This paper presents an analytical framework to construct approximate homogenization solutions for the macroscopic elastic dielectric response — under finite deformations and finite electric fields — of dielectric elastomer composites with two-phase isotropic particulate microstructures. The central idea consists in employing the homogenization solution derived in Part I of this work for ideal e...

In this paper we shall investigate the normal surface displacement of the isotropic elastic half-space z > 0, due to a normal point force, F, which moves with constant speed, V, in the xdirection over the surface z = 0. This problem defines the Green's function for a class of elastodynamic contact problems for the half-space in which a frictionless rigid indenter moves at constant speed over th...

The Laser Interferometric Gravitational-Wave Observatory (LIGO) is designed to detect the Gravitational Waves (GW) predicted by Albert Einstein’s general theory of relativity. The advanced LIGO project is ongoing an upgrade to increase the detection sensitivity by more than a factor of 10, which will make the events detection a routine occurrence. In addition to using higher power lasers, heavi...

We use Noether's theorem to derive energy-momentum tensors for a simple elastic material, a nonsimple elastic material of grade two, a simple elastic dielectric and a nonsimple elastic dielectric of grade two. The technique is easily extendable to a nonsimple elastic dielectric of any grade. Introduction The concept of the force acting on a defect, e.g., an impurity, vacant lattice site, disloc...

The static offsets caused by earthquakes are well described by elastostatic models with a discontinuity in the displacement along the fault. A traditional approach to model this discontinuity is to align the numerical mesh with the fault and solve the equations using finite elements. However, this distorted mesh can be difficult to generate and update. We present a new numerical method, inspire...

1 I n t r o d u c t i o n The developments reported in this paper lie in the area of formulations for structural optimization where optimal material properties may be predicted at once along with other attributes of design such as material distribution, shape, and layout or topology. For the linearly elastic continuum structure, the model for this design problem stated in its primitive form has...

A 3-D finite element method (FEM) formulation for the prediction of unknown boundary conditions in linear steady thermoelastic continuum problems is presented. The present FEM formulation is capable of determining displacements, surface stresses, temperatures, and heat fluxes on the boundaries where such quantities are unknown or inaccessible, provided such quantities are sufficiently over-spec...

The integral equations encountered in boundary element methods are frequently solved numerically using collocation with spline trial functions. Convergence proofs and error estimates for these approximation methods have been only available in the following cases: Fredholm integral equations of the second kind [4], [7], one-dimensional pseudodifferential equations and singular integral equations...