The notion of hyperbolicity of a partial differential equation (PDE), or a system of PDE’s, is central for the field theories of mathematical physics. It is closely related to the well-posedness of the Cauchy problem and to the causal structure underlying these theories. In standard theories describing relativistic fields in vacuo this causal structure is that given by the spacetime metric, a s...

This paper develops the foundations of the multisymplectic formulation of nonsmooth continuum mechanics. It may be regarded as a PDE generalization of previous techniques that developed a variational approach to collision problems. These methods have already proved of value in computational mechanics, particularly in the development of asynchronous integrators and efficient collision methods. T...

In one-dimensional case, it is shown that the basic principles of quantum mechanics are properties of the set of intermediate cardinality. PACS numbers: 03.65.Bz, 02.10.Cz The concept of discrete space is not a unique alternative of the continuous space. Since discrete space is a countable set, there is an intermediate possibility connected with the continuum problem: space may be neither conti...

Results of molecular-mechanics simulations of axial and torsional deformations of a single wall carbon nanotube are used to find Young’s modulus, the shear modulus, and the wall thickness of an equivalent continuum tube made of a linear elastic isotropic material. These values are used to compare the response of the continuum tube in bending and buckling with that obtained from the molecular me...

We consider continuous media in which contact edge forces are present. Introducing the notion of quasibalanced contact force distribution, we are able to prove the conjectures made in [Noll, 1990] concerning the representation of contact edge forces. We first generalise the Noll theorem on Cauchy postulate. Then we adapt the celebrated Cauchy tetrahedron construction to find a representation th...

For a class of systems obeying Euler's equation of motion the existence of a quantity to be named "proper mechanical energy" (PME) is shown which, together with internal energy, results in a quantity to be named "proper energy" (PE), which is conserved under conditions of time-dependent potentials. The appertaining formal structure for the continuum mechanics of such systems is the counterpart ...

In one-dimensional case, it is shown that the basic principles of quantum mechanics are properties of the set of intermediate cardinal-ity. The concept of discrete space is not a unique alternative of the continuous space. Since discrete space is a countable set, there is an intermediate possibility connected with the continuum problem: space may be neither continuous nor discrete. The commonly...

In continuum mechanics, the equations of motion for mixtures were derived through the use of a variational principle by Bedford and Drumheller in [1978]. Only immiscible mixtures were investigated. We have chosen a different approach. In this paper, we first write the equations of motion for each constituent of an inviscid miscible mixture of fluids without chemical reactions or diffusion. The ...

2014 The continuum mechanics framevork for analyzing necking and shear band instabilities is discussed. The predicted onset of instability depends sensitively on the material’s constitutive characterization, not only through properties, such as strain hardening and strain rate sensitivity, that can be measured in proportional loading tests, but also through the material’s response to a change i...