530 research outputs found
A theoretical model for power generation via liquid crystal elastomers
Motivated by the need for new materials and green energy production and
conversion processes, a class of mathematical models for liquid crystal
elastomers integrated within a theoretical charge pump electrical circuit is
considered. The charge pump harnesses the chemical and mechanical properties of
liquid crystal elastomers transitioning from the nematic to isotropic phase
when illuminated or heated to generate higher voltage from a lower voltage
supplied by a battery. For the material constitutive model, purely elastic and
neoclassical-type strain energy densities applicable to a wide range of
monodomain nematic elastomers are combined, while elastic and photo-thermal
responses are decoupled to make the investigation analytically tractable. By
varying the model parameters of the elastic and neoclassical terms, it is found
that liquid crystal elastomers are more effective than rubber when used as
dielectric material within a charge pump capacitor
A note on non-homogeneous deformations with homogeneous Cauchy stress for a strictly rank-one convex energy in isotropic hyperelasticity
It has recently been shown that for a Cauchy stress response induced by a
strictly rank-one convex hyperelastic energy potential, a homogeneous Cauchy
stress tensor field cannot correspond to a non-homogeneous deformation if the
deformation gradient has discrete values, i.e. if the deformation is piecewise
affine linear and satisfies the Hadamard jump condition. In this note, we
expand upon these results and show that they do not hold for arbitrary
deformations by explicitly giving an example of a strictly rank-one convex
energy and a non-homogeneous deformation such that the induced Cauchy stress
tensor is constant. In the planar case, our example is related to another
previous result concerning criteria for generalized convexity properties of
conformally invariant energy functions, which we extend to the case of strict
rank-one convexity
Hyperelastic bodies under homogeneous Cauchy stress induced by non-homogeneous finite deformations
We discuss whether homogeneous Cauchy stress implies homogeneous strain in isotropic nonlinear elasticity. While for linear elasticity the positive answer is clear, we exhibit, through detailed calculations, an example with inhomogeneous continuous deformation but constant Cauchy stress. The example is derived from a non rank-one convex elastic energy
Likely equilibria of stochastic hyperelastic spherical shells and tubes
In large deformations, internally pressurised elastic spherical shells and
tubes may undergo a limit-point, or inflation, instability manifested by a
rapid transition in which their radii suddenly increase. The possible existence
of such an instability depends on the material constitutive model. Here, we
revisit this problem in the context of stochastic incompressible hyperelastic
materials, and ask the question: what is the probability distribution of stable
radially symmetric inflation, such that the internal pressure always increases
as the radial stretch increases? For the classic elastic problem, involving
isotropic incompressible materials, there is a critical parameter value that
strictly separates the cases where inflation instability can occur or not. By
contrast, for the stochastic problem, we show that the inherent variability of
the probabilistic parameters implies that there is always competition between
the two cases. To illustrate this, we draw on published experimental data for
rubber, and derive the probability distribution of the corresponding random
shear modulus to predict the inflation responses for a spherical shell and a
cylindrical tube made of a material characterised by this parameter.Comment: arXiv admin note: text overlap with arXiv:1808.0126
Likely oscillatory motions of stochastic hyperelastic solids
Stochastic homogeneous hyperelastic solids are characterised by strain-energy
densities where the parameters are random variables defined by probability
density functions. These models allow for the propagation of uncertainties from
input data to output quantities of interest. To investigate the effect of
probabilistic parameters on predicted mechanical responses, we study radial
oscillations of cylindrical and spherical shells of stochastic incompressible
isotropic hyperelastic material, formulated as quasi-equilibrated motions where
the system is in equilibrium at every time instant. Additionally, we study
finite shear oscillations of a cuboid, which are not quasi-equilibrated. We
find that, for hyperelastic bodies of stochastic neo-Hookean or Mooney-Rivlin
material, the amplitude and period of the oscillations follow probability
distributions that can be characterised. Further, for cylindrical tubes and
spherical shells, when an impulse surface traction is applied, there is a
parameter interval where the oscillatory and non-oscillatory motions compete,
in the sense that both have a chance to occur with a given probability. We
