King post truss as a motif for internal structure of (meta)material with controlled elastic properties

One of the most interesting challenges in the modern theory of materials consists in the determination of those microstructures which produce, at the macro-level, a class of metamaterials whose elastic range is many orders of magnitude wider than the one exhibited by ‘standard’ materials. In Dell’Isola et al. (2015 Zeitschrift für angewandte Mathematik und Physik 66, 3473- 3498. (doi: 10.1007/s00033-015-0556-4)), it was proved that, with a pantographic microstructure constituted by ‘long’ microbeams it is possible to obtainmetamaterials whose elastic range spans up to an elongation exceeding 30%. In this paper, we demonstrate that the same behaviour can be obtained bymeans of an internal microstructure based on a king post motif. This solution shows many advantages: it involves only microbeams; all constituting beams are undergoing only extension or compression; all internal constraints are terminal pivots. While the elastic deformation energy can be determined as easily as in the case of long-beam microstructure, the proposed design seems to have obvious remarkable advantages: it seems to be more damage resistant and therefore to be able to have a wider elastic range; it can be realized with the same three-dimensional printing technology; it seems to be less subject to compression buckling. The analysis which we present here includes: (i) the determination of Hencky-type discrete models for king post trusses, (ii) the application of an effective integration scheme to a class of relevant deformation tests for the proposed metamaterial and (iii) the numerical determination of an equivalent second gradient continuum model. The numerical tools which we have developed and which are presented here can be readily used to develop an extensive measurement campaign for the proposed metamaterial

Micromechanical stress–displacement model for rough interfaces: Effect of asperity contact orientation on closure and shear behavior

AbstractThe coupled normal-shear contact behavior of rough surfaces remains a problem of interest with applications in many practical engineering problems. In this paper, we have further developed a micromechanical approach for obtaining the stress–displacement behavior of rough interfaces. The micromechanical approach considers the mechanics of asperity contacts and utilizes statistical description of interface roughness. Here we have focused upon the role of asperity contact orientations. To that end, we have incorporated asperity contact relative curvature distribution in our model and derived a relationship for the extent of asperity contact orientations in terms of the asperity contact relative curvature and interface closure. This relationship allows us to define the range of asperity contact orientation as the interface is subjected to combined normal and shear loading. We have consequently refined our stress–displacement relationship and its numerical evaluation procedure to include the asperity contact relative curvature distributions. We find that the asperity contact relative curvature has a significant effect on the extent of asperity contact orientation, and consequently on the shear behavior of the interface. We also find that the coupling between the normal and the shear responses, the interface frictional strength and the shear displacement hardening behavior are closely related to the extent of asperity contact orientations

Micromechanical model of rough contact between rock blocks with application to wave propagation

This is the published version. Copyright 2008 De Gruyter Open.The relationship between effective stiffness of rough contacts of rock blocks and transmission of plane waves is well known. Effective stiffness of a rough contact may be related to the force-deformation behavior of the asperity contacts and the statistical description of rock joint surface topography through micromechanical methods. In this paper, a micromechanical methodology for computing the overall rock contact effective stiffness is utilized along with the imperfectly bonded interface model to investigate how transmitted and reflected wave amplitudes are affected by the incident wave frequency, rock joint closure and the existing rock joint normal stress conditions. As a result, expressions for reflected and transmitted wave amplitudes as well as group time delay of the wave-packets are obtained and parametrically evaluated

Granular micromechanics model for cementitious materials

Granular micromechanics is a strong tool for modeling the behavior of different types of materials wherein the global (i.e., macroscopic) response of the material is assumed to be derivable as a summation of the local (i.e., microscopic) responses between grains that compose the material point. Cementitious materials are clear examples of micromechanically complicated materials in which microscopic response significantly influences the global behavior. Modeling of these materials using traditional tensorial constitutive equations leads to the neglect of several microscopic features. Because in granular micromechanics, interactions between all particles are taken into account separately, the method naturally provides a robust tool for implementing different micromechanical features in the material structure. By introducing potential and dissipation functions at the local scale, a Clausius–Duhem type inequality in the microscopic scale is obtained and an expression of macroscopic Cauchy stress in terms of interparticle kinematics and forces is developed. Subsequently, we introduce a set of interparticle interaction functions to establish thermodynamically consistent intergranular constitutive relations particularly applicable to cementitious materials. As a result we obtain force laws which ensure asymmetric behavior in tension and compression. Updated loading–unloading–reloading criteria are implemented in the model with the capability of modeling damage and plasticity. Damage parameter in tangential direction is defined as a function of not only the tangential displacement component, but also the normal component of displacement as well as the average stress. Normal compressive force law parameters are also obtained as functions of the average stress which enables the model to capture the effects of confining stress. Tensile and compressive triaxial tests with different confining stresses have been simulated indicating “brittle” to “ductile” transition of the material behavior by increasing the confining stress. Biaxial failure surface is computed and the effect of change in the direction of loading and the resulting induced anisotropy on the failure stress state is captured. Moreover, volume control tests with different ratios of normal versus lateral strain increments and with different initial hydrostatic confining pressures have been modeled providing failure envelopes in the q–p (deviatoric stress–mean stress) plane

Development of Livelihood Index for Different Agro-Climatic Zones of India

A livelihood index has been developed for different agro-climatic zones of India, based on the secondary data for TE 2003. Six different sub-indices obtained are indicators of Infrastructure Status, Agricultural Status, Nutritional Status, Economic Status, Health and Sanitation Status and Food Availability Status in respective zones. A total of 57 variables have been considered for this study. Finally, a composite integrated livelihood index has been developed which indicates the livelihood status of different agro-climatic zones in the country. Also, 103 districts of low agricultural productivity have been identified within low livelihood regions. The results of this study have been compared with those of backward districts identified under Wage Employment Program by the Task Force of Planning Commission of India. It is found that about 60 per cent districts identified in this study are the same as identified by the Task Force. Further, the spatial distributions of the identified districts under the study have been mapped using GIS maps and it has been observed that almost same region of the country has been found to be most backward in both the studies. The study has revealed regional disparity in the development process and has suggested to formulate appropriate policies to bridge this disparity gap.Productivity Analysis, Resource /Energy Economics and Policy,

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Mechanical Properties of Cemented Sands Based on Inter-Particle Contact Behavior

The mechanical properties of cemented sands are modelled using a micromechanical approach. The derived model accounts for the packing structure, the particle properties and the contact properties