One-dimensional wave propagation in an initially deformed incompressible medium with different behaviour in tension and compression

The propagation of 1-dimensional waves in an initially deformed incompressible medium with different moduli in tension and compression is investigated. Depending on the sign of the initial strains, various possibilities of propagation are shown to exist. The governing equations are nonlinear and a hardening or softening behaviour in shear may be present. Simple wave analytical solutions are given in a semi-infinite incompressible half-space. It is shown that in some situations, a shear pulse applied to the surface of an initially deformed half-space propagates linearly up to a specific value of the shear deformation and nonlinearly after that point.     

Strength criterion for materials with different strengths in tension and compression

It is shown that the fracture of materials which have different strengths in tension and compression and are highly sensitive to the sign of the spherical tensor can be described by using a criterion of the ductility of anisotropic bodies based on the invariance of the form of the limiting surface. Calculated values of breaking stress are compared with experimental values obtained by testing specimens of two types of concrete in a plane stress state. Translated from Problemy Prochnosti, No. 5, pp. 31–37, May, 1996.     

Harmonic wave propagation in viscoelastic heterogeneous materials Part II: Effective complex moduli

The effective complex moduli of a heterogeneous periodic viscoelastic medium has been determined through its dispersion and damping curves. These curves give the values of complex wave numbers in terms of frequencies and wave direction. The solution of Christoffel's equations of an equivalent viscoelastic homogeneous medium for judiciously selected wave directions provides us simple relations between complex wave numbers belonging to the heterogeneous medium and its effective complex moduli. Based on this method two examples have been treated. The one, a viscoelastic homogeneous material, to show the accuracy of this method. The other, a fiber composite material, to illustrate the applicability of the method.     

An anisotropic model of damage for brittle materials with different behavior in tension and compression

Zusammenfassung Der Artikel beschreibt ein kontinuummechanisches Schadensmodell für elastische Verformungen unter Berücksichtigung der Entstehung und des Wachstums von plättchen-förmigen Einschlüssen in spröden Werkstoffen. Das Modell beschreibt gleichzeitig das anisotrope Schadensverhalten und die verschiedenen Schadenbildungsprozesse unter Zug- und Druckbelastungen. Das zugehörige Werkstoffgesetz als auch die Schadensgleichungen beruhen auf der Theorie der irreversiblen Thermodynamik, wobei die notwendigen Modellparameter durch einfache Versuche bestimmt werden. Die theoretischen Ergebnisse werden experimentellen Daten für Grauguß unter zweiachsigen Spannungszuständen gegenübergestellt.

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The article outlines a continuum damage mechanics model for elastic deformation associated with the appearance and growth of parallel penny-shaped microcracks in brittle materials. The model is able to describe simultaneously the anisotropic nature of damage and the difference between the damaging processes under tensile and compressive loading types. Constitutive equation and damage evolution equations are developed on the basis of irreversible thermodynamic theory. Model parameters are determined from basic experiments formulated. The theoretical results are compared with the experimental data for two-dimensional stress states of gray cast iron.

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Support of the Alexander von Humboldt Stiftung (A.Z.) and of the DAAD (E.Y) is gratefully acknowledged.     

拉压弹性模量差异对泡沫铝夹芯板三点弯曲模拟的影响

泡沫铝材料是一种典型的拉压双模量材料,即受拉与受压时弹性模量不同。使用ABAQUS有限元软件对泡沫铝夹芯板的三点弯曲行为进行了模拟。首先,对泡沫铝芯层采用可压缩泡沫模型,通过对芯层的受拉区和受压区采用不同的弹性模量来讨论拉压弹性模量差异对夹芯板三点弯曲行为的影响。同时,在泡沫铝压缩响应一致的情况下,对可反映拉压弹性模量差异的孔洞模型和未考虑拉压弹性模量差异的可压缩泡沫模型的夹芯板三点弯曲模拟结果进行了比较。研究表明,泡沫铝芯层的弹性模量对夹芯板的三点弯曲行为模拟有较大影响。若不考虑泡沫铝拉压弹性模量的差异,得到的夹芯板三点弯曲情况下的加载刚度和屈服荷载明显偏低。     

Constitutive equations of creep under changing multiaxial stresses for materials with different behavior in tension and compression

