Finite Deformations Of Fibre-Reinforced Elastic Solids With Fibre-Bending Stiffness - Part II: Determination Of The Spherical Part Of The Couple-Stress

The indeterminacy of the spherical part of the couple-stress is a well-known drawback of any theoretical formulation stemming from the Cosserat couple-stress theory of elasticity. The relevant theory of finite elastic deformations of solids reinforced by a family of fibres that resist bending [1] is not an exception. The present communication extends and completes that theory in a manner that enables it to measure the spherical part of the couple-stress tensor outside the conventional equilibrium considerations. To achieve this, the present study reconsiders an extra piece of information that has surprisingly emerged already in [1] but, so far, is left unexplained and unexploited. Namely, the fact that the energy stored in a fibrous composite elastic solid with fibre-bending stiffness involves a couple-stress generated term which does not influence the relevant couple-stress constitutive equation. The thus resulting new theoretical development complements the theory presented in [1] without dismissing any of the theoretical results detailed or the conclusions drawn there. Its validity embraces boundary value problems concerning both finite and infinitesimal elastic deformations of polar fibrous composites. In the latter case, its applicability is also tested and verified, through the successful determination of the spherical couple-stress of a polar transversely isotropic elastic plate subjected to pure bending

Determination of the spherical part of the couple-stress in a polar fibre-reinforced elastic plate subjected to pure bending

This communication provides initial information and understanding of the manner that a newly developed theoretical mechanism [12] is applied in specific boundary value problems met in polar linear elasticity of fibrous composites, and thus enables determination of the spherical part of the couple-stress tensor. In this context, it tests the applicability of the implied mechanism/method in the case that a rectangular plate reinforced by a single family of unidirectional fibres is subjected to pure bending. The problem solution is obtained for either non-polar or polar material behaviour, where fibres are considered perfectly flexible or resistant in bending, respectively, and provides clear evidence of the correctness of the principal argument that underpins the proposed method. Namely, that the general rotation field of the plate deformation differs from the fibre rotation field. That newly discovered method enables an extra energy term that emerges in the strain energy function of the fibrous composite plate to relate with the spherical part of the couple-stress tensor outside conventional equilibrium conventions. It thus leads to the determination of the spherical part of the couple-stress and its distribution throughout the plate body in a complete and comprehensive manner

On the characterisation of polar fibrous composites when fibres resist bending – Part III: The spherical part of the couple-stress

Part II (Soldatos 2018b) identified some theoretical disagreement between the generally anisotropic polar linear elasticity of Mindlin and Tiersten (1962) and its counterpart developed in (Spencer and Soldatos, 2007; Soldatos, 2014) for fibrous composites with embedded fibres resistant in bending. The present communication shows that this disagreement is essentially due to inherent features of fibre-splay types of deformation and, consequently, generalises the couple-stress theory in a manner that creates room for newly emerged fibre-splay type of kinematic variables to enter and be accounted for. Relevant fundamental theorems, associate in Part II with the Mindlin and Tiersten model, are generalised accordingly to meet the needs and requirements of the proposed new formulation. Interestingly and importantly, the outlined generalisation enables formation of a convincing answer to a long-standing question regarding the indeterminacy of the spherical part of the couple-stress tensor, at least as far as polar elasticity of fibre-reinforced materials is concerned. The manner thus is demonstrated in which the spherical part of the couple-stress can be determined in polar linear elasticity of fibrous composites that exhibit transverse isotropy due to an embedded family of fibres resistant in bending

On the constitution of polar fiber-reinforced materials

This article presents important constitutive refinements and simplifications in the theory of polar elasticity of materials reinforced by a single family of fibres resistant in bending. One of these simplifications is achieved by paying attention to forms of the strain energy which are symmetric with respect to the symmetric and the antisymmetric parts of the fibre gradient tensor. This leads to the identification of a restricted version of the theory that is predominantly influenced by the fibre-splay mode of deformation. The lack of ellipticity of the governing equations of polar elasticity and the anticipation of existence of weak discontinuity surfaces even in the small deformation regime are also investigated. The manner in which potential activation of such surfaces is related with the action of either the fibre-bending or the fibre-splay deformation mode, as well as with their conjoined combination and coupling with their fibre-twist counterpart, is examined. The proposed constitutive equations can be simplified via the use of a new set of fourteen independent spectral invariants of the deformation. This set serves as an irreducible functional basis of relevant invariants or as an irreducible integrity basis of polynomial invariants. For instance, its use here enables identification of fourteen classical invariants that emerge as mutually independent from the known set of thirty-three in total classical invariants. In the special case of polynomial invariants, this result paves the way for identification of a corresponding minimal integrity basis

Origin of the High-K Tertiary magmatism in Northern Greece: Implications for mantle geochemistry and geotectonic setting.

