Titlebook: Handbook of Nonlocal Continuum Mechanics for Materials and Structures; George Z. Voyiadjis Living reference work 2020Latest edition

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Cosserat Approach to Localization in Geomaterials,uch as masonry, granular assemblies, fault gouges, porous media, and biomaterials. Cosserat continuum is a special case of what is called micromorphic, generalized or higher-order continua. Due to the presence of internal lengths in its formulation, Cosserat continuum is quite attractive for address

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Crack Initiation and Propagation in Laminated Composite Materials,fety engineers, and accident investigators. Because crack morphology on laminated windshield contains important information on energy mitigation, pedestrian protection, and accident reconstruction. In this chapter, we investigated the propagation characteristics for both radial and circular cracks i

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Dispersion of Waves in Micromorphic Media and Metamaterials,n metamaterials. Dispersion is defined as that phenomenon according to which the speed of propagation of elastic waves is not a constant, but depends on the wavelength of the traveling wave. In practice, all materials exhibit dispersion if one considers waves with sufficiently small wavelengths, sin

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Dynamic Brittle Fracture from Nonlocal Double-Well Potentials: A State-Based Model,el is developed within a state-based peridynamic formulation. At each instant of the evolution, we identify the softening zone where strains lie above the strength of the material. We show that deformation discontinuities associated with flaws larger than the length scale of nonlocality . can become

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ZEST

Finite Differences and Finite Elements in Nonlocal Fracture Modeling: A Priori Convergence Rates,previous chapter, we considered a differentiable version of the original bond-based model introduced in Silling (J Mech Phys Solids 48(1):175–209, 2000). There we showed, for a fixed horizon of nonlocal interaction ., that well-posed formulations of the model can be developed over H?lder spaces and

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Fractional Differential Calculus and Continuum Mechanics, since people working on various fields using fractional calculus take for granted that a fractional physical problem is set up by simple substitution of the conventional derivatives to any kind of the plethora of fractional derivatives. However, that procedure is meaningless, although popular, sinc

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Fractional Nonlocal Continuum Mechanics and Microstructural Models,act fractional-order difference operators. Continuous limit of suggested lattice operators gives continuum fractional derivatives of non-integer orders. The proposed approach gives a new microstructural basis to formulation of theory of nonlocal materials with power-law nonlocality. Moreover these l