# Thermoelastic expansion

#### Steven L. Jacques, Guenther Paltauf

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

 where M = Bulk Modulus [Pa/strain], strain is dimensionless = ρcs2, ρ = density [kg/m3], cs = sound velocity [m/s] β = Thermal expansivity [strain/degreeC], strain is dimensionless rho = Density [kg/m3] Cp = Specific heat [(J/(kg degC)] Γ = Grueneisen coefficient [dimensionless] μa = Absorption coefficient [m-1] H = Radiant exposure [J/m2] W = Energy depostion [J/m3]

The energy deposition W = μaH [J/m3].

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

The strain ε = βΔT [dimensionless].

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

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