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In the present contribution the concept of isogeometric analysis is extended towards the numerical solution of the problem of gradient elasticity in two dimensions. In gradient elasticity the strain energy becomes a function of the strain and its derivative. This assumption results in a governing differential equation which contains fourth order derivatives of the displacements. The numerical solution of this equation with a displacement-based finite element method requires the use of C 1 -continuous elements, which are mostly limited to two dimensions and simple geometries. This motivates the implementation of the concept of isogeometric analysis for gradient elasticity. This NURBS based interpolation scheme naturally includes C 1 and higher order continuity of the approximation of the displacements and the geometry. The numerical approach is implemented for two-dimensional problems of linear gradient elasticity and its convergence behavior is studied.

The tracking control system of the VLT Survey Telescope Rev. Sci. Instrum. 83, 094501 (2012) Multi-functional dielectric elastomer artificial muscles for soft and smart machines App. Phys. Rev. 2012, 7 (2012 Multi-functional dielectric elastomer artificial muscles for soft and smart machines J. Appl. Phys. 112, 041101 (2012) Tactile feedback control for a gripper driven by SMA springs AIP Advances 2, 032134 (2012) Light sailboats: Laser driven autonomous microrobots

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Dielectric elastomer actuators (DEAs) with a typical sandwich structure of electrode-elastomer-electrode arrangement provide large deformation. DEAs outperform most large displacement actuators in terms of light weight, low cost, and high efficiency. The actuation mechanism of DEAs relies primarily on the electrostatic force or the Maxwell stress which is due to the reaction of material polarization in an electric field. By a dynamic nonlinear electromechanical continuum model implemented with the finite element method, the dynamic response of a homogeneous DEA is studied. Results show that the actuation magnitudes can be increased when the frequency of the applied electric field approaches to the eigenfrequency of the DEAs. The dynamic nonlinear electromechanical modelDielectric elastomers are widely used for artificial muscles and haptic displays, thanks to its practical features e.g. large deformation up to 300%, low cost and high fracture toughness. In an actuator setup the material is usually sandwiched between two compliant electrodes. Due to the electromechanical coupling effect, dielectric elastomers can be actuated under an electric loading. To achieve various applications, the material works usually under dynamic electric loadings, and hence the dynamic response of the material should be taken into account. In the following a dynamic nonlinear continuum model is presented, which takes the electromechanical coupling into account. The large deformation of the material is treated as a nonlinear mapping of the body from its reference configuration B 0 to the actual or current configuration B at time t, i.e. x = χ(X, t), see e.g. [1]. The fundamental quantity to describe the kinematics of the motion is the deformation gradient Fwhere the gradient Grad with a capital initial character is to be computed with respect to the coordinates of the reference configuration. The material involves both electric and mechanical fields. In terms of the electrostatics in the current configuration, the theory of dielectrics can be applied, namely the Gauß equation and the definition of the electric field,where D is the dielectric displacement, E is the true electric field, ϕ is the electric potential, and no free volume charge is considered. The relation between the electric displacement and the electric field is given through,where P is the material polarization, κ 0 is the vacuum permittivity, and κ r is the relative permittivity of the dielectric elastomer. Different from the dielectrics in the case of small deformations, the material polarization has a nonlinear dependence on the true electric field which involves the volume change J = detF . In the formulation the time dependent effect in electrostatics is neglected. In terms of the mechanics, one has the following equilibrium in the absence of mechanical volume forcein which σ M is the mechanical stress, f E the electrostatic volume force due to the material polarization, u the displacement vector, c and ρ are the damping coefficient and the mass density. The last tw...