations can be determined without especially physical considerations, the simulation for mechanical deformations caused by impact will become easy. Thus, this paper tries to determine dynamic constitutive equations as polynomials which can describe various curves and be easily treated. Polynomials approximate given data more precisely with increase in the number of the involved parameters. However, as the number of parameters increases, the calculation of the equations become more difficult. Furthermore, it is not necessarily appropriate that the equation fits measured data considerably precisely, because the measured data usually contain some errors. Therefore this paper proposes the determination method for dynamic constitutive equations based on an information criterion 'AIC'. The information criterion will evaluate the appropriateness of approximate equations and reveal the required minimum number of the parameters to be used. The proposed method demonstrates that 'AIC' will easily determine appropriate dynamic constitutive equations.

A unified continuum theory of liquid crystals

A unified continuum theory is proposed governing physical behavior of all liquid crystals whose molecules are modelled with rigid directors. Balance laws and constitutive equations are given and thermodynamic restrictions are obtained. Chiral and nonchiral liquid crystals are shown to differ only in their symmetry groups and smectic liquid crystals in a constraint on twist elasticities. Dynamic constitutive equations include translation and gyration viscosities coupled with heat conduction. The theory is shown to give the director (Oseen-Frank) theory under special conditions valid for that theory.

A unified continuum theory of electrodynamics of liquid crystals

A unified continuum theory is proposed governing the physical behavior of all liquid crystals subject to electromagnetic (E-M) fields. Balance laws, static and dynamic constitutive equations are given. Nematic, cholesteric, smectic, chiral and nonchiral liquid crystals are discussed. Constitutive equations include the effects of gyration viscosities coupled with heat and electric conduction and E-M fields. The second law of thermodynamics and conditions of material stability are used to restrict the material moduli. The theory is shown to give the director (Oseen-Frank) theory under special conditions valid for that theory.

Dynamic Constitutive Equations and Behaviour of Brass at High Strain Rates

This paper presents an experimental study of the mechanical properties of brass at high strain rates. The brass tested is the copperzinc alpha-beta and beta two-phase alloy in the cold-worked state. Experiments were conducted using an extended tension split Hopkinson bar apparatus. It is found that, at lower strain rates, the stress-strain curve is smooth, exhibiting no well-defined yield stress, but at higher strain rates the stress-strain curve not only shows a well-defined yield stress but also displays a very pronounced drop in stress at yield. The flow stress is found to increase with increasing strain rate, but the increase is more significant for the yield stress than for the flow stress, showing that the yield stress is more sensitive to the strain rate than the flow stress away from the yield point. Based on the experimental results, empirical strain-rate-dependent constitutive equations are recommended. The suggested constitutive equations provide a reasonable estimate of the strain-rate-sensitive behaviour of materials.

An Estimation of Dynamic Constitutive Equations of Carbon Steels by Means of the Nonlinear Least Squares Method. An Examination by the Use of Experimental Data.

An Estimation of Dynamic Constitutive Equations of Carbon Steels by Means of the Nonlinear Least Squares Method. An Examination by the Use of Experimental Data.

An Estimation of the Dynamic Constitutive Equations by using the Method of Nonlinear Least Squares. The Results of Estimation Using the Experimental Velues.

An estimation method of the dynamic constitutive equations using the observed strain data by means of the method of nonlinear least squares is described. By using this method some experiments were performed such that the constitutive equation for aluminum involving two unknown parameters was estimated using the strain wave and the residual strain profile induced in a finite-length bar subjected to longitudinal impact. The stress-strain rate curves obtained by using the estimated constitutive equations were compared with the ordinary experimental values. As a result, it was concluded that the present method is practically useful. It was also found that the estimation was enabled by either the experimental values of the strain wave or the experimental values of residual strain.

An Estimation of the Dynamic Constitutive Equations by using the Method of Nonlinear Least Squares.

An estimation method of the dynamic constitutive equations using the method of least squares is described. In this paper, the unknown parameters in the constitutive equations of which the functional form is known were estimated. The estimation is performed by using the method of nonlinear least squares utilizing the Gauss-Newton method because the constitutive equations are nonlinear. Numerical simulation were done such that the unknown parameters in the constitutive equation were estimated from the value of the strain wave in a long bar subjected to longitudinal impact. The stability of the estimation and influence of experimental error on the estimated parameters were examined. As a result, it was concluded that the present method is practically useful.