A Second Gradient Model for Deformable Porous Matrices Filled with an Inviscid Fluid

dell'Isola, F.; Sciarra, Giulio; Batra, R.C.

doi:10.1007/1-4020-3865-8_25

Cited by 5 publications

(4 citation statements)

References 7 publications

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“…As a result of his connection with Maugin and his group, in addition to the co-direction of Maurini’s PhD conducted with Joel Pouget, there are some works in the field of poroelasticity [56,57]. It is from these last works that the studies with Sciarra on poroelasticity developed [58–61].…”

Section: The “Piezoelectric Years”mentioning

confidence: 99%

Maestro and his pupils: History of a scientific production

Bersani

Cazzani

Giorgio

et al. 2022

Mathematics and Mechanics of Solids

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Section: The “Piezoelectric Years”mentioning

confidence: 99%

Maestro and his pupils: History of a scientific production

Bersani

Cazzani

Giorgio

et al. 2022

Mathematics and Mechanics of Solids

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“…The balance of moments is obtained from (20) and must be satisfied by taking into account not only the edge and wedge forces but also the double forces,…”

Section: Explicit Form Of the Balances Of Forces And Momentsmentioning

confidence: 99%

“…Another possibility is to consider higher-order gradient theories, in which the deformation energy depends on second and/or higher gradients of the displacement [17,33,40]. This is done in the literature for both monophasic systems (see [14,15,19,22,24,25,44,57], in which continuous systems are investigated, and [1,26,56,64] for cases of lattice/woven structures) and for biphasic (see, e.g., [16,18,20,21,41,45,60,61]) or granular materials [72]. Unlike classical Cauchy continua [4,62,63], second-and higher-order continua can respond to concentrated forces and other generalized contact actions (highly localized stress/strain concentration effects are studied, e.g., in [10]).…”

Section: Introductionmentioning

confidence: 99%

Gedanken experiments for the determination of two-dimensional linear second gradient elasticity coefficients

Placidi

Andreaus

Corte

et al. 2015

Z. Angew. Math. Phys.

132

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In the present paper, a two-dimensional solid consisting of a linear elastic isotropic material, for which the deformation energy depends on the second gradient of the displacement, is considered. The strain energy is demonstrated to depend on 6 constitutive parameters: the 2 Lamé constants (λ and μ) and 4 more parameters (instead of 5 as it is in the 3D-case). Analytical solutions for classical problems such as heavy sheet, bending and flexure are provided. The idea is very simple: The solutions of the corresponding problem of first gradient classical case are imposed, and the corresponding forces, double forces and wedge forces are found. On the basis of such solutions, a method is outlined, which is able to identify the six constitutive parameters. Ideal (or Gedanken) experiments are designed in order to write equations having as unknowns the six constants and as known terms the values of suitable experimental measurements.Mathematics Subject Classification. 74B99 · 74Q15.

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“…It is also possible to use second-or higher-order gradient theories, where, respectively, the deformation energy is a function of second-or higher-order displacement gradients [45][46][47][48]. Such a possibility is accomplished in the literature not only for monophasic [49][50][51][52][53][54] but also for biphasic (e.g., [55][56][57][58][59][60][61]) or granular material [62]systems and in cases of lattice/woven structures [63][64][65]. An important characteristic of second-and higher-order continua is that, unlike classical Cauchy continua, they can respond to concentrated forces and to other generalized contact actions (e.g., [66]).…”

Section: Introductionmentioning

confidence: 99%

Identification of two-dimensional pantographic structure via a linear D4 orthotropic second gradient elastic model

2016

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A linear elastic second gradient orthotropic two-dimensional solid that is invariant under (Formula presented.) rotation and for mirror transformation is considered. Such anisotropy is the most general for pantographic structures that are composed of two identical orthogonal families of fibers. It is well known in the literature that the corresponding strain energy depends on nine constitutive parameters: three parameters related to the first gradient part of the strain energy and six parameters related to the second gradient part of the strain energy. In this paper, analytical solutions for simple problems, which are here referred to the heavy sheet, to the nonconventional bending, and to the trapezoidal cases, are developed and presented. On the basis of such analytical solutions, gedanken experiments were developed in such a way that the whole set of the nine constitutive parameters is completely characterized in terms of the materials that the fibers are made of (i.e., of the Young’s modulus of the fiber materials), of their cross sections (i.e., of the area and of the moment of inertia of the fiber cross sections), and of the distance between the nearest pivots. On the basis of these considerations, a remarkable form of the strain energy is derived in terms of the displacement fields that closely resembles the strain energy of simple Euler beams. Numerical simulations confirm the validity of the presented results. Classic bone-shaped deformations are derived in standard bias numerical tests and the presence of a floppy mode is also made numerically evident in the present continuum model. Finally, we also show that the largeness of the boundary layer depends on the moment of inertia of the fibers

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A Second Gradient Model for Deformable Porous Matrices Filled with an Inviscid Fluid

Cited by 5 publications

References 7 publications

Maestro and his pupils: History of a scientific production

Maestro and his pupils: History of a scientific production

Gedanken experiments for the determination of two-dimensional linear second gradient elasticity coefficients

Identification of two-dimensional pantographic structure via a linear D4 orthotropic second gradient elastic model

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