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A modelling framework is adopted and adapted here to model the rate-dependent deformation behaviour of liquid crystal elastomers (LCEs). On using an isotropic hyperelastic strain energy function W I 1 , I 2 of binomial form, previously employed for capturing the (quasi-static) deformation of polydomain LCEs, an extension is presented for application to the rate-dependent behaviour of LCEs by incorporating the deformation rate into the model parameters. That is, the model parameters of the core hyperelastic strain energy function W are considered to evolve with, i.e., be a function of, the deformation rate. A specific measure of deformation rate ɛ ̇ is utilised, and a particular functional dependency of the hyperelastic model parameters on ɛ ̇ , of a skewed exponential form, is devised and presented. The ensuing rate-dependent model W r is then applied to a range of extant experimental datasets, encompassing various LCE specimens and across different deformation rates, under uniaxial loading and including both tension and compression deformations. The model is shown to capture and predict the data favourably. Given the simplic of devising and implementing the presented modelling framework, the flexibility it provides for incorporating different choices of strain energy W function as well as the functional form(s) of the dependency of the model parameters on the deformation rate, and the accuracy of the modelling results, the application of this modelling approach to capturing the rate-dependent deformation behaviour of LCEs is hereby presented. • A new modelling approach to capture the rate-dependent behaviour of LCEs. • A new hyperelastic function augmented to incorporate the deformation rate. • A simple and flexible framework, adaptable to many other strain energy functions. • Accurate correlation with rate-dependent data of various LCE specimens. [ABSTRACT FROM AUTHOR]

We study the oscillations of a spherical shell of a rate-type viscoelastic solid subject to a pressure difference between the inner and the outer surface. The stable equilibrium configurations, in the class of spherically symmetric deformations, correspond to the minima of the elastic energy function. Numerical simulations indicate that the way in which the equilibrium state is reached, strongly depends on the material parameters. [ABSTRACT FROM AUTHOR]

Structure evolution during deformation of isotropic auxetic foams is investigated by simple compression experiments. It is shown that the main feature observed in the experimental data can be accurately described by an isotropic hyperelastic model with an Ogden-type strain energy function. The model can be easily implemented in a finite element code and, hence, can be used to simulate foams undergoing complex structural deformations. [ABSTRACT FROM AUTHOR]

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We review the main aspects of the celebrated Gent constitutive model for rubberlike materials. Emphasis is placed on the case of damageable materials describing possible damage and deformation localization. [ABSTRACT FROM AUTHOR]

Abstract: A material is of coaxial type if the Cauchy stress tensor and the strain tensor are coaxial for all deformations. Clearly a hyperelastic material is of coaxial type if and only if it is isotropic. Here we present a weaker definition of materials of coaxial type. Anisotropic materials may be of a coaxial type in a weak sense if for a given specific we have that . We denote these materials -coaxial. We show that for transverse isotropic materials weak coaxial constitutive equations may be characterized using universal relations. We discuss the impact of -coaxial materials in the modeling of soft tissues. We conclude that -coaxial materials are a strong evidence that in real world materials two anisotropic invariants are always necessary to model in a meaningful and correct way single fiber reinforced materials. [Copyright &y& Elsevier]

A classical problem in the framework of nonlinear elasticity theory is the characterization of the materials that may sustain a pure state of anti-plane shear in the absence of body forces. This problem has been solved by Knowles and by Hill in the framework of isotropic and incompressible elasticity in the seventies. Here we provide a simpler and shorter proof of these classical results. Moreover, we extend these results to nonlinear elastodynamics and we provide some new special solutions. [ABSTRACT FROM AUTHOR]

We consider deformations and motions that correspond to a non-uniform axial stretch superimposed to a general pseudoplane deformation of the first kind. We provide the general determining equation for this kind of solution when the constitutive equation for the stress tensor is derived from the elastic neo-Hookean strain-energy density. Then we provide some explicit solutions which are generalizations of the non-symmetric torsion of a slab and some finite-amplitude pseudo-planar elliptical motions. [ABSTRACT FROM PUBLISHER]

Investigates the helical shear problem for a circular cylindrical tube composed of an isotropic hyperelastic incompressible material. Constitutive models that account for hardening at large deformations; Characterization of the stress fields and displacements; Mechanical properties of elastomeric materials.

A class of inhomogeneous deformations is studied in the framework of the nonlinear theory of hyperelastic incompressible bodies whose material properties can depend on the material point in a particular way. Applications of the results obtained to finite thermoelasticity are given. [ABSTRACT FROM PUBLISHER]

Two classes of elastic constrained materials are considered: the Bell materials where the constraint implies an inextensibility in the simple mean, and the Ericksen material where the constraint implies inextensibility in the quadratic mean. We classify, for both materials, all the universal solutions that fall into the family of the generalized plane deformations. One of these families, which is universal also for incompressible materials, allows us to generate a very interesting new universal relation. [ABSTRACT FROM AUTHOR]