Abstract
This article proposes a simplified way to solve solid mechanic problems in micropolar elasticity using the solution found in the classic theory of elasticity as a starting point. In this study, an analysis of the linear isotropic micropolar elasticity is conducted based on the properties imposed on the micropolar medium by the constitutive and equilibrium equations. To ascertain how the micropolar medium responses deviate from Hooke’s theory of elasticity, different loading conditions were classified. Three cases have been found so far: the rotational couple response, the quasi-classic equilibrium of momentum response and the general case. This study is the first in a series planned to explore the use of commercial packages of finite element in order to solve micropolar elasticity problems.
Highlights
There are a number of elasticity theories which are based on the assumption that a solid is a continuous medium [1]
This section concentrates on the Linear Isotropic Micropolar Elasticity Theory and presents the equations that are used in the remaining part of the paper
The objective of this paper is to present a simple way to solve the micropolar isotropic material strength for engineering applications
Summary
There are a number of elasticity theories which are based on the assumption that a solid is a continuous medium [1] One such theory is the classic elasticity theory based on Hooke’s law and is the one on which most of the commonly used materials in engineering are based. In the case of human bones, several factors affect the mechanical response among which are age, gender and density Because of these factors there is a wide range in the variation among the mechanical properties of this solid [2] and alternative elasticity theories should be used to model them properly. The focus is on the determination of the condition that does not conform to the rotational coupled behaviour This latter is still a classical-type equilibrium of momentum equation and, a displacement field similar to the classical elasticity, can be assumed. The final section presents a methodology to solve iteratively all other loading conditions that do not fall under the cases considered in the previous sections; it is still an exact solution
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