MAC Models in Continuum Mechanics and Physics

The mathematical models in continuum mechanics and physics have sometimes singularities in solution. The singularities could be physical like stresses under applied force or they could be nonphysical like displacements under the applied force in the classical linear isotropic elasticity theory. The nonphysical singularity has also the classical membrane under the applied force and the heat conduction equation under the heat flux applied at the point. The nonlocal and also gradient theories in continuum mechanics are used to avoid the physical singularities in stresses in fracture mechanics, for example. The MAC theory accepts the physical singularities but it removes the nonphysical singularities using the simplest theories. MAC means the method of additional conditions and it works with the given traditional theory with the applied condition which removes the nonphysical singularity or\and the strange behavior of the solution at infinity. The simplest theories are chosen to present MAC in this book: string, heat conduction, membrane, elasticity and hydrodynamics. The number of theories, where could be used MAC, can be increased easily using the examples from this book