It is natural to consider a quantum system in the continuum limit of space-time configuration. Incorporating also, Einstein’s special relativity, leads to the quantum theory of fields. Non-relativistic quantum mechanics and classical mechanics are special cases. By studying vacuum expectation values (Wightman functions W (n; z) where z denotes the set of n complex variables) of products of quan...

Carbon nanotubes (CNTs) possess extremely high stiffness, strength and resilience, and may provide the ultimate reinforcing material for the development of nanocomposites. Evaluating the effective elastic properties of such nanoscale materials is a difficult task. Modelings and simulations using continuum mechanics models can play significant roles in this development. In this paper, the nanost...

In the present study, small scale effect on critical buckling loads of triangular nano- composite plates under uniform in-plane compression is studied. Since at nano-scale the structure of the plate is discrete, the size dependent nonlocal elasticity theory is employed to develop an equivalent continuum plate model for this nanostructure incorporating the changes in its mechanical behavior. The...

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...