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Concept# Classical physics

Summary

Classical physics is a group of physics theories that predate modern, more complete, or more widely applicable theories. If a currently accepted theory is considered to be modern, and its introduction represented a major paradigm shift, then the previous theories, or new theories based on the older paradigm, will often be referred to as belonging to the area of "classical physics".
As such, the definition of a classical theory depends on context. Classical physical concepts are often used when modern theories are unnecessarily complex for a particular situation. Most often, classical physics refers to pre-1900 physics, while modern physics refers to post-1900 physics, which incorporates elements of quantum mechanics and relativity.
Overview
Classical theory has at least two distinct meanings in physics. In the context of quantum mechanics, classical theory refers to theories of physics that do not use the quantisation paradigm, which includes classical mechanics and rel

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In this thesis, an original law of adhesion is developed and then coupled to the classical law of unilateral contact with threshold friction, in order to study the phenomenon of fibre/matrix debonding in composite materials. This tribological law is developed within the framework of standard generalized materials adapted to interfaces. Thus, the law is derived from a free energy potential ψc and a dissipation potential Φc. The adhesive interface is interpreted as a bundle of links connecting the two contact surfaces. Each link is assumed to have a plastic behavior with softening and damage, caused by stretching, to represent the loss of adhesion. An internal variable ga measuring an irreversible adhesive gap is introduced and associated by energetic duality to an adhesive stress pa. The ranges of ga and pa are limited by two characteristic constants of adhesion, gM and pM respectively. pM is the maximum adhesive tension below which the links remain elastic. Above this limit, debonding and damage of the links occur as ga increases. Once ga reaches the value gM, total rupture of the adhesive bond occurs. This adhesion law is then mounted in parallel to the contact and friction laws into a unique law. The law is regularized using either the approximate penalty method or the exact augmented Lagrangian method, in option. The regularized laws are implemented in a node-to-node contact element of the finite element code TACT. The adhesive force is computed by means of a predictor-corrector with projection algorithm for integrating the evolution of ga, and the relevant Jacobian tensors required for the resolution of non-linearities by the iterative scheme of Newton are calculated. This is accomplished for the penalty and the augmented Lagrangian regularizations. A traction test of a glass/epoxy interface in the normal direction is designed and used to experimentally determine the parameters pM and gM of such an interface (pM directly and gM indirectly). Numerical simulations of adhesion between a rigid punch and an elastic half-space enable the comparison of the proposed model of adhesion to the classical theories of adhesion. A numerical simulation of the standard pull-out test of a fibre embedded in a matrix is then performed, and the numerical shear distribution along the interface is compared to the analytical one existing for this experiment. The results are in good agreement with existing ones. Finally, a crack propagation in a fibrous composite is simulated.

A functional integration approach – whose main ingredient is the Hubbard-Stratonovich transformation – for the quantum nonrelativistic many-fermion problem is investigated. With this method, the ground state energy correponds to a systematic expansion in powers of a small parameter related to the number of fermions. It is a functional of a potential determined by a self-consistent equation. The semiclassical Hartree energy is obtained at lowest order of the expansion, the exchange energy at first order, and the correlation energy at second order. This approach is applied to large neutral atoms, for which the correlation energy is computed. This approach is also applied to many-electron quantum dots with harmonic confinement. The self-consistent equation is solved as a function of a small parameter depending on the confinement strength. The Hartree and exchange energies are computed in powers of this parameter, and the correlation energy is computed at lowest order. The energy oscillations, arising from the Hartree energy, are also evaluated; they are related to the periodic orbits of the classical dynamics of the self-consistent potential.

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