Stress-Strain Flashcards

1
Q

What are three characteristics of mechanical properties?

A

-Intrinsic to the material
-Independent of the testing conditions
-Define the material’s response to mechanical loading

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2
Q

What happens during strain-hardening?

A

Plastic deformation and dislocations in the material occur

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3
Q

Define stresses

A

Internal forces generated by external loads applied to a component

-Coordinate system dependent
-Not uniform within a solid

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4
Q

Define strains

A

Internal deformations due to applied load

Measure of elongation, compression, and shear deformations

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5
Q

What is the proper name for the relationship between stresses and strains?

A

A constitutive law

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6
Q

What is the formula for uniaxial stress?

A

Uniaxial stress = applied load/initial cross-section perpendicular to the applied load

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7
Q

What does a positive/negative normal stress indicate?

A

Positive normal stress = tension, negative normal stress = compression

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8
Q

Define traction vector

A

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

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9
Q

What is the traction vector definition of stresses?

A

Tractions exerted on the plane of a small cube within the material with faces perpendicular to the Cartesian axes

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10
Q

What notation is used for stresses and strains?

A

A tensor

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11
Q

What stresses are present in a lap shear test using glue?

A

Shear stress in the xy direction which is not uniform in this case

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12
Q

What stresses are present in pure bending?

A

One principle stress which is equal to -My/I where I is the second moment of inertia

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13
Q

How do stresses affect bone development?

A

Bone architecture follows the directions of principal stresses

Bone is densest where bending stresses are highest

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14
Q

What is the constitutive law for linear elasticity?

A

Isotropic Hooke’s law - can compute stresses from strains or vice versa

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15
Q

What are two examples of material properties?

A

Poisson’s ratio and Young’s modulus

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16
Q

What is the condition for linearizing a problem?

A

Low strain (<5%)

17
Q

What happens to the total Green strain tensor (aka Lagrangian strain) during the small strain approximation?

A

The second order terms are neglected

18
Q

What is true/Cauchy stress?

A

Force in the current state divided by area in the current state

19
Q

What is nominal/1st Piola-Kirchhoff stress/engineering stress?

A

Force in the current state divide by area in the reference state

20
Q

What is engineering strain?

A

Elongation divided by length in the reference state

21
Q

What is natural strain?

A

Increment in length divided by length in the reference state

22
Q

When engineering strain is much less than one, what is the relationship between engineering/natural/Lagrange strain?

A

The three quantities are approximately equal

23
Q

What is stretch?

A

Length in the current state divided by length in the reference state

24
Q

What are the work conjugates?

A

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)

25
Q

What is the Neo-Hookean model? What materials does it work well for?

A

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

26
Q

What additional material aspect did the Gent model account for?

A

The chain stiffening at large strains (>100%)

27
Q

To what strain, are the four hyperelastic material models valid?

A

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

28
Q

What are the three components of continuum mechanics?

A

-Geometry of deformation
-Balance of forces
-Material model