Viscoelasticity

About: Viscoelasticity is a research topic. Over the lifetime, 26605 publications have been published within this topic receiving 599038 citations.

On a fully three-dimensional finite-strain viscoelastic damage model: Formulation and computational aspects

Abstract: A fully three-dimensional finite-strain viscoelastic model is developed, characterized by: (i) general anisotropic response, (ii) uncoupled bulk and deviatoric response over any range of deformations, (iii) general relaxation functions, and (iv) recovery of finite elasticity for very fast or very slow processes; in particular, classical models of rubber elasticity (e.g. Mooney-Rivlin). Continuum damage mechanics is employed to develop a simple isotropic damage mechanism, which incorporates softening behavior under deformation, and leads to progressive degradation of the storage modulus in a cyclic test with increasing amplitude (Mullins' effect). A numerical integration procedure is proposed which trivially satisfies objectivity and bypasses the use of midpoint configurations. The resulting algorithm can be exactly linearized in closed form, and leads to symmetric tangent moduli. Quasi-incompressible response is accounted for within the context of a three-field variational formulation of the Hu-Washizu type.

Linear rheology of viscoelastic emulsions with interfacial tension

Abstract: Emulsions of incompressible viscoelastic materials are considered, in which the addition of an interfacial agent causes the interfacial tension to depend on shear deformation and variation of area. The average complex shear modulus of the medium accounts for the mechanical interactions between inclusions by a self consistent treatment similar to the Lorentz sphere method in electricity. The resulting expression of the average modulus includes as special cases the Kerner formula for incompressible elastic materials and the Oldroyd expression of the complex viscosity of emulsions of Newtonian liquids in time-dependent flow.

A diffuse-interface method for simulating two-phase flows of complex fluids

Abstract: Two-phase systems of microstructured complex fluids are an important class of engineering materials. Their flow behaviour is interesting because of the coupling among three disparate length scales: molecular or supra-molecular conformation inside each component, mesoscopic interfacial morphology and macroscopic hydrodynamics. In this paper, we propose a diffuse-interface approach to simulating the flow of such materials. The diffuse-interface model circumvents certain numerical difficulties in tracking the interface in the classical sharp-interface description. More importantly, our energy-based variational formalism makes it possible to incorporate complex rheology easily, as long as it is due to the evolution of a microstructure describable by a free energy. Thus, complex rheology and interfacial dynamics are treated in a unified framework. An additional advantage of our model is that the energy law of the system guarantees the existence of a solution. We will outline the general approach for any two-phase complex fluids, and then present, as an example, a detailed formulation for an emulsion of nematic drops in a Newtonian matrix. Using spectral discretizations, we compute shear-induced deformation, head-on collision and coalescence of drops where the matrix and drop phases are Newtonian or viscoelastic Oldroyd-B fluids. Numerical results are compared with previous studies as a validation of the theoretical model and numerical code. Finally, we simulate the retraction of an extended nematic drop in a Newtonian matrix as a method for measuring interfacial tension.

Viscoelastic properties of fluid-saturated cracked solids

Abstract: The effective elastic moduli of a fluid-saturated solid containing thin cracks depend on the degree of interconnection between the cracks. Three separate regimes may be identified: (1) dry (drained), in which fluid in cracks can flow out of bulk regions of compression, (2) saturated isobaric, in which fluid may flow from one crack to another but no bulk flow takes place, and (3) saturated isolated, in which there is no communication of fluid between cracks. Transitions between these cases involve fluid flow, resulting in dissipation of energy. Relaxation of shear stresses in viscous fluid inclusions also results in dissipation. Viscoelastic moduli are derived, by using a self-consistent approximation, that describe the complete range of behavior. There are two characteristic frequencies near which dissipation is largest and the moduli change rapidly with frequency. The first corresponds to fluid flow between cracks, and its value can be estimated from the crack geometry or permeability. The second corresponds to the relaxation of shear stress in an isolated viscous fluid inclusion; its value may also be estimated. Variations of crack geometry result in a distribution of characteristic frequencies and cause Q to be relatively constant over many decades of frequency. Fluid flow between cracks accounts for attenuation of seismic waves in water-saturated rocks and attenuation observed in laboratory measurements on water-saturated rocks and partially molten aggregates. Attenuation in a partially molten upper mantle is probably due to fluid flow between cracks, although grain boundary relaxation in an unmelted upper mantle could also account for the seismic low-velocity zone. Grain boundary relaxation in the mantle may cause the long-term shear modulus to be around 20% less than that measured from seismic observations.

Principles of polymer engineering

Abstract: Introduction. 1: Structure of the molecule. 2: Structure of polymeric solids. 3: The elastic properties of rubber. 4: Viscoelasticity. 5: Yield and fracture. 6: Reinforced polymers. 7: Forming. 8: Design. Further reading, Answers, Index