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 in which a newly developed theoretical mechanism (Soldatos in Int J Solids Struct 202:217–225, 2020) is applied in specific boundary value problems met in polar linear elasticity of fibrous composites and thus enables the 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.

Thermal- Elastic Waves of Microstretch Semiconductor Medium with Rotation Field during Photothermal Excitation

A mathematical novel model for elastic semiconductor medium with microstretch properties is investigated. The generalized model is studied in the context of photo-thermoelasticity theory when the semiconductor medium is excited. The governing equations describe the coupled between the propagation of the elastic-thermal-plasma waves when the thermo-microstretch elastic semiconductor material is studied during a rotation field. The linear medium has an isotropic properties. The photothermal transport processes occurs during a two dimension (2D) elastic and electronic deformation when the microinertia of microelement is taken into account. The harmonic wave method can be used to obtain the general solutions for the basic physical variables. The complete analytical solutions of the considered variables are obtained when some mechanical-thermal and plasma conditions are applied on the boundary of the semiconductor medium. The numerical simulations of silicon (Si) and Germanium (Ge) media are constructed graphically with many comparisons according to a new parameters with thermal memories and rotation parameter.