Experimental Micro Mechanics Methods for Conventional and Negative Poisson’s Ratio Cellular Solids as Cosserat Continua

Continuum representations of micromechanical phenomena in structured materials are described, with emphasis on cellular solids. These phenomena are interpreted in light of Cosserat elasticity, a generalized continuum theory which admits degrees of freedom not present in classical elasticity. These are the rotation of points in the material, and a couple per unit area or couple stress. Experimental work in this area is reviewed, and other interpretation schemes are discussed. The applicability of Cosserat elasticity to cellular solids and fibrous composite materials is considered as is the application of related generalized continuum theories. New experimental results are presented for foam materials with negative Poisson’s ratios.

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New insights on homogenization for hexagonal-shaped composites as Cosserat continua

Meccanica ◽

10.1007/s11012-021-01355-x ◽

2021 ◽

Author(s):

Marco Colatosti ◽

Nicholas Fantuzzi ◽

Patrizia Trovalusci ◽

Renato Masiani

Keyword(s):

Continuum Theory ◽

Representative Elementary Volume ◽

Elementary Volume ◽

Displacement Fields ◽

Micropolar Continuum ◽

Rigid Particles ◽

Hexagonal Shape ◽

Classical Models ◽

Elastic Interfaces ◽

Cosserat Continua

AbstractIn this work, particle composite materials with different kind of microstructures are analyzed. Such materials are described as made of rigid particles and elastic interfaces. Rigid particles of arbitrary hexagonal shape are considered and their geometry is described by a limited set of parameters. Three different textures are analyzed and static analyses are performed for a comparison among the solutions of discrete, micropolar (Cosserat) and classical models. In particular, the displacements of the discrete model are compared to the displacement fields of equivalent micropolar and classical continua realized through a homogenization technique, starting from the representative elementary volume detected with a numeric approach. The performed analyses show the effectiveness of adopting the micropolar continuum theory for describing such materials.

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SHEARING TESTS APPLIED TO PANTOGRAPHIC STRUCTURES

Acta Polytechnica CTU Proceedings ◽

10.14311/app.2017.7.0001 ◽

2016 ◽

Vol 7 ◽

pp. 1 ◽

Cited By ~ 12

Author(s):

Gregor Ganzosch ◽

Francesco Dell’Isola ◽

Emilio Turco ◽

Tomasz Lekszycki ◽

Wolfgang H. Müller

Keyword(s):

Rapid Manufacturing ◽

Pantographic Structures ◽

Deformation Response ◽

Shear Loads ◽

Generalized Continuum ◽

Complete Failure ◽

Elastic Cylinders ◽

Inextensible Fibers ◽

Fabric Materials ◽

Continuum Theories

With the advancements in 3D printing technology, rapid manufacturing of fabric materials with complex geometries became possible. By exploiting this technique, different materials with different structures have been developed in the recent past with the objective of making generalized continuum theories useful for technological applications. So-called pantographic structures are introduced: Inextensible fibers are printed in two arrays orthogonal to each other in parallel planes. These superimposed planes are inter-connected by elastic cylinders. Five differently-sized samples were subjected to shear-like loading while their deformation response was analyzed. Results show that deformation behavior is strong non-linear for all samples. Furthermore, all samples were capable to resist considerable external shear loads without leading to complete failure of the whole structure. This extraordinary behavior makes these structures attractive to serve as an extremely tough metamaterial.

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A Finite-Temperature Continuum Theory Based on Interatomic Potentials

Journal of Engineering Materials and Technology ◽

10.1115/1.2019865 ◽

2005 ◽

Vol 127 (4) ◽

pp. 408-416 ◽

Cited By ~ 63

Author(s):

H. Jiang ◽

Y. Huang ◽

K. C. Hwang

Keyword(s):

Temperature Dependence ◽

Finite Temperature ◽

Interatomic Potential ◽

Coefficient Of Thermal Expansion ◽

Harmonic Approximation ◽

Continuum Theory ◽

Single Wall Carbon Nanotubes ◽

Interatomic Potentials ◽

Atomistic Models ◽

Continuum Theories

There are significant efforts to develop continuum theories based on atomistic models. These atomistic-based continuum theories are limited to zero temperature (T=0K). We have developed a finite-temperature continuum theory based on interatomic potentials. The effect of finite temperature is accounted for via the local harmonic approximation, which relates the entropy to the vibration frequencies of the system, and the latter are determined from the interatomic potential. The focus of this theory is to establish the continuum constitutive model in terms of the interatomic potential and temperature. We have studied the temperature dependence of specific heat and coefficient of thermal expansion of graphene and diamond, and have found good agreements with the experimental data without any parameter fitting. We have also studied the temperature dependence of Young’s modulus and bifurcation strain of single-wall carbon nanotubes.

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