A theory of creep that describes kinematic hardening of polycrystalline materials with different behavior in tension and compression is presented. A structure of the equivalent effective stress in the equation for creep deformation as well as structures of the equivalent effective stress in the describing creep hardening and of equivalent back stress in the describing thermal softening are based on three independent material characteristics obtained from uniaxial tension tests, uniaxial compression tests, and pure torsion tests for different values of constant stress at constant temperatures. A satisfactory agreement is obtained between the theoretical results and the experimental data of the creep under multiaxial loading with constant stresses for isothermal processes as well as under uniaxial nonproportional and multiaxial nonproportional loadings for both isothermal and nonisothermal conditions. Materialgleichungen für das Kriechen unter veräderlichen mehrachsigen Spannungszuständen für Materialien mit unterschiedlichem Verhalten unter Zug- und Druckbelastung Zusammenfassung Eine Kriechtheorie zur Beschreibung der kinematischen Verfestigung polykristalliner Materialien mit unterschiedlichem Verhalten unter Zug- und Druckbelastung wird vorgestellt. Die Gleichungen für die Kriechverformung und die Kriechverfestigung werden in Abhängigkeit von der äquivalenten effektiven Spannung formuliert. Die Gleichung zur Beschreibung der thermischen Erweichung hängt von einer äquivalenten Rückspannung ab. Alle Gleichungen basieren auf drei unabhängigen Materialeigenschaften, die aus einachsigen Zug-, einachsigen Druck- sowie reinen Torsionsversuchen für unterschiedliche konstante Spannungen und konstante Temperaturen bestimmt werden können. Es wird eine befriedigende Übereinstimmung dieser Theorie mit experimentellen Daten sowohl für Kriechen unter mehrachsiger Beanspruchung mit konstanten Spannungen in isothermen Prozessen als auch für einachsige und mehrachsig-nichtproportionale Belastungen unter isothermen und nichtisothermen Bedingungen gefunden.The research described in this paper is sponsored by the Alexander von Humboldt Foundation. The first writer wishes to thank Dr. Oleg Artyushenko, Ms. Oksana Kovalenko and Mrs. Elena Novichenko for helpful advises and fruitful discussions.     

Analysis of wave propagation in thick-section composite laminates using effective moduli

Effective moduli for thick-section composite laminates were used to represent the laminates as homogeneous but anisotropic media. Harmonic waves propagating parallel and normal to the layering were considered. Dispersion curves for various stacking sequences were obtained from the effective modulus method and from exact layer-by-layer analysis. The results indicate that for long wavelengths, the effective modulus solutions converge to the exact solutions. As the wavelength decreases, the effective modulus solution starts to deviate from the exact solution. The amount of deviation depends on the mode of wave motion, stacking sequence, and number of plies in the laminate. The effective modulus model together with a global-local method were also used to study the transient response in a layered cylinder subjected to blast loading. The stress fields obtained from the effective modulus model agreed very well with those obtained using layer-by-layer analysis.     

Stress-strain relations for composites with different stiffnesses in tension and compression

Some fibrous composites exhibit different mechanical properties in tension as compared to those in compression. Proper material modelling is required to enable correct behavioural prediction of components made of such composites. Though the models due to Ambartsumyan, Bert and Jones are often used, there are still many unanswered questions pertaining to material modelling. In Bert's model the strain transverse to the fibres and the shear strain are discontinuous when the fibre strain is zero. In Jones' model, cross compliances in tension-compression zones are assumed to depend on the magnitudes of principal stresses.Here we have proposed a new model for bimodulus orthotropic materials with zonewise symmetric linear constitutive laws valid for biaxial fields and dependent on the signs of both normal stresses and strains, referred to material axes. This model maintains strain continuity in the entire biaxial field and has ten independent elastic constants compared to eight each in Bert's and Jones' model. Applicability of the present model is illustrated by considering limited experimental data available on Aramid cord-rubber and ATJ graphite.List of symbols L, T Axes parallel and transverse to fibres - S _SS ^± Shear compliance for ± _LT - S _Lt ,S _Lc Compliances inL-direction for uniaxial tension and compression applied inL-direction - S _Tt ,S _Tc Compliances inT-direction for uniaxial tension and compression applied inT-direction - S _TL ^(t) Cross compliance corresponding to uniaxial load inL- orT-direction maintaining _L > 0 - S _TL ^(c) Cross compliance corresponding to uniaxial load inL- orT-direction maintaining _L < 0 - S _LL ⁺,S _TT ⁺,S _TL ⁺ Compliances when _L > 0 and _T > 0 - S _LL ^–,S _TT ^–,S _TL ^– Compliances when _L < 0 and _T < 0 - S _Lt ^– Compliance inL-direction when _L < 0 under the combined action of tensile _L and _T - S _Tt ^– Compliance inT-direction when _T < 0 under the combined action of tensile _L and _T - S _Lc ⁺ Compliance inL-direction when _L > 0 under the combined action of compressive _L and _T - S _Tc Compliance inT-direction when _T > 0 under the combined action of compressive _L and _T - ₁ , ₂ ; ₃, ₄ Parameters defined in Eqs. (12); (12) - _L , _T , _LT Strains with respect toL-,T-axes - _L , _T , _LT Stresses with respect toL-,T-axes - Orientation of fibres with respect toL-axis - S ₁₁,S ₂₁ Compliances referred to axes oriented at an angle toL-,T-axes     

