Degradation of elastic modulus in elastoplastic coupling with finite strains

An elastic potential W is postulated for the case of the finite-strain theory of elastoplastic coupling with damage effects. The potential is defined in terms of the invariants of two internal variables p and q. The internal variables are used to express the degradation of the elastic stiffness tensor due to the accumulation of plastic strains. The material damage is independently introduced to both Lame's coefficients H and G. The physical significance of this softening of the elastic stiffness is demonstrated experimentally in uniaxial loading, reverse loading of metals at finite strains.

For elastoplastic coupling, the Il'Iushin postulate does not yield normality of the plastic strain increment. An associative flow rule is postulated in this work for the combined components of the plastic strain increment and the elastic coupling strain increment.

The formulation is implemented in the Langrangian coordinate system. Through the use of the Oldroyd or Truesdell stress rate, the equivalent consistent spatial coordinate formulation is presented.     

On strain localization analysis of elastoplastic materials at finite strains

The problem of strain localization into planar bands of rate-independent elastoplastic solids with smooth yield surface and plastic potential is analyzed reconsidering the work of Rice and Rudnicki in 1980. It is shown that strain localization with elastic unloading on one side of the band first becomes possible either at localization in the comparison solid corresponding to the loading branch of the constitutive equation or at the snap-back threshold. The elastic unloading is shown to start from the condition of neutral loading, occurring in fact at the onset of localization. The case of localization with elastic unloading into the band and plastic loading outside that was not considered by Rice and Rudnicki is taken into account.     

Conditions for the existence of discontinuity surfaces of irreversible strains in elastoplastic media

Constraints are obtained on the stresses of a plastically compressed elastoplastic medium at which the occurrence of discontinuities of irreversible strains is possible. The loading surfaces are taken to be piecewise linear closed surfaces. Velocities of motion of irreversible-strain discontinuity surfaces are calculated.     

An experimental determination of the fields of strains and stresses in the elastoplastic range

In order to determine the fields of strains and stresses in the elastic and plastic ranges, for the plane-stress problem, a so-called chromorheological (CHR) model has been utilized. On one side of the model the development of plastic deformations, including the elastoplastic boundaries at any stage of loading, can be either visually observed or recorded on film. On the other side of the model, a birefringent coating is adhered from which regular experimental data can be obtained. These data, together with the yield condition, render the possibility of finding the state of stresses at all the points of the known elastoplastic boundaries. The problem of stress in the plastic range is statically determinate. The experiment provides all the data on the boundaries, and thereby the field of stresses in the plastic range can be calculated. The field of strains in the elastic and plastic zones can be obtained by the well-known method of photoelasticity. In this way, the relationship between stresses and strains in the plastic zones can be worked out. The effectiveness of the approach on a strip with a central hole has been proven by experimental research.     

A 3-phase model for the numerical analysis of semi-crystalline polymer films in finite elastoplastic strains

In this paper, the mechanical behavior of semi-crystalline polymer films in finite elastoplastic strains is investigated. A 3-phase constitutive model has been specially developed in a previous paper and validated for various materials in both uniaxial and biaxial uniform hot drawing. In the present study, the numerical implementation of this 3-phase model in a finite element software is outlined in the perspective of using this model in more general non-uniform cases of complex geometries and/or loadings. In the present case, only polyethylene films at room temperature are considered. First, uniaxial tensile experimental tests are performed so as to calibrate the model parameters. Then, for validation purposes, two series of experimental tests are conducted on tensile specimens with central holes and double edge notched tensile (DENT) specimens. During these tests, digital image correlation is used to analyze the strain (or displacement) field history during loading. Finally, numerical computations are performed with the help of the finite element software including the 3-phase model previously implemented (cohesive elements are also needed for the simulation of the crack propagation in DENT specimens). In both cases, the comparison between the experimental and numerical force–displacement curves, together with the comparisons between the experimental and numerical strain fields at different times, give very satisfactory results.     

Electroconvection of liquid dielectrics

Ponderomotive forces, which are responsible for electroconvection, were investigated in relation to the properties of the liquid and the strength of the electric field of an infinite charged plate. The obtained solutions were used to obtain a parameter of the relative intensification of heat transfer in various dielectrics in an external electrostatic field.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 13–18, July–August, 1971.     

Modeling viscoelastic dielectrics

Dielectric elastomers, as an important category of electroactive polymers, are known to have viscoelastic properties that strongly affect their dynamic performance and limit their applications. Very few models accounting for the effects of both electrostatics and viscoelasticity exist in the literature, and even fewer are capable of making reliable predictions under general loads and constraints. Based on the principles of non-equilibrium thermodynamics, this paper develops a field theory that fully couples the large inelastic deformations and electric fields in deformable dielectrics. Our theory recovers existing models of elastic dielectrics in the equilibrium limit. The mechanism of instantaneous instability, which corresponds to the pull-in instability often observed on dielectric elastomers, is studied in a general non-equilibrium state. The current theoretical framework is able to adopt most finite-deformation constitutive relations and evolution laws of viscoelastic solids. As an example, a specific material model is selected and applied to the uniform deformation of a dielectric elastomer. This model predicts the stability criteria of viscoelastic dielectrics and its dependence on loading rate, pre-stress, and relaxation. The dynamic response, as well as the hysteresis behavior of a viscoelastic dielectric elastomer under cyclic electric fields, is also studied.     

On thermoelastic dielectrics

Constitutive equations for a linear thermoelastic dielectric are derived from the energy balance equation assuming dependence of the stored energy function on the strain tensor, the polarization vector, the polarization gradient tensor and entropy. A method is indicated for constructing a hierarchy of constitutive equations for materials with arbitrary symmetry by introducing various thermodynamic potentials. Maxwell's relations are constructed for the thermodynamic potential W^L. The entropy inequality is used to obtain stability conditions for an elastic dielectric in equilibrium under prescribed boundary constraints. Frequencies are explicitly determined for a plane wave propagating along the x₁-axis in an infinite centro-symmetric isotropic thermoelastic dielectric.     

Instability of elastoplastic plane flows

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 152–156, May–June, 1991.     

Buckling of an elastoplastic bar

Buckling of a bar of an elastoplastic material is studied. It is shown that for any (σ-?) diagram of the bar material, the limit load (the longitudinal external force) in dimensionless variables that the bar can withstand does not exceed the current bending stiffness of the most loaded (in terms of the bending moment) section.