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1. Maugis-Dugdale model of elastic contact ( contact pressure )
pH Hertz contact pressure (Pa)
FH Hertz contact force (N)
πpi
aContact radius (m)
rRadius (-a<r<a) (m)
Variables...
  valueunitslink
pH
FH
a
r
2. Maximum contact pressure between two spheres
p0Maximum contact pressure (Pa)
FForce applied on the contact area (N)
πpi
aRadius of the circle of the contact area (m)
Variables...
  valueunitslink
p0
F
a
3. Johnson-Kendall-Roberts (JKR) model of elastic contact between two spheres ( contact radius)
aContact radius (m)
RRadius R = (R1*R2)/(R1+R2) (m)
EYoung's modulus of the two spheres (Pa)
FForce applied on the body (N)
γHalf of the total surface energy of both surfaces per unit area (J/m2)
πpi
Variables...
  valueunitslink
a
R
E
F
γ
4. Derjaguin-Muller-Toporov (DMT) model of elastic contact between two spheres (contact radius)
aThe contact radius (m)
RRadius R = (R1*R2)/(R1+R2) (m)
EYoung's modulus of the two spheres (Pa)
FForce applied on the body (N)
γHalf of the total surface energy of both surfaces per unit area (J/m2)
πpi
Variables...
  valueunitslink
a
R
E
F
γ
5. Maugis-Dugdale model of elastic contact between two spheres( contact force)
FHHertzian contact force (N)
E Young's modulus of the two spheres (Pa)
aContact radius (m)
RRadius R =(R1*R2)/(R1+R2) (m)
Variables...
  valueunitslink
FH
E
a
R
6. Effective Radius of a Contact Area between two spheres
RThe effective Radius of the Contact Area (m)
R1Radius of one sphere (m)
R2Radius of the other sphere (m)
Variables...
  valueunitslink
R
R1
R2
7. Pressure in a Contact Area between two spheres
pr Pressure in the Contact Area (Pa)
p0The maximum contact pressure (Pa)
rDistance from the center of the circle (m)
aThe radius of the circle (contact area) (m)
Variables...
  valueunitslink
pr
p0
r
a
8. Radius of a contact area between a sphere and an elastic half-space
aRadius of the contact area (m)
RRadius of the sphere (m)
dDepth of the half-space (m)
Variables...
  valueunitslink
a
R
d
9. Johnson-Kendall-Roberts (JKR) model of elastic contact between two spheres ( pull-off force)
FcThe tensile load ( contact radius equal to zero) (N)
γHalf of the total surface energy of both surfaces per unit area (J/m2)
πpi
RRadius R = (R1*R2)/(R1+R2) (m)
Variables...
  valueunitslink
Fc
γ
R
10. Total force on a contact area between a rigid conical indenter and an elastic half-space related to the contact radius
FTotal force on the contact area (N)
πpi
EModulus of elasticity ( Young's modulus) (Pa)
νPoisson's ratio (dimensionless)
aContact radius (m)
θAngle between the plane and the side surface of the cone (radians)
Variables...
  valueunitslink
F
E
ν
a
θ
11. Maugis-Dugdale model of elastic contact between two spheres (depth of penetration)
dHPenetration due to elastic compression (m)
aContact radius (m)
RRadius R = (R1*R2)/(R1+R2) (m)
Variables...
  valueunitslink
dH
a
R
12. Elastic modulus of a contact area between a sphere and an elastic half-space
EModulus of elasticity ( Young's modulus) of the contact area (Pa)
ν1Poisson's ratio of the sphere (dimensionless)
E1Young's Modulus of material one (sphere) (Pa)
ν2Poisson's ratio of the half-space (dimensionless)
E2Young's Modulus of material two ( half-space) (Pa)
Variables...
  valueunitslink
E
ν1
E1
ν2
E2
13. Force aplied at a contact area between a sphere and an elastic half-space
FForce aplied at the contact area (N)
EModulus of elasticity ( Young's modulus) (Pa)
RRadius of the sphere (m)
dDepth of the half-space (m)
Variables...
  valueunitslink
F
E
R
d
14. Maximum contact pressure between a rigid cylinder and an elastic half-space
p0Maximum contact pressure (Pa)
πpi
EModulus of elasticity ( Young's modulus) (Pa)
dThe indentation depth (m)
aRadius of the cylinder (m)
Variables...
  valueunitslink
p0
E
d
a
15. Pressure distribution on a Contact Area between a rigid cylinder and an elastic half-space
prPressure on the Contact Area (Pa)
p0Maximum contact Pressure (Pa)
rDistance from the center of the circle of the contact area (m)
aRadius of the cylinder (m)
Variables...
  valueunitslink
pr
p0
r
a
16. Radius of a Contact Area between two cylinders with parallel axes
aRadius of the Contact Area (m)
R1Radius of one of the cylinders (m)
R2Radius of the other cylinder (m)
dIndentation depth (m)
Variables...
  valueunitslink
a
R1
R2
d
17. Depth of indentation of a Contact Area between two spheres
dThe depth of indentation of the Contact Area (m)
aRadius of the circle of the contact area (m)
RThe effective radius (m)
Variables...
  valueunitslink
d
a
R
18. Radius of a Contact Area between two spheres related to the force
aRadius of the circle (contact area) (m)
FForce applied on the contact area (N)
REffective Radius (m)
EModulus of elasticity ( Young's modulus) (Pa)
Variables...
  valueunitslink
a
F
R
E
19. Total indentation depth of a contact area between a rigid cylinder and an elastic half-space
dTotal indentation depth (m)
πpi
ϵDepth of the contact region (m)
Variables...
  valueunitslink
d
ϵ
20. Bradley model of the force applied on a contact area between two spheres
FzTotal force of adhesion between the two rigid spheres. between the spheres (N)
πpi
γHalf of the total surface energy of both surfaces per unit area (J/m2)
R1Radius of one of the spheres (m)
R2Radius of the second sphere (m)
z0The equilibrium separation of the two planes (m)
zDistance from one sphere to the other (m)
Variables...
  valueunitslink
Fz
γ
R1
R2
z0
z
21. Force on a Contact Area between a rigid cylinder and an elastic half-space
FForce on the Contact Area (N)
aRadius of the cylinder (m)
EModulus of elasticity ( Young's modulus) (Pa)
dThe indentation depth (m)
Variables...
  valueunitslink
F
a
E
d
22. Depth of the contact region between a rigid conical indenter and an elastic half-space
ϵDepth of the contact region (m)
aRadius of the contact area (circle) (m)
θAngle between the plane and the side surface of the cone (radians)
Variables...
  valueunitslink
ϵ
a
θ
23. Maximum Pressure on a Contact Area between two cylinders with parallel axes
p0Maximum pressure (Pa)
EModulus of elasticity ( Young's modulus) (Pa)
FApplied force (N)
πpi
LLength of the contact area (of the cylinders) (m)
RThe contact radius (m)
Variables...
  valueunitslink
p0
E
F
L
R
24. Force on a Contact Area between two cylinders with parallel axes
FForce on the Contact Area (N)
πpi
EModulus of elasticity ( Young's modulus) (Pa)
LLength of the contact area (m)
dIndentation depth (m)
Variables...
  valueunitslink
F
E
L
d
25. Total force on a contact area between a rigid conical indenter and an elastic half-space related to the total depth
FTotal force on the contact area (N)
EModulus of elasticity ( Young's modulus) (Pa)
πpi
νPoisson's ratio (dimensionless)
dTotal indentation depth (m)
θAngle between the plane and the side surface of the cone (radians)
Variables...
  valueunitslink
F
E
ν
d
θ

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