scholarly journals Towards Recognition of Scale Effects in a Solid Model of Lattices with Tensegrity-Inspired Microstructure

Solids ◽  
2021 ◽  
Vol 2 (1) ◽  
pp. 50-59
Author(s):  
Wojciech Gilewski ◽  
Anna Al Sabouni-Zawadzka
Keyword(s):  
Mechanical Properties ◽  
Continuum Model ◽  
Scale Effects ◽  
Theory Of Elasticity ◽  
Solid Model ◽  
Gradient Theory ◽  
General Description ◽  
Normal Forces ◽  
Second Gradient ◽  
Proposed Model

This paper is dedicated to the extended solid (continuum) model of tensegrity structures or lattices. Tensegrity is defined as a pin-joined truss structure with an infinitesimal mechanism stabilized by a set of self-equilibrated normal forces. The proposed model is inspired by the continuum model that matches the first gradient theory of elasticity. The extension leads to the second- or higher-order gradient formulation. General description is supplemented with examples in 2D and 3D spaces. A detailed form of material coefficients related to the first and second deformation gradients is presented. Substitute mechanical properties of the lattice are dependent on the cable-to-strut stiffness ratio and self-stress. Scale effect as well as coupling of the first and second gradient terms are identified. The extended solid model can be used for the evaluation of unusual mechanical properties of tensegrity lattices.

Dislocations in gradient elasticity revisited

2006 ◽  
Vol 462 (2075) ◽  
pp. 3465-3480 ◽  
Author(s):  
Markus Lazar ◽  
Gérard A Maugin
Keyword(s):  
Gradient Elasticity ◽  
Theory Of Elasticity ◽  
Gradient Theory ◽  
Two Dimensional ◽  
Helmholtz Equations ◽  
Plastic Distortion ◽  
Second Gradient ◽  
The Fourier Transform ◽  
Fourier Type ◽  
Edge Dislocations

In this paper, we consider dislocations in the framework of first as well as second gradient theory of elasticity. Using the Fourier transform, rigorous analytical solutions of the two-dimensional bi-Helmholtz and Helmholtz equations are derived in closed form for the displacement, elastic distortion, plastic distortion and dislocation density of screw and edge dislocations. In our framework, it was not necessary to use boundary conditions to fix constants of the solutions. The discontinuous parts of the displacement and plastic distortion are expressed in terms of two-dimensional as well as one-dimensional Fourier-type integrals. All other fields can be written in terms of modified Bessel functions.

Continuum model of microstructure induced softening for strain gradient materials

2018 ◽  
Vol 24 (8) ◽  
pp. 2374-2391 ◽  
Author(s):  
Massimo Cuomo
Keyword(s):  
Continuum Model ◽  
Large Scale ◽  
Scale Effects ◽  
Gradient Material ◽  
Complex Materials ◽  
Gradient Plasticity ◽  
Gradient Materials ◽  
Second Gradient ◽  
Evolution Laws ◽  
Anelastic Deformation

Gradient plasticity has been introduced to predict localization bands induced by softening or damage, and has been extended to micromorphic models used for materials with microstructure and scale effects. Motivated by the consideration that in complex materials there may exist different mechanisms for the evolution of anelastic deformation at the small and at the large scale, and that they may interact, in the paper a model of second gradient material with two different evolution laws for the macroscopic and for the microscopic plastic strain is proposed, the latter related to the presence of second gradient deformation. The model is intended to be used for metamaterials, and its relevant properties can be obtained from an homogenization analysis at the microlevel.

scholarly journals Soft and Stiff Simplex Tensegrity Lattices as Extreme Smart Metamaterials

Materials ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 187 ◽  
Author(s):  
Anna Al Sabouni-Zawadzka ◽  
Wojciech Gilewski
Keyword(s):  
Continuum Model ◽  
Theory Of Elasticity ◽  
Structural Members ◽  
Qualitative Properties ◽  
Normal Forces ◽  
Shear Modes ◽  
Actual Configuration ◽  
Deformation Modes ◽  
Extreme Materials

The present paper is dedicated to an evaluation of novel cellular metamaterials based on a tensegrity pattern. The materials are constructed from supercells, each of which consists of a number of simplex modules with different geometrical proportions. Mechanical properties of the metamaterial can be controlled by adjusting the level of self-equilibrated forces or by changing the properties of structural members. A continuum model based on the equivalence of strain energy of the 3D theory of elasticity with a discrete formulation is used to identify the qualitative properties of the considered metamaterials. The model allows the inclusion of nonlinearities related to the equations of equilibrium in actual configuration of the structure with self-equilibrated set of normal forces typical for tensegrities. The lattices are recognised as extreme metamaterials according to the eigensolution of the equivalent elasticity matrices of the continuum model. The six representative deformation modes are defined and discussed: stiff, soft and medium extensional modes and high (double) as well as low shear modes. The lattices are identified as unimode or nearly bimode according to the classification of extreme materials.

A Numerical Description of a Liquid-Vapor Interface Based on the Second Gradient Theory

1995 ◽  
Vol 22 (1) ◽  
pp. 1-14 ◽  
Author(s):  
Didier Jamet ◽  
Olivier Lebaigue ◽  
Jean-Marc Delhaye ◽  
N. Coutris
Keyword(s):  
Gradient Theory ◽  
Vapor Interface ◽  
Second Gradient ◽  
Liquid Vapor

USE OF STRAIN GRADIENT THEORY FOR MODELING THE SIZE-DEPENDENT PULL-IN OF ROTATIONAL NANO-MIRROR IN THE PRESENCE OF MOLECULAR FORCE

2013 ◽  
Vol 27 (18) ◽  
pp. 1350083 ◽  
Author(s):  
Y. TADI BENI ◽  
M. ABADYAN
Keyword(s):  
Strain Gradient ◽  
Continuum Theory ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Cross Sectional ◽  
Size Dependent ◽  
Proposed Model ◽  
Molecular Force ◽  
Intrinsic Material Length ◽  
Material Length

Experiments reveal that mechanical behavior of nanostructures is size-dependent. Herein, the size dependent pull-in instability of torsional nano-mirror is investigated using strain gradient nonclassic continuum theory. The governing equation of the mirror is derived taking the effect of electrostatic Coulomb and molecular van der Waals (vdW) forces into account. Variation of the rotation angle of the mirror as a function of the applied voltage is obtained and the instability parameters i.e., pull-in voltage and pull-in angle are determined. Nano-mirrors with square and circular cross-sectional beams are investigated as case studies. It is found that when the thickness of the torsional nano-beam is comparable with the intrinsic material length scales, size effect can substantially increase the instability parameters of the rotational mirror. Moreover, the effect of vdW forces on the size-dependent pull-in instability of the system is discussed. The proposed model is able to predict the experimental results more accurately than the previous classic models and reduce the gap between experiment and previous theories.

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