Remarks on explicit strong ellipticity conditions for anisotropic or pre-stressed incompressible solids

We present a set of explicit conditions, involving the components of the elastic stiffness tensor, which are necessary and sufficient to ensure the strong ellipticity of an orthorhombic incompressible medium. The derivation is based on the procedure developed by Zee & Sternberg (Arch. Rat. Mech. Anal., 83, 53-90 (1983)) and, consequently, is also applicable to the case of the homogeneously pre-stressed incompressible isotropic solids. This allows us to reformulate the results by Zee & Sternberg in terms of components of the incremental stiffness tensor. In addition, the resulting conditions are specialized to higher symmetry classes and compared with strong ellipticity conditions for plane strain, commonly used in the literature.The first author’s work and the second author’s visit to Brunel University were partly supported by Brunel University’s ‘BRIEF’ award scheme

The choice of pathogenetic therapy for a patient with dorsalgia: A review

Musculoskeletal pain syndromes are one of the common causes of temporary disability associated with a decrease in the quality of life of patients. Dorsalgia (DA) is the most common form of these syndromes. Currently, osteoarthritis of the facet joints has been replaced as one of the main mechanisms for the occurrence of DA. The article discusses the main causes of DA development, important inflammatory processes in its symptoms. The issues of treatment of patients with DA are discussed. Information about the efficacy and safety of the use of Nise® (nimesulide) is given

Adhesive contact problems for a thin elastic layer : Asymptotic analysis and the JKR theory

Contact problems for a thin compressible elastic layer attached to a rigid support are studied. Assuming that the thickness of the layer is much less than the characteristic dimension of the contact area, a direct derivation of asymptotic relations for displacements and stress is presented. The proposed approach is compared with other published approaches. The cases are established when the leading-order approximation to the non-adhesive contact problems is equivalent to contact problem for a Winkler–Fuss elastic foundation. For this elastic foundation, the axisymmetric adhesive contact is studied in the framework of the Johnson–Kendall–Roberts (JKR) theory. The JKR approach has been generalized to the case of the punch shape being described by an arbitrary blunt axisymmetric indenter. Connections of the results obtained to problems of nanoindentation in the case that the indenter shape near the tip has some deviation from its nominal shape are discussed. For indenters whose shape is described by power-law functions, the explicit expressions are derived for the values of the pull-off force and for the corresponding critical contact radius