Solyaev, Yury; Lurie, Sergey; Barchiesi, Emilio; Placidi, Luca On the dependence of standard and gradient elastic material constants on a field of defects. (English) Zbl 1446.74090 Math. Mech. Solids 25, No. 1, 35-45 (2020). Summary: In this work, we consider a strain gradient elasticity theory with an extended number of field variables: the displacement vector and an additional scalar field defining the internal micro-deformation. The total internal energy of the model depends on the strain, the micro-deformation function, their gradients, and the coupling. The considered model can be treated as gradient/micromorphic. Moreover, the micro-deformation field can be treated as a field of scalar defects distributed along the medium. Based on analytic (one-dimensional) solutions of uniform/non-uniform deformation of the rod, we introduce (i) an apparent stiffness and (ii) an apparent length scale parameter. Subsequently, we provide a variant of continuum-on-continuum homogenization by equating tip displacements for the gradient/micromorphic medium and an equivalent strain gradient one. Elongation of the gradient/micromorphic rod is therefore equated with the corresponding elongation of the equivalent strain gradient rod, whose behavior is characterized by the apparent material constants. Subsequently, the non-dimensional coupling number is identified with a damage parameter. It is shown that, on the one hand, the apparent stiffness of the rod is reduced when such parameter increases. On the other hand, the apparent length scale parameter (i.e. the apparent second gradient elastic coefficient) increases when the damage parameter increases. Therefore, it is shown that the presence of defects in a second gradient linear elastic material may increase its apparent strain gradient behavior. Cited in 4 Documents MSC: 74B99 Elastic materials 74A60 Micromechanical theories Keywords:strain gradient elasticity; micro-dilatation theory; field of defects; apparent stiffness; apparent length scale parameter PDFBibTeX XMLCite \textit{Y. Solyaev} et al., Math. Mech. Solids 25, No. 1, 35--45 (2020; Zbl 1446.74090) Full Text: DOI References: [1] Piccardo, G, Ferrarotti, A, Luongo, A. Nonlinear generalized beam theory for open thin-walled members. Math Mech Solids 2017; 22(10): 1907-1921. · Zbl 1386.74078 [2] Piccardo, G, Ranzi, G, Luongo, A. A complete dynamic approach to the generalized beam theory cross-section analysis including extension and shear modes. Math Mech Solids 2014; 19(8): 900-924. · Zbl 1299.74109 [3] Auffray, N, dell’Isola, F, Eremeyev, VA, Madeo, A, Rosi, G. Analytical continuum mechanics à la Hamilton-Piola least action principle for second gradient continua and capillary fluids. Math Mech Solids 2015; 20(4): 375-417. · Zbl 1327.76008 [4] Khakalo, S, Niiranen, J. 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