Generalized scleronomic model of the harmonic deformation of elastoviscoplastic bodies

Сенченков, И. К.; Zhuk, Ya. A.; Tabieva, G. A.; Chervinko, O. P.

doi:10.1007/bf02700655

Cited by 4 publications

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“…Thus, the standard linearization scheme leads to a monoharmonic model equivalent to the exact energy model. [47,48]. An analysis of the complex characteristics obtained by the standard harmonic-linearization scheme shows that the loss moduli ′′ G and ′′ λ are determined by the period-average dissipation rate.…”

Section: Harmonic-linearization Method Standard Schemementioning

confidence: 98%

“…By analogy with stresses, we arrive at a complex equation for amplitudes [47,48]:~⑀ p = λe, (2.12) whereλ is the complex plastic coefficient,λ λ λ = ′− ′′ i . It is a matter of direct verification to show that the approximate equations (2.3) The former (Π s ) may be regarded as a parameter reflecting the period-average or maximum stored energy [55].…”

Section: Harmonic-linearization Method Standard Schemementioning

confidence: 99%

“…Such an idea can be gained by comparing the solutions of specific classes of problems obtained based on the exact and each of the approximate models. [43,44,47,97]. Relations …”

Section: Mechanical Features Of Various Harmonic-linearization Schemesmentioning

confidence: 99%

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Modeling the thermomechanical behavior of physically nonlinear materials under monoharmonic loading

2004

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We analyze approximate approaches to the modeling of the thermomechanical behavior of physically nonlinear materials under harmonic loading. The approaches are based on various harmonic-linearization schemes and the concept of complex moduli. Mechanical and mathematical features of various schemes are considered. Some modifications of the model are proposed to account for various aspects of material behavior under harmonic loading. The problems of vibration and dissipative heating of physically nonlinear bodies are formulated. The main thermomechanical characteristics are analyzed for some classes of problems.Introduction. Many structural elements and technological objects experience cyclic deformation during use or treatment [2,3,[30][31][32]61]. Loads are sometimes so high that the deformation process becomes nonlinear and mechanical elements may suffer low-cycle fatigue. Apart from purely mechanical fatigue failure, polymeric products may undergo thermal failure, i.e., softening or even melting due to vibrational heating, which is because of high hysteresis losses and low heat conductivity [32,59,60].In the cases mentioned, modeling the thermomechanical behavior of nonlinearly dissipative materials is one of the major tasks to be accomplished in evaluating the durability or working characteristics of cyclically deformed bodies.There are currently two approaches to solve such problems. One employs the constitutive equations valid for arbitrary or, at least, rather wide classes of loading histories. Quasistatic problems for inelastic bodies, specifically beams and plates, were addressed in [77,81,82]; and vibration problems for viscoplastic structures in [66,73,78,79].This approach was used to solve problems for thin-walled structural members (mainly beams) in a practically important formulation that allows for the elastoviscoplasticity and geometrical nonlinearity of the material. Such formulations in combination with well-tested computational schemes allow us to analyze mechanical effects of the interaction of physical and geometrical nonlinearities, specifically snap buckling of initially curved elements [92] and chaotic motions in such elements under harmonic loading [42,89].By using exact models under harmonic loading, we can study a number of effects accompanying vibrations such as snap buckling, drift of average plastic strain, dynamic buckling, chaotic motions, etc. Study of such processes is difficult because of

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Section: Harmonic-linearization Method Standard Schemementioning

confidence: 98%

Section: Harmonic-linearization Method Standard Schemementioning

confidence: 99%

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Modeling the thermomechanical behavior of physically nonlinear materials under monoharmonic loading

2004

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“…How to determine the parameters of the approximate model is described in Senchenkov et al (1997a), in detail. Specific parameters corresponding to the chosen material are taken from Zhuk andSenchenkov (2000, 2001).…”

Section: Numerical Analysismentioning

confidence: 99%

“…To overcome these difficulties in the specific case of harmonic loading, a simplified model of thermo-mechanically coupled processes was developed by Karnaukhov (1982), Senchenkov et al (1997a, b). The model is based on the concept of complex moduli, determined by a modified technique of equivalent linearization (Karnaukhov 1982;Senchenkov et al 1997a). In terms of these moduli, the initial problem is reduced to a scleronomous system of equations for complex amplitudes of mechanical field quantities -displacements, stresses, total and inelastic strains.…”

