In elementary quantum mechanics it is customary to describe the motion of a spinless particle by means of its coordinate r and momentum p operators. In such a description any physical operator is necessarily a function o f t and p, and in this sense r and p form a complete set of operators [1]. In solids one often works with a one-band approximation which considerably restricts the freedom of m...

The paper recalls the concept of duality in Mathematics and extends it to Solid Mechanics. One important application of duality is to restore some symmetry between current fields and their adjoint ones. This leads to many alternative schemes for numerical analyses, different from the classical one as used in classical formulation of boundary value problems (Finite Element Method). Usually, Cons...

This paper presents the implementation of eXtended Finite Element Method (XFEM) in general-purpose commercial software COMSOL Multiphysics for first time. An enrichment strategy is proposed, consistent with structure software. To this end, each set functions, an additional Solid Mechanics module incorporated into numerical framework, coupled compatible modifications to internal variables. The L...

New derivations of Young–Laplace’s and Young’s equations for a liquid drop deposited on a smooth solid substrate are presented, based on an integral form of equilibrium conditions applied to appropriately selected finite portions of the drop. A simple proof for the gravity independence of the contact angle is constructed and compared with a commonly utilized but more involved proof based on the...

This paper presents a new computational framework for the simulation of solid mechanics on general overlapping grids with adaptive mesh refinement (AMR). The approach, described here for time-dependent linear elasticity in two and three space dimensions, is motivated by considerations of accuracy, efficiency and flexibility. We consider two approaches for the numerical solution of the equations...

There is no doubt that atherosclerosis is one of the most important health problems in the Western Societies. It is well accepted that atherosclerosis is associated with abnormal stress and strain conditions. A compelling observation is that the epicardial arteries develop atherosclerosis while the intramural arteries do not. Atherosclerotic changes involving the epicardial portion of the coron...