Here 0 < ρ ∈ C(Ω) denotes the density, S is the Piola-Kirchhoff stress tensor which obeys the relation SF T = FS where F = I + ∇u is the deformation gradient. Divergence and transpose are taken with respect to the Euclidean metric | · |. The elasticity tensor C maps infinitesimal strain tensors E = (∇u+∇u )/2 to symmetric stress tensors CE. C represents the material properties on the elastic me...

Launched before the atomic hypothesis took hold, elasticity theory is a spectacular achievement. A continuum-level description, it provides a powerful toolkit for determining how architecturally simple solids such as crystals respond macroscopically to stress, whilst encoding microscopic, atomic-realm details parsimoniously, via a few parameters. Solids that are architecturally complex at the a...

The governing equations of three dimensional elasticity problems include the six Beltrami-Michell stress compatibility equations, the three differential equations of equilibrium, and the six material constitutive relations; and these are usually solved subject to the boundary conditions. The system of fifteen differential equations is usually difficult to solve, and simplified methods are usual...

in this study, the physical properties (size, mass, volume, density, geometric diameter, sphericity and friction coefficient on galvanized steel and wood surface) and some mechanical properties of flesh and skin tissue (modulus of elasticity, bioyield stress, yield strain and toughness) for small, medium and large melons of ghasri variety were determined. means comparison was done by duncan’s m...

Nowadays total joint replacements are widely used in the world, so in average 800,000 joint surgeries are done yearly only in Europe and North America. However implant loosening is and remains as the major issue of all implant failures and therefore causes revision surgery procedures. Studies and experiments have identified poor fixation of implants most likely is the main cause of long term im...

Higher order gradient elasticity theories are widely applied to determine the wave propagation characteristics of micro-sized structures. The novelty this paper, firstly, is using Second Strain Gradient (SSG) theory explore mechanism a 2D beam grid. strong formulas continuum model including governing equations and boundary conditions derived by Hamilton principle. Then, valuable long-range Latt...

In this study, the effect of finite strain on bending of the geometrically nonlinear of micro laminated composite Euler-Bernoulli beam based on Modified Couple Stress Theory (MCST) is studied in thermal environment. The Green-Lagrange strain tensor according to finite strain assumption and the principle of minimum potential energy is applied to obtain governing equation of motion and boundary c...