A modified formulation of quasi-linear viscoelasticity for transversely isotropic materials under finite deformation

Abstract

The theory of quasi-linear viscoelasticity (QLV) is modified and developed for transversely isotropic (TI) materials under finite deformation. For the first time, distinct relaxation responses are incorporated into an integral formulation of nonlinear viscoelasticity, according to the physical mode of deformation. The theory is consistent with linear viscoelasticity in the small strain limit and makes use of relaxation functions that can be determined from small-strain experiments, given the time/deformation separability assumption. After considering the general constitutive form applicable to compressible materials, attention is restricted to incompressible media. This enables a compact form for the constitutive relation to be derived, which is used to illustrate the behaviour of the model under three key deformations: uniaxial extension, transverse shear and longitudinal shear. Finally, it is demonstrated that the Poynting effect is present in TI, neo-Hookean, modified QLV materials under transverse shear, in contrast to neo-Hookean elastic materials subjected to the same deformation. Its presence is explained by the anisotropic relaxation response of the medium.

Soft metamaterials with dynamic viscoelastic functionality tuned by pre-deformation

“…We shall study nonlinear viscoelastic media that behave in a manner described by the QLV theory [40,45,71]. The general constitutive expression for anisotropic media takes the form boldπvefalse(tfalse)=∫−normal∞tGfalse(t−sfalse):true0∂πnormale(s)∂s ds, where π is the second Piola–Kirchhoff stress with superscripts ‘’ and ‘’ referring to the viscoelastic and elastic stresses, respectively, and G is a fourth-order reduced relaxation tensor, where reduced refers to the fact that it is non-dimensional, unlike the relaxation tensor in linear viscoelasticity, which has dimensions of stress, see e.g.…”

“…We shall study nonlinear viscoelastic media that behave in a manner described by the QLV theory [40,45,71]. The general constitutive expression for anisotropic media takes the form…”

“…Modelling such media requires an explicit time-dependent model to be formulated [39]. In recent times, Fung's theory of quasi-linear viscoelasticity (QLV) has been revisited given its (relative) ease of implementation for large deformation problems [40][41][42][43], and also given its potential to be employed for problems associated with compressible media [44] and for anisotropic materials with distinct relaxation responses in principal directions [45]. The isotropic QLV theory is essentially equivalent to the theory of Simo, based on internal variables and evolution equations in the incompressible limit [46].…”

Nitrogen Triflorida (NF3) : Termodinamika dan Transpor Elektron NF3

“…Rescigno menggunakan metode variasi Kohn kompleks dan memperoleh diferensial elastis (143; 144) dan perpindahan cross-momentum (dalam rentang energi elektron 0,2-10 eV) juga sebagai penampang untuk eksitasi disosiatif (145)(146)(147) dari singlet (148)(149)(150) terendah dan triplet (151; 152) keadaan tereksitasi (153) secara elektronik (154) (dari ambang energi hingga 25 eV). Boesten mengukur diferensial elastis penampang, integral elastis (155)(156)(157) dan cross-sections momentum-transfer (157)(158)(159) (melalui energi elektron kisaran 1,5-100 eV), serta lintas-bagian diferensial untuk eksitasi getaran. Joucoski dan Bettega menghitung diferensial, integral dan perpindahan momentum lintas-bagian (untuk energi elektron hingga 60 eV) menggunakan multichannel Schwinger metode dalam pendekatan pertukaran statis fixed-nuclei (160)(161)(162)(163)(164)(165) .…”

A Recruitment Model of Tendon Viscoelasticity That Incorporates Fibril Creep and Explains Strain-Dependent Relaxation

“…Experiments show that rates of relaxation and creep are dependent on the strain or stress level that is being imposed [22,23]. The latter rules out the possibility of employing quasilinear viscoelasticity (QLV) (which is based on the work of Fung [24] and has recently been reinterpreted by De Pascalis et al [25], extended to the case of transverse isotropy by Balbi et al [26] and employed for modeling viscoelastic inflation problems by De Pascalis et al [27]) with a single scalar relaxation function. QLV assumes that the viscous relaxation rate is independent of the instantaneous local strain and is a special case of the more general constitutive model developed by Pipkin and Rogers [28].…”