Nonlinear large deflection buckling analysis of compression rod with different moduli

Many novel materials exhibit a property of different elastic moduli in tension and compression. One such material is graphene, a wonder material, which has the highest strength yet measured. Investigations on buckling problems for structures with different moduli are scarce. To address this new problem, first, the nondimensional expression of the relation between offset of neutral axis and deflection curve is derived based on the phased integration method, and then using the energy method, load–deflection relation of the rod is determined; second, based on the improved constitutive model for different moduli, large deformation finite element formulations are developed, and combined with the arc-length method, finite element iterative program for rods with different moduli is established to obtain buckling critical loads; third, material mechanical properties testing of graphite, which is the raw material of graphene, is performed to measure the tensile and compressive elastic moduli; moreover, buckling tests are also conducted to investigate the buckling behavior of this kind of graphite rod. By comparing the calculation results of the energy method and finite element method with those of laboratory tests, the analytical model and finite element numerical model are demonstrated to be accurate and reliable. The results show that it may lead to unsafe results if the classic theory was still adopted to determine the buckling loads of those rods composed of a material having different moduli. The proposed models could provide a novel approach for further investigation of nonlinear mechanical behavior for other structures with different moduli.     

Plastic wave propagation in materials with prestraining and strain rate history effects

Abstract

The plastic wave propagation in materials with prescribed prestraining and strain rate history effects is investigated. The development is within the framework of the endochronic theory of viscoplasticity. The stress‐time, strain‐time profiles and wave velocity at different strain levels have been obtained theoretically and presented for comparison with experimental data on 1100–0 A1. Furthermore, the difference between the total strain rate and the plastic strain rate in the calculation have been thoroughly disscussed.     

Modeling of high-frequency wave propagation in structured materials

This paper presents a theoretical investigation of ultrasonic wave propagation in a fabricated porous aluminum plate whose microstructure consists of columnar pores oriented normal to the plate surface. Attention is restricted to the symmetric modes which are seen to be compatible with a plane wave source whose wavefronts are vertically incident on the plate. The analysis shows the existence of two fundamental modes, a fast mode and a slow mode, which together transmit energy through the microstructure. The reflectivity and impedance properties of the plate are determined, and it is shown how these vary with frequency, pore spacing, and porosity. By varying the latter during the manufacturing process, a material may be fabricated whose acoustic impedance can be set to any desired value between that of water and solid aluminum.     

Models of ultrasonic wave propagation in epoxy materials

This paper is concerned with modeling ultrasonic wave propagation in epoxy materials to better understand NDE procedures and to provide reliable input to more complex models of guided wave propagation in layered structures. Different physical models are considered in the context of how well they simulate the (known) linear relationship between bulk wave attenuation coefficients and frequency. The identified models are then extended to simulate wave propagation in materials with mechanical properties, which vary gradually in the spatial dimension. This is achieved using electric circuit transmission line analogs to the viscoelastic mechanical system. Verifying experimental results are included.     

Benchmark problems for wave propagation in elastic materials

The application of the new numerical approach for elastodynamics problems developed in our previous paper and based on the new solution strategy and the new time-integration methods is considered for 1D and 2D axisymmetric impact problems. It is not easy to solve these problems accurately because the exact solutions of the corresponding semi-discrete elastodynamics problems contain a large number of spurious high-frequency oscillations. We use the 1D impact problem for the calibration of a new analytical expression describing the minimum amount of numerical dissipation necessary for the new time-integration method used for filtering spurious oscillations. Then, we show that the new numerical approach for elastodynamics along with the new expression for numerical dissipation for the first time yield accurate and non-oscillatory solutions of the considered impact problems. The comparison of effectiveness of linear and quadratic elements as well as rectangular and triangular finite elements for elastodynamics problems is also considered.     

Micromechanics of seismic wave propagation in granular materials

In this study experimental data on a model soil in a cubical cell are compared with both discrete element (DEM) simulations and continuum analyses. The experiments and simulations used point source transmitters and receivers to evaluate the shear and compression wave velocities of the samples, from which some of the elastic moduli can be deduced. Complex responses to perturbations generated by the bender/extender piezoceramic elements in the experiments were compared to those found by the controlled movement of the particles in the DEM simulations. The generally satisfactory agreement between experimental observations and DEM simulations can be seen as a validation and support the use of DEM to investigate the influence of grain interaction on wave propagation. Frequency domain analyses that considered filtering of the higher frequency components of the inserted signal, the ratio of the input and received signals in the frequency domain and sample resonance provided useful insight into the system response. Frequency domain analysis and analytical continuum solutions for cube vibration show that the testing configuration excited some, but not all, of the system’s resonant frequencies. The particle scale data available from DEM enabled analysis of the energy dissipation during propagation of the wave. Frequency domain analysis at the particle scale revealed that the higher frequency content reduces with increasing distance from the point of excitation.