Thermoelastic expansion

The pressure generated in an object by thermoelastic expansion due to a very short laser pulse is described:

M

= Bulk Modulus [Pa/strain], strain is dimensionless

= ρc_s²,

c_s

= sound velocity [m/s]

β

= Thermal expansivity [strain/degreeC], strain is dimensionless

ρ

= Density [kg/m³]

C_p

= Specific heat [(J/(kg degC)]

Γ

= Grueneisen coefficient [dimensionless]

μ_a

= Absorption coefficient [m^-1]

H

= Radiant exposure [J/m²]

W

= Energy depostion [J/m³]

The energy deposition W = μ_aH [J/m³].

The temperature rise ΔT = (energy deposition)/(rho C_p) [degree C].

The strain ε = βΔT [dimensionless].

The stress or pressure = Mε [J/m³] = [kg/(m s²] = [Pa].

The Grueneisen coefficient Γ = Mβ/(ρ C_p) [dimensionless].

The units of pressure (P) are (force)/(area). The units of energy deposition (W) are (energy)/(volume) = (force x distance)/(area x distance) in which the distance term cancels to equal (force)/(area). Hence the units of pressure and energy deposition are identical. The conversion factor for pressure is 1 J/m³ = 1 Pa = 10^-5 [bar].