Stress-Strain Flashcards
What are three characteristics of mechanical properties?
-Intrinsic to the material
-Independent of the testing conditions
-Define the material’s response to mechanical loading
What happens during strain-hardening?
Plastic deformation and dislocations in the material occur
Define stresses
Internal forces generated by external loads applied to a component
-Coordinate system dependent
-Not uniform within a solid
Define strains
Internal deformations due to applied load
Measure of elongation, compression, and shear deformations
What is the proper name for the relationship between stresses and strains?
A constitutive law
What is the formula for uniaxial stress?
Uniaxial stress = applied load/initial cross-section perpendicular to the applied load
What does a positive/negative normal stress indicate?
Positive normal stress = tension, negative normal stress = compression
Define traction vector
The force exerted by one component formed during a virtual cut onto an infinitesimally small area on the other component
Traction vectors depend on how the cut was made
What is the traction vector definition of stresses?
Tractions exerted on the plane of a small cube within the material with faces perpendicular to the Cartesian axes
What notation is used for stresses and strains?
A tensor
What stresses are present in a lap shear test using glue?
Shear stress in the xy direction which is not uniform in this case
What stresses are present in pure bending?
One principle stress which is equal to -My/I where I is the second moment of inertia
How do stresses affect bone development?
Bone architecture follows the directions of principal stresses
Bone is densest where bending stresses are highest
What is the constitutive law for linear elasticity?
Isotropic Hooke’s law - can compute stresses from strains or vice versa
What are two examples of material properties?
Poisson’s ratio and Young’s modulus
What is the condition for linearizing a problem?
Low strain (<5%)
What happens to the total Green strain tensor (aka Lagrangian strain) during the small strain approximation?
The second order terms are neglected
What is true/Cauchy stress?
Force in the current state divided by area in the current state
What is nominal/1st Piola-Kirchhoff stress/engineering stress?
Force in the current state divide by area in the reference state
What is engineering strain?
Elongation divided by length in the reference state
What is natural strain?
Increment in length divided by length in the reference state
When engineering strain is much less than one, what is the relationship between engineering/natural/Lagrange strain?
The three quantities are approximately equal
What is stretch?
Length in the current state divided by length in the reference state
What are the work conjugates?
Increment of work in the current state divided by reference state volume (denoted as s delta lambda)
Increment of work in the current state divided by the current state volume (denoted as sigma delta epsilon)
What is the Neo-Hookean model? What materials does it work well for?
A hyperelastic material model for predicting the nonlinear stress-strain behavior of materials undergoing large deformations
There is a compressible and incompressible version
Works well for rubbery materials such as rubbers and hydrogels
What additional material aspect did the Gent model account for?
The chain stiffening at large strains (>100%)
To what strain, are the four hyperelastic material models valid?
Hookean - linear (up to 5% strain)
Neo-Hookean - up to 100% strain
Mooney-Rivlin - up to 400% strain
Gent or Arruda-Boyce - until 600% strain
What are the three components of continuum mechanics?
-Geometry of deformation
-Balance of forces
-Material model
