Strain gradient elasticity within the symmetric BEM formulation

Terravecchia, S.; Panzeca, T.; Polizzotto, Castrenze

doi:10.3221/igf-esis.29.07

Cited by 3 publications

(2 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Numerical investigation of pantographic structures requires the development of new techniques [18][19][20][21][22][23][24][25][26]. In addition, the proper employment of existing methods, for example [27], are used to obtain the dynamics of such a class of microstructured materials.…”

Section: Introductionmentioning

confidence: 99%

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

2016

View full text Add to dashboard Cite

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

show abstract

Section: Introductionmentioning

confidence: 99%

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

2016

View full text Add to dashboard Cite

show abstract

“…The deficiencies of classical approaches when the material behavior exhibits size-scale effects are investigated in [59], and in [47] a novel invariance requirement (micro-randomness) in addition to isotropy is formulated, which implies conformal invariance of the curvature. The numerical investigation of structures of the type considered also requires special attention, and it is therefore important in the development of novel techniques [5][6][7][8][9]37,38,[48][49][50][51]65] or the proper employment of the existing ones (see, for instance, [68], where Galerkin boundary element method is used to address a class of strain gradient elastic materials).…”

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.

135

View full text Add to dashboard Cite

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.

show abstract

Analytical Solutions of 2-dimensional Second Gradient Linear Elasticity for Continua with Cubic-D4 Microstructure

Placidi¹,

Rosi²,

Barchiesi³

2019

Advanced Structured Materials

View full text Add to dashboard Cite

Strain gradient elasticity within the symmetric BEM formulation

Cited by 3 publications

References 9 publications

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

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

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

Analytical Solutions of 2-dimensional Second Gradient Linear Elasticity for Continua with Cubic-D4 Microstructure

Contact Info

Product

Resources

About