MATS_16102: PART ONE Flashcards
Give the meaning of this symbol:
G
Shear modulus
Give the meaning of this symbol:
E
Young’s modulus
Give the meaning of this symbol:
K
Bulk modulus
Give the meaning of this symbol:
ν
Poisson’s Ratio
Give the meaning of this symbol:
Λ
Total elastic energy
Give the meaning of this symbol:
Uv
Elastic potential energy
0.5* Fe2 or 0.5* εσ2
Give the meaning of this symbol:
𝜏xy
Shear stress on face x in the y direction
It’s a component of the Cauchy stress tensor
σij‘
Deviatoric stress tensor
σH | εH
Hydrostatic stress (tensor) | Hydrostatic strain (tensor)
εV
Volumetric strain
Gotten directly from the Cauchy stress tensor.
εV=3εH
How can a Cauchy stress tensor be identified
By its symmetry
The non-(primary) diagonal terms are paired and are the same number
Define a traction
The force applied over a unit area in a given direction
What rank of tensor is a vector
A rank 1 tensor
It needs ONE parameter to be fully defined: its direction
What is the rank of a tensor?
The amount of parameters needed to define it
What is the constraint on the range of application for Hooke’s law?
It is only applicable for small strains
State the 2 assumptions of the Voigt model for composites:
- The two materials have the same strain
- The applied force is shared between the materials in the composite
State the 2 assumptions of the Reiss model for composites:
- Strain is shared
- Stress is the same for both materials in the composite
The Voigt model describes —– loading direction?
Parallel loading direction
Defines the longitudinal Young’s modulus
The Reiss model describes —– loading direction?
Perpendicular loading direction
Defines the tranverse Young’s modulus
In a Cauchy stress tensor, the diagonal terms represent?
Volumetric stresses
In a Cauchy stress tensor, the non-diagonal terms represent?
Shear stresses
What do the rows of the Cauchy stress tensor represent?
The traction vectors acting on the x,y and z faces
from top to bottom
In what situations does a Cauchy stress tensor apply?
For a body experiencing small deformations
Give an equation relating bulk and Young’s moduli
E = K (1 - 2ν)
Give an equation relating Shear and Young’s moduli
E = 2G (1+ ν)
Poisson’s ratio describes the strain response of a material in what direction?
⊥ to the direction of the force.
E describes strain response parallel to the direction of the force.
True or False:
Pressure is equal to the negative of hydrostatic stress
True
True or False:
Hydrostatic stress is applied in all directions
True
Give the formula for true stress
σt=
Give the formula for true stress
σt=