Tertiary plutonic and volcanic rocks cropping out in the Rhodope Massif (N. Greece) are studied using existing and new geochemical and isotopic data. Most of these rocks belong to the post-collisional magmatism formed as part of the prolonged extensional tectonics of the Rhodope region in Late Cretaceous– Paleogene time. This magmatism is considered to be of mantle origin; however, the character of the mantle source is controversial. Rock bulk chemistry and compositional variations show magmas with calc-alkaline to high-K calc-alkaline and shoshonitic features associated with magmatism at convergent margins. Initial 87Sr/86Sr, 143Nd/144Nd ratios, Pb isotopes and REE composition of the mafic rocks indicate mainly an enriched mantle source, even if some rocks indicate a depleted mantle source. Low- and High-K mafic members of these rocks coexist indicating a strongly heterogeneous mantle source. The High-K character of some of the mafic rocks is primarily strongly related to mantle enrichment by subduction-related components, rather than crustal contamination. The geochemical characteristics of the studied rocks (e.g Ba/Th,Th/Yb,Ba/La, U/Th, Ce/Pb) indicate that primarily sediments and/or sediment melts, rather than fluid released by the subducted oceanic crust controlled the source enrichment under the Rhodope Massif

Insomnia and its correlates in a representative sample of the Greek population

<p>Abstract</p> <p>Background</p> <p>Insomnia is a major public health concern affecting about 10% of the general population in its chronic form. Furthermore, epidemiological surveys demonstrate that poor sleep and sleep dissatisfaction are even more frequent problems (10-48%) in the community. This is the first report on the prevalence of insomnia in Greece, a southeastern European country which differs in several socio-cultural and climatic aspects from the rest of European Community members. Data obtained from a national household survey (n = 1005) were used to assess the relationship between insomnia symptoms and a variety of sociodemographic variables, life habits, and health-related factors.</p> <p>Methods</p> <p>A self-administered questionnaire with questions pertaining to general health and related issues was given to the participants. The Short Form-36 (Mental Health subscale), the Athens Insomnia Scale (AIS) as a measure of insomnia-related symptoms, and the International Physical Activity Questionnaire (IPAQ) were also used for the assessment.</p> <p>Results</p> <p>The prevalence of insomnia in the total sample was 25.3% (n = 254); insomnia was more frequent in women than men (30.7% vs. 19.5%) and increased with age. Multiple regression analysis revealed a significant association of insomnia with low socio-economical status and educational level, physical inactivity, existence of a chronic physical or mental disease and increased number of hospitalizations in the previous year.</p> <p>Conclusions</p> <p>The present study confirms most findings reported from other developed countries around the world regarding the high prevalence of insomnia problems in the general population and their association with several sociodemographic and health-related predisposing factors. These results further indicate the need for more active interventions on the part of physicians who should suspect and specifically ask about such symptoms.</p

Axial-flexural coupled vibration and buckling of composite beams using sinusoidal shear deformation theory

A finite element model based on sinusoidal shear deformation theory is developed to study vibration and buckling analysis of composite beams with arbitrary lay-ups. This theory satisfies the zero traction boundary conditions on the top and bottom surfaces of beam without using shear correction factors. Besides, it has strong similarity with Euler–Bernoulli beam theory in some aspects such as governing equations, boundary conditions, and stress resultant expressions. By using Hamilton’s principle, governing equations of motion are derived. A displacement-based one-dimensional finite element model is developed to solve the problem. Numerical results for cross-ply and angle-ply composite beams are obtained as special cases and are compared with other solutions available in the literature. A variety of parametric studies are conducted to demonstrate the effect of fiber orientation and modulus ratio on the natural frequencies, critical buckling loads, and load-frequency curves as well as corresponding mode shapes of composite beams