An Introduction to Biomechanics pp 104-153 | Cite as

# Equilibrium, Universal Solutions, and Inflation

## Abstract

Let us begin by recalling three important observations from Chapters 1 and 2. First, equilibrium requires that Σ* F* =

**0**and Σ

*=*

**M****0**. Second, if a body is in equilibrium, then each of its parts are likewise in equilibrium. Third, there may exist at each point

*p*in a body (cf. Fig. 2.4) nine components of stress, six of which are independent, which we denote as σ

_{(face)(direction)}relative to the coordinate system of choice. Because stress may vary from point to point within a body, the components at a nearby point

*q*may have different values. (Note: It is usually convenient to refer components at different points to the same coordinate system.) Now, if we consider a small cube of material, centered about point

*p*which is located at (

*x*,

*y*,

*z*) and has stresses σ

_{ xx }, σ

_{ xy }, ..., σ

_{ zz }, then the stresses on the faces of the cube may differ from those at the center; that is, if the

*xx*component at the center of the cube is σ

_{ xx }, then on the positive and negative

*faces*of the cube, at distances ±Δ

*x*/2 from the center, we may have σ

_{ xx }+ Δσ

_{ xx }and σ

_{ xx }− Δσ

_{ xx }, respectively (i.e., values slightly greater than or less than that at point

*p*).

## Keywords

Abdominal Aortic Aneurysm Radial Stress Maximum Shear Stress Circumferential Stress Universal Solution## Preview

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