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A state-based micropolar peridynamic theory for linear elastic solids is proposed. The main motivation is to introduce additional micro-rotational degrees of freedom to each material point and thus naturally bring in the physically relevant material length scale parameters into peridynamics. Non-ordinary type modeling via constitutive correspondence is adopted here to define the micropolar peridynamic material. Along with a general three dimensional model, homogenized one dimensional Timoshenko type beam models for both the proposed micropolar and the standard non-polar peridynamic variants are derived. The efficacy of the proposed models in analyzing continua with length scale effects is established via numerical simulations of a few beam and plane-stress problems. [ABSTRACT FROM AUTHOR]

Abstract: The goal of this study is to understand the physical meaning and evaluate the intrinsic length scale parameters, featured in the theories of gradient elasticity, by deploying the analytical treatment and experimental measurements of the dispersion of elastic waves. The developments are focused on examining the propagation of longitudinal waves in an aluminum rod with periodically varying cross-section. First, the analytical solution for the dispersion relationship, based on the periodic cell analysis of a bi-layered laminate and Bloch theorem, is compared to two competing models of gradient elasticity. It is shown that the customary gradient elastic model with two length-scale parameters is able to capture the dispersion accurately up to the beginning of the first band gap. On the other hand, the gradient elastic model with an additional length scale (affiliated with the fourth-order time derivative in the field equation) is shown to capture not only the first dispersion branch before the band gap, but also the band gap itself and the preponderance of the second branch. Closed form relations between the microstructure parameters and the intrinsic length scales are obtained for both gradient elasticity models. By way of the asymptotic treatment in the limit of a weak contrast between the laminae, a clear physical meaning and scaling of the length-scale parameters was established in terms of: (i) the microstructure (given by the size of the unit cell and the contrast between the laminae), and (ii) thus induced dispersion relationship (characterized by the location and the width of the band gap). The analysis is verified through an experimental observation of wave dispersion, and wave attenuation within the band gap. A comparison between the analytical treatment, the gradient elastic model with three intrinsic length scales, and experimental measurements demonstrates a good agreement over the range of frequencies considered. [Copyright &y& Elsevier]

Abstract: A plane strain study of wedge indentation of a thin film on a substrate is performed. The film is modelled with the strain gradient plasticity theory by Gudmundson [Gudmundson, P., 2004. A unified treatment of strain gradient plasticity. Journal of the Mechanics and Physics of Solids 52, 1379–1406] and analysed using finite element simulations. Several trends that have been experimentally observed elsewhere are captured in the predictions of the mechanical behaviour of the thin film. Such trends include increased hardness at shallow depths due to gradient effects as well as increased hardness at larger depths due to the influence of the substrate. In between, a plateau is found which is observed to scale linearly with the material length scale parameter. It is shown that the degree of hardening of the material has a strong influence on the substrate effect, where a high hardening modulus gives a larger impact on this effect. Furthermore, pile-up deformation dominated by plasticity at small values of the internal length scale parameter is turned into sink-in deformation where plasticity is suppressed for larger values of the length scale parameter. Finally, it is demonstrated that the effect of substrate compliance has a significant effect on the hardness predictions if the effective stiffness of the substrate is of the same order as the stiffness of the film. [Copyright &y& Elsevier]