refer to the dynamic evolution of these elastic systems, which exhibit inherent
uncertainties due to the material properties, as `likely oscillatory motions'
Likely striping in stochastic nematic elastomers
For monodomain nematic elastomers, we construct generalised elastic-nematic constitutive models
combining purely elastic and neoclassical-type strain-energy densities. Inspired by recent developments
in stochastic elasticity, we extend these models to stochastic-elastic-nematic forms where
the model parameters are dened by spatially-independent probability density functions at a continuum
level. To investigate the behaviour of these systems and demonstrate the eects of the
probabilistic parameters, we focus on the classical problem of shear striping in a stretched nematic
elastomer for which the solution is given explicitly. We nd that, unlike in the neoclassical case
where the inhomogeneous deformation occurs within a universal interval that is independent of
the elastic modulus, for the elastic-nematic models, the critical interval depends on the material
parameters. For the stochastic extension, the bounds of this interval are probabilistic, and the
homogeneous and inhomogeneous states compete in the sense that both have a a given probability
to occur. We refer to the inhomogeneous pattern within this interval as `likely striping'
Instabilities in liquid crystal elastomers
Stability is an important and fruitful avenue of research for liquid crystal
elastomers. At constant temperature, upon stretching, the homogeneous state of
a nematic body becomes unstable, and alternating shear stripes develop at very
low stress. Moreover, these materials can experience classical mechanical
effects, such as necking, void nucleation and cavitation, and inflation
instability, which are inherited from their polymeric network. We investigate
the following two problems: First, how do instabilities in nematic bodies
change from those found in purely elastic solids? Second, how are these
phenomena modified if the material constants fluctuate? To answer these
questions, we present a systematic study of instabilities occurring in nematic
liquid crystal elastomers, and examine the contribution of the nematic
component and of fluctuating model parameters that follow probability laws.
This combined analysis may lead to more realistic estimations of subsequent
mechanical damage in nematic solid materials
A microstructure-based hyperelastic model for open-cell solids
Mesoscopic continuum hyperelastic models for open-cell solids subject to large elastic deformations are derived from the architecture of the cellular body and the microscopic responses of the cell walls. These models are valid for general structures, with randomly oriented cell walls, made from an arbitrary isotropic nonlinear hyperelastic material, and subject to finite triaxial stretches. Their analyses provide global descriptors of the cellular structure, such as nonlinear stretch and shear moduli, and Poisson's ratio. Comparisons with numerical simulations show that the mesoscopic models capture well the mechanical responses under large strain deformations of three-dimensional periodic structures and of two-dimensional honeycombs made from a neo-Hookean material
A theoretical model for power generation via liquid crystal elastomers
Motivated by the need for new materials and green energy production and conversion processes, a class of mathematical models for liquid crystal elastomers (LCEs) integrated within a theoretical charge pump electrical circuit is considered. The charge pump harnesses the chemical and mechanical properties of LCEs transitioning from the nematic to isotropic phase when illuminated or heated to generate higher voltage from a lower voltage supplied by a battery. For the material constitutive model, purely elastic and neoclassical-type strain energy densities applicable to a wide range of monodomain nematic elastomers are combined, while elastic and photothermal responses are decoupled to make the investigation analytically tractable. By varying the model parameters of the elastic and neoclassical terms, it is found that LCEs are more effective than rubber when used as dielectric material within a charge pump capacitor
A theoretical liquid crystal elastomer model that mimics the elasticity of cat skin
A mathematical model for nematic liquid crystal elastomers is proposed that mimics the elastic response of cat skin where reorientation of dermal fibres produces an increase in the thickness direction under tensile stretch. To capture this unusual effect, the uniaxial order parameter in the nematic elastomer model is allowed to decrease then increase again, and the critical stretch at which this change of monotonicity occurs and where the director also rotates suddenly is predicted. In addition, the model parameters are described by probability density functions and their uncertainty is propagated numerically to the predicted mechanical results
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