Section: Introductionmentioning

confidence: 99%

Monoharmonic Approach to Investigation of the Vibrations and Self‐heating of Thin‐wall Inelastic Members

Zhuk

Сенченков

2009

Journal of Civil Engineering and Management

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Abstract. An approximate formulation is given to a dynamic coupled thermo-mechanical problem for physically nonlinear inelastic thin-walled structural elements within the framework of a geometrically linear theory and the KirchhoffLove hypotheses. A simplified model is used to describe the vibrations and dissipative heating of inhomogeneous physically non-linear bodies under harmonic loading. Unsteady vibration self-heating problem is solved. The dissipative function obtained from the solution for steady-state vibrations is used to simulate internal heat sources. For the partial case of forced vibrations of a beam, the amplitude-frequency characteristics of the field quantities are studied within a wide frequency range. The temperature characteristics for the first and second resonance modes are compared.

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Correspondence principles for complex shear characteristics in a nonisothermal model of monoharmonic approximation for physically nonlinear materials

Chervinko

Сенченков

2008

Int Appl Mech

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The Bodner-Partom nonisothermal flow model and the generalized method of harmonic linearization are used to calculate the complex shear modulus and compliance for AMg-6 aluminum alloy. The strainand stress-controlled cycles of loading in the temperature range 20-400°C are considered. The correspondence between the shear modulus and the compliance is studied. It is similar to the inverse proportionality condition in the theory of linear viscoelasticity. It is established that representing the modulus and compliance as functions of the strain amplitude is better than as functions of the stress amplitude due to the universal description of the characteristics for soft and hard cycles and high accuracy of correspondence Introduction. Modeling the mechanical behavior of inelastic materials and structural members under cyclic loading is of theoretical and practical importance in studying the dissipation and accumulation of energy in materials, evaluating the highand low-cycle fatigue of structural members, damping vibrations, etc. [9,10,15,18,[20][21][22].A fundamental result in the theory of linear viscoelasticity is experimental and theoretical justification of the concept of complex mechanical characteristics that describe the behavior of a material under harmonic loading [1,3,11,17]. In these publications, the concept of complex characteristics was generalized to nonisothermal processes for specific classes (thermorheologically simple) materials. In linear viscoelasticity, the complex characteristics provide an exact description of the mechanical behavior of materials in stationary processes. For physically nonlinear materials, this concept was used together with various schemes of harmonic linearization to develop approximate models. The capabilities of these schemes were studied in [5,7,8]. It was established in [12,13] that determining the complex characteristics is an ambiguous procedure, and its result is greatly dependent on the choice of a functional space whose norm is used to approximate nonlinear (generally, polyharmonic) reactions of a material to harmonic loading by a monoharmonic process. By using a mechanical interpretation for such a norm, it is possible to find an approximation corresponding to the mechanical problem of interest. Relevant results are reviewed in [4,19].The publications cited above deal with isothermal processes. The complex characteristics are assumed independent of temperature. Such a model is applicable when thermal perturbations are small. It is obvious that it cannot describe such important processes as vibrational heating under loading of high amplitudes and vibrations at high external temperatures. Moreover, in justifying the concept of complex characteristics for nonlinear materials, it is of practical and methodological importance to test the principle of correspondence between the modulus and the compliance in the cases of soft (stress-controlled) and hard (strain-controlled) cyclic loading.The present paper uses the complete system of equations of the nonisothermal Bodner-...

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Generalized scleronomic model of the harmonic deformation of elastoviscoplastic bodies

Cited by 4 publications

References 4 publications

Modeling the thermomechanical behavior of physically nonlinear materials under monoharmonic loading

Modeling the thermomechanical behavior of physically nonlinear materials under monoharmonic loading

Monoharmonic Approach to Investigation of the Vibrations and Self‐heating of Thin‐wall Inelastic Members

Correspondence principles for complex shear characteristics in a nonisothermal model of monoharmonic approximation for physically nonlinear materials

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