An incorrect inequality in micropolar elasticity theory

1970 ◽  
Vol 21 (3) ◽  
pp. 494-497 ◽  
Author(s):  
Stephen C. Cowin
Keyword(s):  
Elasticity Theory ◽  
Micropolar Elasticity

Micropolar elasticity theory: a survey of linear isotropic equations, representative notations, and experimental investigations

2016 ◽  
Vol 22 (2) ◽  
pp. 224-242 ◽  
Author(s):  
Soroosh Hassanpour ◽  
Glenn R. Heppler
Keyword(s):  
Elasticity Theory ◽  
Elastic Constants ◽  
Couple Stress ◽  
Elastic Moduli ◽  
Experimental Results ◽  
Experimental Investigations ◽  
Micropolar Elasticity ◽  
Classical Elasticity ◽  
Material Constants ◽  
Isotropic Theory

This paper is devoted to a review of the linear isotropic theory of micropolar elasticity and its development with a focus on the notation used to represent the micropolar elastic moduli and the experimental efforts taken to measure them. Notation, not only the selected symbols but also the approaches used for denoting the material elastic constants involved in the model, can play an important role in the micropolar elasticity theory especially in the context of investigating its relationship with the couple-stress and classical elasticity theories. Two categories of notation, one with coupled classical and micropolar elastic moduli and one with decoupled classical and micropolar elastic moduli, are examined and the consequences of each are addressed. The misleading nature of the former category is also discussed. Experimental investigations on the micropolar elasticity and material constants are also reviewed where one can note the questionable nature and limitations of the experimental results reported on the micropolar elasticity theory.

Step-by-Step Simplification of the Micropolar Elasticity Theory to the Couple-Stress and Classical Elasticity Theories

2014 ◽  
Author(s):  
Soroosh Hassanpour ◽  
G. R. Heppler
Keyword(s):  
Elasticity Theory ◽  
Linear Theory ◽  
Elastic Constants ◽  
Couple Stress ◽  
Couple Stress Theory ◽  
Material Model ◽  
Micropolar Elasticity ◽  
Classical Elasticity ◽  
Stress Theory ◽  
Special Case

The micropolar elasticity theory provides a useful material model for dealing with fibrous, coarse granular, and large molecule materials. Though being a well-known and well-developed elasticity model, the linear theory of micropolar elasticity is not without controversy. Specially simplification of the microppolar elasticity theory to the couple-stress and classical elasticity theories and the required conditions on the material elastic constants for this simplification have not been discussed consistently. In this paper the linear theory of micropolar elasticity is reviewed first. Then the correct approach for a consistent and step-by-step simplification of the micropolar elasticity model with six elastic constants to the couple-stress elasticity model with four elastic constants and the classical elasticity model with two elastic constants is presented. It is shown that the classical elasticity is a special case of the couple-stress theory which itself is a special case of the micropolar elasticity theory.

A size-dependent nonlinear microbeam model based on the micropolar elasticity theory

2016 ◽  
Vol 227 (12) ◽  
pp. 3497-3515 ◽  
Author(s):  
Nan Ding ◽  
Xu Xu ◽  
Zhuoqun Zheng
Keyword(s):  
Elasticity Theory ◽  
Micropolar Elasticity ◽  
Size Dependent ◽  
Model Based

scholarly journals Modeling of the Flexible Needle Insertion into the Human Liver

2021 ◽  
Author(s):  
Veturia Chiroiu ◽  
Ligia Munteanu ◽  
Cristian Rugină ◽  
Nicoleta Nedelcu
Keyword(s):  
Elasticity Theory ◽  
Molecular Diagnosis ◽  
Human Liver ◽  
Chemotherapeutic Agent ◽  
Liver Tumors ◽  
Needle Insertion ◽  
Micropolar Elasticity ◽  
Robotic Assisted ◽  
Tumor Modeling

The insertion of the needle is difficult because the deformation and displacement of the organs are the key elements in the surgical act. Liver and tumor modeling are essential in the development of the needle insertion model. The role of the needle is to deliver into the tumor an active chemotherapeutic agent. We describe in this chapter the deformation of the needle during its insertion into the human liver in the context of surgery simulation of the high- robotic-assisted intraoperative treatment of liver tumors based on the integrated imaging-molecular diagnosis. The needle is a bee barbed type modeled as a flexible thread within the framework of the Cosserat (micropolar) elasticity theory.

scholarly journals Homogenization of very rough interfaces for the micropolar elasticity theory

2018 ◽  
Vol 54 ◽  
pp. 467-482 ◽  
Author(s):  
P.C. Vinh ◽  
V.T.N. Anh ◽  
D.X. Tung ◽  
N.T. Kieu
Keyword(s):  
Elasticity Theory ◽  
Micropolar Elasticity ◽  
Rough Interfaces
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