Abstract

Abstract

We define stress and strain splittings appropriate to linearly elastic anisotropic materials with volumetric constraints. The treatment includes rigidtropic materials, which develop no strains under a stress pattern that is a null eigenvector of the compliance matrix. This model includes as special case incompressible materials, for which the eigenvector is hydrostatic stress. The main finding is that pressure and volumetric strain must be redefined as effective quantities. Using this idea, an energy decomposition that exactly separates deviatoric and volumetric energy follows.

Abstract

The Henry problem has played a key role in our understanding of seawater intrusion into coastal aquifers and in benchmarking density dependent flow codes. This paper seeks to modify Henry’s problem to ensure sensitivity to density variations and vertical salinity profiles that resemble field observations. In the proposed problem, the “dispersive Henry problem”, mixing is represented by means of the traditional Scheidegger dispersion tensor (dispersivity times water flux). Anisotropy in the hydraulic conductivity is acknowledged and Henry’s seaside boundary condition of prescribed salt concentration is replaced by a flux dependent boundary condition, which represents more realistically salt transport across the seaside boundary. This problem turns out to be very sensitive to density variations and its solution gets closer to reality. However, an improvement in the traditional Henry problem (gain in sensitivity and realism) can be also achieved if the value of the Peclet number is significantly reduced.

Although the dispersive problem lacks an analytical solution, it can shed light on flow in coastal aquifers. It provides significant information about the factors controlling seawater penetration, width of the mixing zone and influx of seawater. The width of the mixing zone depends basically on dispersion with longitudinal and transverse dispersion controlling different parts of the mixing zone but displaying similar overall effects. Toe penetration is mainly controlled by the horizontal permeability and by the geometric mean of the dispersivities. Finally, transverse dispersivity and the geometric mean of the hydraulic conductivity are the leading parameters controlling the amount of saltwater that enters the aquifer

Abstract

We present a local formulation for 2D Discrete Exterior Calculus (DEC) similar to that of the Finite Element Method (FEM), which allows a natural treatment of material heterogeneity (assigning material properties element by element). It also allows us to deduce, in a principled manner, anisotropic fluxes and the DEC discretization of the pullback of 1-forms by the anisotropy tensor, i.e. we deduce the the discrete action of the anisotropy tensor on primal 1-forms. Due to the local formulation, the computational cost of DEC is similar to that of the Finite Element Method with Linear interpolating functions (FEML). The numerical DEC solutions to the anisotropic Poisson equation show numerical convergence, are very close to those of FEML on fine meshes and are slightly better than those of FEML on coarse meshes.

Abstract

Abstract

Abstract

Abstract

Liquid crystal elastomers (LCEs) are soft materials, which are capable of large deformations induced by temperature changes and ultraviolet irradiation [1]. Since many years, these materials are under investigation in experimental researches as actuator materials. LCEs arise from a nematic polymer melt, consisting of long and flexible polymer chains as well as oriented and rigid rod-like molecules, the so-called mesogens, by crosslinking. In order to numerically simulate LCE materials by using the finite element method, a continuum model is necessary, including in a thermo-viscoelastic material formulation of the polymer chains the orientation effects of the mesogens. This can be performed by introducing a normalized direction vector as an independent field, and deriving from additional (orientational) balance laws independent differential equations [2]. These differential equations describe the independent rotation of the rigid mesogens connected with the flexible polymer chains. The orientation-dependent stress law of LCEs arises from an anisotropic free energy, comparable with fibre-reinforced materials. But, in contrast to fibre-reinforced materials, the direction vector of a LCE model has to be independent. In contrast to [2], we apply a variational principle for deriving a new mixed finite element formulation, which is based on drilling degrees of freedom for describing the mesogens rotation [3]. This principle leads to an extended set of balance laws.

Abstract

Actuation devices made of dielectric elastomers are prone to compression induced wrinkling instabilities, which can adversely affect their performance and may lead to device failure. On the other hand, wrinkles can be used constructively in certain applications demanding a controlled alternation of the surface morphology. The idea of taut states and the natural width under simple tension plays an important role in the analysis of compression generated instability (wrinkling). In case of electrically driven DE membranes, the domain of taut states in the plane of principal stretches is influenced substantially by the applied voltage and the film's constitutive properties. In the recent past, there has been an increasing interest in exploiting anisotropy in the material behavior of dielectric elastomers for improving their actuation performance. Spurred with these ongoing efforts, this paper presents a continuum mechanics based electromechanical model for predicting the thresholds on the domain of taut states of transversely isotropic planar dielectric elastomers. The developed analytical framework uses an amended energy function that accounts for the electromechanical coupling for a class of incompressible transversely isotropic dielectric membranes. The required expressions for the total Cauchy stress tensor and the associated principal stress components are evaluated utilizing the amended energy function. Finally, the concept of natural width under simple tension is implemented to obtained the nonlinear coupled electromechanical equation that evaluates the associated taut states domain of the transversely isotropic planar dielectric elastomers. Our results indicate that the extent of taut domain can be controlled by modifying the level and the principal direction of the transverse isotropy. The taut states domain for a particular level of applied electric field increases with increase in the anisotropy parameter, while the taut domains depleted with the increase in fiber orientations from 00to 900for an applied level of electrical loading. The fiber-reinforced wrinkle-tunable surfaces can be effectively designed and developed using the underlying analytical framework and the trends obtained in this study.