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The electromagnetic fields (D, H) represent contravariant components of an antisymmetric 4‐tensor, while the fields (E, B) represent covariant components of the same 4‐tensor. Both sets are identical in Lorentz frames. The governing equations for them represent equations of balance for the flux of D and the flux B across open surfaces and they are invariant under arbitrary analytic transformation...
This paper wants to draw attention to several issues in electrodynamic field theory and to make way for a rational continuum approach to the subject. The starting point are the balances for magnetic flux and electric charge, both in a very general formulation for volumes and for open surfaces, all of which can deform and be immaterial or material. The spatial point‐of‐view for the description of fields...
As there are different computational methods for simulating problems in generalized mechanics, we present simple applications and their closed‐form solutions for verifying a numerical implementation. For such a benchmark, we utilize these analytical solutions and examine three‐dimensional numerical simulations by the finite element method (FEM) using IsoGeometric Analysis (IGA) with the aid of open...
Fifty years have passed since Truesdell's seminal paper on the origin and status of the balance for the moment of momentum was published in ZAMM. It is time to take stock: Important new developments in the theory of generalized continua with internal degrees of freedom and some fascinating fundamental applications need to be pointed out. Is there new evidence from classical papers regarding its independence...
In order to model the flow of nematic crystals, the theoretical framework according to Ericksen and Leslie is applied. The essentials of the theory are compiled and then specialized to Couette flow. The profiles for linear velocity and orientation angle will be computed and, in particular, we shall also study the rise in temperature due to viscous dissipation, which is frequently ignored by mechanicians...
Especially in metal forming, large plastic deformation occurs in thin plates. The problem of compressing dies is analyzed to evaluate the spreading of a thin layer in between. The velocity of dies is a given function in time so that the kinematics of the process is known. This problem can be considered as a generalization of the classical Prandtl problem by taking inertial effects into account and...
At present information about viscous properties of the eye's sclera is scarce, the main reason being that direct measurements cause technical problems. Nevertheless, coefficients of the sclera viscosity are of paramount interest for biomechanics and ophthalmologists. This paper investigates a method for determining the shear viscosity of the sclera based on a comparison of results from mathematical...
Modeling the motion of the Earth's axis, i.e., its spin, nutation and its precession, is a prime example of our ongoing effort to simulate the behavior of complex mechanical systems. In fact, models of increasing complexity of this motion have been presented for more than 400 years leading to an increasingly accurate description. The objective of this paper is twofold namely, first, to provide a review...
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