The tilted shallow wedge problem

The problem of indentation of a half-plane by a titled, shallow wedge, under frictionless conditions, is studied, using half-plane theory. The contact law itself, together with the pressure distribution and internal state of stress are found. Particular attention is then given to the nature of the pressure and state of stress at the apex, and an asymptotic form appropriate to all angular features within contacts, and therefore of widespread application, is introduced.     

On the Logical Status of the Virtual Work Law

The law of virtual work (VWL) is probably the first law in the history of mechanics; it is previous to the one on the lever, though not completely distinct from it. Here I will discuss the logical status of VWL, that is whether it is an autonomous principle or a theorem of some sort of mechanics. The problem is complicated by the fact that up to now no universally recognised expression has been accepted for it. From this article the problematical nature of VWL demonstrability is quite clear when the mechanics does not characterise completely the constraints. Italian schools in the XVIII century, even if we do not take Lagrange into consideration, had an important role, both in the development of VWL and in the discussion of its role.     

Hyaluronan: from biomimetic to industrial business strategy

Hyaluronan (hyaluronic acid) is a naturally occurring polysaccharide of a linear repeating disaccharide unit consisting of beta-(1-->4)-linked D-glucopyranuronic acid and beta-(1-->3)-linked 2-acetamido-2-deoxy-D-glucopyranose, which is present in extracellular matrices, the synovial fluid of joints, and scaffolding that comprises cartilage. In its mechanism of synthesis, its size, and its physico-chemical properties, hyaluronan is unique amongst other glycosaminoglycans. The network-forming, viscoelastic and its charge characteristics are important to many biochemical properties of living tissues. It is an important pericellular and cell surface constituent; its interaction with other macromolecules such as proteins, participates in regulating cell behavior during numerous morphogenic, restorative, and pathological processes in the body. The knowledge of HA in diseases such as various forms of cancers, arthritis and osteoporosis has led to new impetus in research and development in the preparation of biomaterials for surgical implants and drug conjugates for targeted delivery. A concise and focused review on hyaluronan is timely. This review will cover the following important aspects of hyaluronan: (i) biological functions and synthesis in nature; (ii) current industrial production and potential biosynthetic processes of hyaluronan; (iii) chemical modifications of hyaluronan leading to products of commercial significance; and (iv) and the global market position and manufacturers of hyaluronan.     

Characteristics of the process zone at sharp notch roots

The classical Williams solution for the state of stress at the tip of a semi-infinite notch is re-visited and the two-term singular solution re-written in a form making the mode mixity and load magnitude explicit. This is used to show that, for a 270° solid angle, the majority of notch problems exhibit a process zone which is entirely or substantially mode I in character, which in turn means that the notch strength may practically be governed by a single elastic parameter. A method for finding the practical limit on the load and stress intensity ratio where this holds is described.     

Sur la méthode des approximations successives pour les équations aux derivées partielles du deuxième ordre

Sans résumé Extrait d'une lettre à M. Mittag-Leffler.