# ^^Stress, strain, modulo di Young.

ref:  Storia.

## Situazione: cilindro tirato o pressato assialmente

Ut tensio sic vis. L'allungamento causa la forza elastica.

 *k ΔL → F F=kΔL

## Strain, stress, modulo di Young.

 F =E A L ΔL

 F A =E ΔL L

 σ=Eε

## strain, ε = ΔL/L, allungamento relativo.

 ε = ΔL L

## stress, sforzo, tensione

 σ = F A

it: tensione interna (o sollecitazione interna o sforzo)

en: stress (force per unit area)

## modulo di Young.

 E = σ ε
uniaxial stress
tensile or compressive stress in one direction and no stress in the other directions
modulus
is the diminutive of the Latin term modus which means measure

# Approfon

## Strain stress  VS  stress strain

scelgo: l'ordine della formula, nel senso

stress in funzione di strain,  l'allungamento causa la forza.

# Talk

## Titolo

1. stress, strain
c: originale
2. Strain, stress, modulo di Young.
c: 18_7_2020. Ho unito qui modulo di Young.

schey's equation

Y is the average flow stress of the material

flow stress    sforzo di flusso plastico

## Assumption

stres strain related by known constitutive equations.

constitutive equations
relate stress strain
• elastic deformation: simpler
• permanent deformation: complicated

• elastic deformation
• permanent deformation: plastic flow, fracture, phase change, etc.

Stress-strain_curve (Yield curve (physics))

## Uniaxial stress

A linear element of a structure is one that is essentially one dimensional and is often subject to axial loading only.

When a structural element is subjected to tension or compression its length will tend to elongate or shorten, and its cross-sectional area changes by an amount that depends on the Poisson's ratio of the material.

In engineering applications, structural members experience small deformations and the reduction in cross-sectional area is very small and can be neglected, i.e., the cross-sectional area is assumed constant during deformation.

For this case, the stress is called engineering stress or nominal stress and is calculated using the original cross section.

σe = P/Ao

Ao is the original cross-sectional area.

In some other cases, e.g., elastomers and plastic materials, the change in cross-sectional area is significant. For the case of materials where the volume is conserved (i.e. Poisson's ratio = 0.5), if the true stress is desired, it must be calculated using the true cross-sectional area instead of the initial cross-sectional area, as:

σtrue = ( 1 + εe ) ( σe )

εe   nominal (engineering) strain

σe   nominal (engineering) stress.

The relationship between true strain and engineering strain is given by

εtrue = ln ⁡ ( 1 + εe )

In uniaxial tension, true stress is then greater than nominal stress. The converse holds in compression.