2019
DOI: 10.1177/1081286519861827
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On the dependence of standard and gradient elastic material constants on a field of defects

Abstract: 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 a… Show more

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Cited by 24 publications
(14 citation statements)
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“…In Germain [12], micromorphic media of order one were derived in detail, and subsequently the equations for the general micromorphic medium were presented. For interested readers, we refer to the works of Toupin [15], Eringen [16], Misra and Poorsolhjouy [17], Eremeyev [18] and Solyaev et al [19] for further details.…”
Section: Introductionmentioning
confidence: 99%
“…In Germain [12], micromorphic media of order one were derived in detail, and subsequently the equations for the general micromorphic medium were presented. For interested readers, we refer to the works of Toupin [15], Eringen [16], Misra and Poorsolhjouy [17], Eremeyev [18] and Solyaev et al [19] for further details.…”
Section: Introductionmentioning
confidence: 99%
“…De Angelo et al [28] investigated the behavior of metallic pantographic sheets. In a number of papers, researchers have worked on the identification of constitutive parameters for second gradient materials (see Giorgio [29], Placidi et al [30], Yang et al [31], De Angelo et al [32], Nejadsadeghi et al [33], Solyaev et al [34], and Turco [35]). In a few studies, the 3D deformation of pantographic structures has been investigated in the context of second gradient modeling, for example in the studies presented by Steigmann and dell’Isola [36], Giorgio et al [37, 38], and Scerrato et al [39].…”
Section: Introductionmentioning
confidence: 99%
“…Open problems and challenges that could be tackled in the next future include: (i) a careful analysis of the stiffness parameters used to characterize the elastic response of the whole beam in the largedeformation regime, and in general when de Saint-Venant estimate of stiffness parameters does not apply; such parameters should be related to the material constitutive parameters of the material constituting the meso-beams such as the Young and tangential moduli, and to geometrical parameters of the beams cross-section, as the area, the shear correction factor, and the moment of inertia; (ii) the development of functionally graded materials, meaning those materials having stiffness parameters which are varying along the beam axis; an extended campaign of numerical simulations might unveil new and exotic mechanical behaviors, see [48][49][50][51]; (iii) the development of continuum models, as those developed and exploited, e.g., in [52][53][54][55][56][57][58][59][60], aimed at describing for large displacements systems with many discrete elements of the type presented here; besides being useful in unveiling so-called emerging phenomena, continuum models could help in identifying stiffness parameters; (iv) the exploitation of the presented approach to provide a validation and insight into new and existing approaches for the extension of stability theory in classical elastic media to micromorphic, strain-gradient [61,62], and Cosserat media, see, e.g., [12,[63][64][65][66][67][68][69][70]; (v) the extension of the presented approach to problems where dynamics effects are non-negligible, see, e.g., [71][72][73], like those studied in the active control of vibrations [74]; (vi) the validation of continuum approaches to the study of plane and curved structures moulded as, e.g., shells and tubes, see [75][76][77...…”
Section: Concluding Remarks and Future Challengesmentioning
confidence: 99%