Microstructural length scale parameters to model the high-cycle fatigue behaviour of notched plain concrete

The present paper investigates the importance and relevance of using microstructural length scale parameters in estimating the high-cycle fatigue strength of notched plain concrete. In particular, the accuracy and reliability of the Theory of Critical Distances and Gradient Elasticity are checked against a number of experimental results generated by testing, under cyclic bending, square section beams of plain concrete containing stress concentrators of different sharpness. The common feature of these two modelling approaches is that the required effective stress is calculated by using a length scale which depends on the microstructural material morphology. The performed validation exercise demonstrates that microstructural length scale parameters are successful in modelling the behaviour of notched plain concrete in the high-cycle fatigue regime

Deformation of a two-dimensional, shear deformable cantilever beam using gradient elasticity and finite differences

© 2016 Praise Worthy Prize S.r.l. - All rights reserved. In the paper it has been studied the deformation of a cantilever beam using gradient elasticity and the finite difference method. The basic equilibrium equations are derived for an infinitesimal area for linear and gradient elasticity. Higher order expressions for the strain are considered, and from the differential equilibrium equation for gradient elasticity separate differential equations for the displacements, in terms of the linear solution, were formulated. Subsequently, recursive formulas are derived by replacing the derivatives with difference expressions over points. Computer implementation is performed and the deformation of a cantilever beam (tension, bending, through-the-thickness) is studied with the finite difference method. Solutions of exponential and periodic type are obtained

On some applications of gradient elasticity to composite materials

Some applications of the gradient theory of elasticity to composite materials are discussed. A brief introduction to gradient theory is given and some mathematical aspects are provided. Of particular importance is a constitutive equation of a higher-order strain gradient theory, and a particular form of gradient theory for which the Ru-Aifantis theorem holds. Applications include a fiber pullout from a matrix, stress transfer in short fiber composites, and the transverse shearing of a sandwich plate. Size effects for all three examples are provided. © 2001 Elsevier Science Ltd. All rights reserved