The corner element in classical elasticity and Cosserat elasticity

2021 ◽  
Vol 16 (2) ◽  
pp. 225-235
Author(s):  
Roderic S. Lakes
Keyword(s):  
Classical Elasticity ◽  
Cosserat Elasticity

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

1991 ◽  
Vol 113 (1) ◽  
pp. 148-155 ◽  
Author(s):  
R. Lakes
Keyword(s):  
Degrees Of Freedom ◽  
Fibrous Composite ◽  
Continuum Theory ◽  
Cellular Solids ◽  
Classical Elasticity ◽  
Structured Materials ◽  
Cosserat Elasticity ◽  
Generalized Continuum ◽  
Cosserat Continua ◽  
Continuum Theories

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.

Bending of a Cosserat Elastic Bar of Square Cross Section: Theory and Experiment

2015 ◽  
Vol 82 (9) ◽  
Author(s):  
Roderic Lakes ◽  
W. J. Drugan
Keyword(s):  
Elasticity Theory ◽  
Cross Section ◽  
Surface Deformation ◽  
Length Scale ◽  
Polymer Foam ◽  
Pure Bending ◽  
Classical Elasticity ◽  
Dimensional Solution ◽  
Cosserat Elasticity ◽  
Classical Elasticity Theory

Pure bending experiments on prismatic bars of square cross section composed of reticulated polymer foam exhibit deformation behavior not captured by classical elasticity theory. Perhaps the clearest example of this is the observed sigmoidal deformation of the bars' lateral surfaces, which are predicted by classical elasticity theory to tilt but remain planar upon pure moment application. Such foams have a non-negligible length scale compared to the bars' cross-sectional dimensions, whereas classical elasticity theory contains no inherent length scale. All these facts raise the intriguing question: is there a richer, physically sensible, yet still continuum and relatively simple elasticity theory capable of modeling the observed phenomenon in these materials? This paper reports our exploration of the hypothesis that Cosserat elasticity can. We employ the principle of minimum potential energy for homogeneous isotropic Cosserat linear elastic material in which the microrotation vector is taken to be independent of the macrorotation vector (as prior experiments indicate that it should be in general to model such materials) to obtain an approximate three-dimensional solution to pure bending of a prismatic bar having a square cross section. We show that this solution, and hence Cosserat elasticity, captures the experimentally observed nonclassical deformation feature, both qualitatively and quantitatively, for reasonable values of the Cosserat moduli. A further interesting conclusion is that a single experiment—the pure bending one—suffices to reveal directly, via the observation of surface deformation, the presence of nonclassical elastic effects describable by Cosserat elasticity.

A force-based coupling scheme for peridynamics and classical elasticity

2013 ◽  
Vol 66 ◽  
pp. 34-49 ◽  
Author(s):  
Pablo Seleson ◽  
Samir Beneddine ◽  
Serge Prudhomme
Keyword(s):  
Coupling Scheme ◽  
Classical Elasticity

Representation of Solutions of Some Boundary Value Problems of Elasticity by a Sum of the Solutions of Other Boundary Value Problems

2003 ◽  
Vol 10 (2) ◽  
pp. 257-270
Author(s):  
N. Khomasuridze
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Cognitive Significance ◽  
Cylindrical Coordinates ◽  
Classical Elasticity ◽  
Representation Of Solutions ◽  
Elasticity Problems ◽  
Lamé Coefficients

Abstract Basic static boundary value problems of elasticity are considered for a semi-infinite curvilinear prism Ω = {ρ 0 < ρ < ρ 1, α 0 < α < α 1, 0 < 𝑧 < ∞} in generalized cylindrical coordinates ρ, α, 𝑧 with Lamé coefficients ℎ ρ = ℎ α = ℎ(ρ, α), ℎ𝑧 = 1. It is proved that the solution of some boundary value problems of elasticity can be reduced to the sum of solutions of other boundary value problems of elasticity. Besides its cognitive significance, this fact also enables one to solve some non-classical elasticity problems.

scholarly journals Modeling of Size Effects in Bending of Perforated Cosserat Plates

2017 ◽  
Vol 2017 ◽  
pp. 1-19 ◽  
Author(s):  
Roman Kvasov ◽  
Lev Steinberg
Keyword(s):  
Finite Element ◽  
Stress Concentration ◽  
Numerical Study ◽  
The Finite Element Method ◽  
Classical Elasticity ◽  
Element Analysis ◽  
Plate Deformation ◽  
The Finite Element Analysis ◽  
Circular Holes ◽  
Different Shapes

This paper presents the numerical study of Cosserat elastic plate deformation based on the parametric theory of Cosserat plates, recently developed by the authors. The numerical results are obtained using the Finite Element Method used to solve the parametric system of 9 kinematic equations. We discuss the existence and uniqueness of the weak solution and the convergence of the proposed FEM. The Finite Element analysis of clamped Cosserat plates of different shapes under different loads is provided. We present the numerical validation of the proposed FEM by estimating the order of convergence, when comparing the main kinematic variables with an analytical solution. We also consider the numerical analysis of plates with circular holes. We show that the stress concentration factor around the hole is less than the classical value, and smaller holes exhibit less stress concentration as would be expected on the basis of the classical elasticity.

Concurrent coupling of peridynamics and classical elasticity for elastodynamic problems

2019 ◽  
Vol 344 ◽  
pp. 251-275 ◽  
Author(s):  
Xiaonan Wang ◽  
Shank S. Kulkarni ◽  
Alireza Tabarraei
Keyword(s):  
Classical Elasticity
Sign in / Sign up

Export Citation Format

Share Document