There is described a spacetime formulation of both nonrelativistic and relativistic elasticity. Specific attention is devoted to the causal structure of the theories and the availability of local existence theorems for the initial-value problem. Much of the presented material is based on joint work of B.G.Schmidt and the author (in Class.Quantum Grav.20 (2003), 889-904).

physics education is the nearly complete absence of continuum mechanics in the typical undergraduate or graduate curriculum. Continuum mechanics refers to field descriptions of mechanical phenomena, which are usually modeled by partial differential equations. The Navier–Stokes equations for the velocity and pressure fields of Newtonian fluids provide an important example, but continuum modeling...

An approach to weak balance laws in Continuum Mechanics is presented, involving densities with only divergence measure, which relies on the balance of power. An equivalence theorem between Cauchy powers and Cauchy fluxes is proved. As an application of this method, the construction of the stress tensor when the body is an orientable differential manifold is achieved under very general assumptions.

1. Preliminary concepts: Definitions and theoretical framework 2. Kinematics of deformation 2.1. The continuum setting: Mathematical description 2.2. Displacement, deformation and motion 2.3. Stretch, shear and strain 2.4. Change of reference frame and objective tensors 3. Balance laws 3.1. Mass and conservation of mass 3.2. Force, torque and theory of stress 3.3. Euler’s laws of motion 3.4. En...

Correction of the present defect in quantum education throughout the world must be performed by the new breakthrough in quantum mechanics which was re ntly achieved due to the inverse problem approach. It allows finding infinite (!) number of exactly solvable mod ls instead of only about ten previously known about 100 years. It means an incomparable more convenient bas or the quantum education ...

The recent appearance of nonlocal methods is examined in the light of traditional continuum mechanics. A comparison of nonlocal approaches in the fields of solid and fluid mechanics reveals that no consistent definition of a nonlocal theory has been used. We suggest a definition based on the violation of the principle of local action in continuum mechanics. From the consideration of the implica...

We derive a cluster expansion for the electric susceptibility kernel of a dielectric suspension of spherically symmetric inclusions in a uniform background. This also leads to a cluster expansion for the effective dielectric constant. It is shown that the cluster integrals of any order are absolutely convergent, so that the dielectric constant is well defined and independent of the shape of the...