Mechanics of Time-dependent Materials 

About: Mechanics of Time-dependent Materials is an academic journal published by Springer Science+Business Media. The journal publishes majorly in the area(s): Viscoelasticity & Creep. It has an ISSN identifier of 1385-2000. Over the lifetime, 764 publications have been published receiving 13305 citations.

Poisson's Ratio in Linear Viscoelasticity – A Critical Review

Abstract: Poisson's ratio is an elastic constant defined as the ratio of thelateral contraction to the elongation in the infinitesimal uniaxialextension of a homogeneous isotropic body. In a viscoelastic materialPoisson's ratio is a function of time (or frequency) that depends on thetime regime chosen to elicit it. It is important as one of the materialfunctions that characterize bulk behavior. This paper develops the linear theory of the time- orfrequency-dependent Poisson's ratio, and it reviews work on itsexperimental determination. The latter poses severe difficulties in viewof the high accuracy required. Thus, reliable information on theviscoelastic Poisson's ratio is as yet rather scanty. The paper also reports on attempts to measure the Poisson's ratioof a viscoelastic material as a function of temperature. Lateralcontraction in creep and at constant rate of extension receivesattention as well.

Nonlinear Viscoelastic and Viscoplastic Constitutive Equations Based on Thermodynamics

Abstract: An approach to modeling the mechanical behavior of fiber reinforced and unreinforced plastics with an evolving internal state is described. Intrinsic nonlinear viscoelastic and viscoplastic behavior of the resin matrix is taken into account along with growth of damage. The thermodynamic framework of the method is discussed first. The Gibbs free energy is expressed in terms of stresses, internal state variables (ISVs), temperatureand moisture content. Simplifications are introduced based on physical models for evolution of the ISVs and on experimental observations of thedependence of strain state on stress state and its history. These simplifications include use of master creep functions that account for multiaxial stresses, environmental factors and aging in a reduced time and other scalars. An explicit representation of the strains follows, which isthen specialized to provide three-dimensional homogenized constitutiveequations for transversely isotropic, fiber composites. Experimentalsupport for these equations is briefly reviewed. Finally, physicalinterpretation of some of the constitutive functions is discussed usingresults from a microcracking model as well as molecular rate process andfree volume theories. It is shown that the present thermodynamicformulation leads to a generalized rate process theory that accounts for abroad distribution of thermally activated transformations in polymers.

Measurement of Creep Compliance of Solid Polymers by Nanoindentation

Abstract: Methods to measure the local surface creep compliance of time-dependent materials are proposedand validated in the regime of linear viscoelasticity using nanoindentation. Two different bulkpolymers, Polymethyl Methacrylate (PMMA) and Polycarbonate (PC), were employed in thevalidation study; though it is expected that the methods developed herein can be applied for verysmall amounts of materials and heterogeneous materials. Both Berkovich and sphericalnanoindenters were used to indent into the material in nanoindentation tests. Two loading historieswere used: (1) a ramp loading history, in which the indentation load and displacement wererecorded; and (2) a step loading history, in which the indentation displacement was recorded as afunction of time. Analysis of the linearly viscoelastic material response was performed to measurethe creep compliance functions for the two materials under two different loading histories. The limitof linearly viscoelastic behavior for each of the two materials was determined through theobservation of the indent impression recovery after complete unloading; it is postulated that linearityis achieved if indentation impression is fully recovered after unloading. Results fromnanoindentation tests generally agree well with data from conventional tension and shear tests. It hasthus validated the techniques of measuring linear creep compliance in the glassy state usingnanoindentation with the Berkovich and spherical indenter tips.

On the fractional order model of viscoelasticity

Abstract: Fractional order models of viscoelasticity have proven to be very useful for modeling of polymers. Time domain responses as stress relaxation and creep as well as frequency domain responses are well represented. The drawback of fractional order models is that the fractional order operators are difficult to handle numerically. This is in particular true for fractional derivative operators. Here we propose a formulation based on internal variables of stress kind. The corresponding rate equations then involves a fractional integral which means that they can be identified as Volterra integral equations of the second kind. The kernel of a fractional integral is integrable and positive definite. By using this, we show that a unique solution exists to the rate equation. A motivation for using fractional operators in viscoelasticity is that a whole spectrum of damping mechanisms can be included in a single internal variable. This is further motivated here. By a suitable choice of material parameters for the classical viscoelastic model, we observe both numerically and analytically that the classical model with a large number of internal variables (each representing a specific damping mechanism) converges to the fractional order model with a single internal variable. Finally, we show that the fractional order viscoelastic model satisfies the Clausius–Duhem inequality (CDI).

A constitutive equation for the elasto-viscoplastic deformation of glassy polymers

Abstract: Constitutive equations for finite elastic-plastic deformation of polymers and metals are usually formulated by assuming an isotropic relation between the Jaumann rate of the Cauchy-stress tensor and the strain-rate tensor. However, the Jaumann-stress rate is known to display spurious non- physical behaviour in the elastic region. Replacing the Jaumann-stress rate by a Truesdell-stress rate results in an adequate description in the elastic region, but gives rise to a volume decrease during plastic flow in tensile deformation. In this paper a "compressible-Leonov model" is introduced, in which the elastic volume response is rigorously separated from the elasto-viscoplastic isochoric de- formation. This has the advantage that the model can be extended in a straightforward way to include a spectrum of relaxation times. It is shown that in the limit of small elastic strains, the compressible Leonov model reduces to the Jaumann-stress rate model, but diverges from the Truesdell-stress rate model. Finally, a comparison is made of the above mentioned models in a homogeneous uniaxial ten- sile test and a homogeneous plane-stress shear test, using polycarbonate (PC) as a model system. All models considered in this paper are "single mode" models (i.e. one relaxation time), and, therefore, cannot describe the full (non)linear viscoelastic region, nor the strain-hardening or strain-softening response.