Example materials

Disclaimer: Most of these material models are appropriate for teaching/learning purposes. Research-level models must be vetted for the specific application.

Water Ice

The properties of ice depend on the grain structure, temperature and strain rates. Nominal values for the Young’s modulus \(E=9\) GPa and poisson’s ratio \(\nu=0.32\) [Petrovic, 2003]. The corresponding shear modulus \(G = \frac{E}{2(1+\nu)} = 3.38\) GPa. Cold ice under uniaxial strain has a Hugoniot Elastic Limit of 0.62 GPa [Stewart and Ahrens, 2005]. The average tensile strength for ice is 1.43 MPa at low strain rates [Petrovic, 2003]; the dynamic spall strength of ice is about 17 MPa [Lange and Ahrens, 1983]. The relationship between the Hugoniot Elastic Limit and the von Mises yield stress is:

\(\sigma_{vm} = \frac{(1-2\nu) \sigma_{HEL}}{(1-\nu)} = 0.328\) GPa.

Bulk modulus of ice is about 10 GPa at 150 K [Neumeier, 2018].

There are multiple options for the equation of state for H₂O, each with various strengths and weaknesses and should be chosen based on the desired application.

Example configuration file entry (mks):

mat1:
    str:
        type   : 'VM'
        gmod   : 3.38E9
        ys     : 0.328E9
        kmod   : 10.0E9
        cs0    : 3305.0
    frac:
        pfrac   : 17.0E6
        nrhomin : 0.9

Aluminum 6061

Al 6061 data from https://www.matweb.com/.

mat1:
    str:
        type   : 'VM'
        gmod   : 26.0E9
        ys     : 207.0E6
    frac:
        pfrac   : 276.0E6
        nrhomin : 0.9

Copper

Annealed copper shear modulus (46 GPa) and Poisson’s ratio (0.343) from https://www.matweb.com/.

Hugoniot elastic limit and tensile strength are dependence on temperature, strain rate, propagation distance, etc. [Zaretsky and Kanel, 2013]. These are nominal values for demonstration purposes only. For an HEL of 0.2 GPa, \(\sigma_{vm}=0.0956\) GPa.

Dynamic spall strength from https://aip.scitation.org/doi/full/10.1063/1.3607294

mat1:
    str:
        type   : 'VM'
        gmod   : 46.0E9
        ys     : 0.0956E9
    frac:
        pfrac   : 1.35E9
        nrhomin : 0.9

Stainless steel 304

Most parameters from [Duffy and Ahrens, 1997]. \(\nu_0=0.29\).

\(c_v=502.416\) J/K/kg from https://www.engineersedge.com/materials/specific_heat_capacity_of_metals_13259.htm

Need tensile strength; this is a guess.

All values mks.

mat1:
    eos:
        name   : 'Steel 304'
        type   : 'MGR'
        rhoref : 7870.0
        c0     : 4580.0
        s1     : 1.49
        gamma0 : 2.2
        cv     : 502.416
    str:
        type   : 'VM'
        gmod   : 78.0E9
        ys     : 0.2E9
    frac:
        pfrac   : 1.0E9
        nrhomin : 0.9

Quartz

alpha quartz

\(\alpha\)-quartz is not well represented by a simple material model. These values provide a coarse representation for teaching.

Wackerle (1962) HEL strongly dependent on orientation. Nominal \(\sigma_{HEL}=10\) GPa.

\(\nu=0.08\) https://agupubs.onlinelibrary.wiley.com/doi/full/10.1002/2017JB014606

\(\sigma_{vm} = \frac{(1-2\nu) \sigma_{HEL}}{(1-\nu)} = 9.3\) GPa.

Shear modulus http://www-odp.tamu.edu/publications/204_SR/103/103_t1.htm https://link.springer.com/article/10.1007/s00269-014-0711-z

Dynamic tensile strength approximately 1 GPa https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2022GL100468

mat1:
    eos:
        name   : 'Quartz'
        type   : 'MGR'
        rhoref : 2648.0
        c0     : 620.0
        s1     : 1.74
        gamma0 : 0.84
        cv     : 740.0
    str:
        type   : 'VM'
        gmod   : 44.4E9
        ys     : 9.3E9
    frac:
        pfrac  : 1.0E9
        nrhomin: 0.9

Fused quartz

The following US-up relationship for fused silica shock-compressed to 44–72 GPa was determined using the results from this study: US = 0.62(7) + 1.74(2)uP. [Berryman et al., 2019]

Poisson’s ratio is 0.17 https://www.heraeus.com/en/hca/fused_silica_quartz_knowledge_base_1/properties_1/properties_hca.html#tabs-608478-6

Wackerle 1962, FS HEL about 9.5 GPa. Ys = (1-2*.17)/(1-.17)*9.5E9; assume spall is Ys/10.

Gamma0 from SESAME. https://sgp.fas.org/othergov/doe/lanl/lib-www/la-pubs/00296704.pdf

Shear modulus and heat capacity from www.accuratus.com

mat1:
    eos:
        name   : 'Fused Silica'
        type   : 'MGR'
        rhoref : 2201.0
        c0     : 620.0
        s1     : 1.74
        gamma0 : 0.65
        cv     : 740.0
    str:
        type   : 'VM'
        gmod   : 31.0E9
        ys     : 7.55E9
    frac:
        pfrac   : 0.755E9
        nrhomin : 0.9

Forsterite

A tabular EOS is available from ststewart/aneos-forsterite-2019

Olivine/Dunite

These olivine parameters were developed in [Marinova et al., 2011].

mat1:
    eos:
        name   : 'Olivine'
        type   : 'TIL'
        rhoref : 3500.0
        E0     : 550.0E6
        EIV    : 4.5E6
        ECV    : 14.5E6
        AA     : 131.0E9
        BB     : 49.0E9
        a      : 0.5
        b      : 1.4
        alpha  : 5.0
        beta   : 5.0
        cv     : 860.0

Lithium Flouride (LiF)

Hugoniot from [Hawreliak et al., 2023]. Grueneisen parameter from [Duffy and Ahrens, 1997]. Heat capacity from Wikipedia.

Poisson’s ratio is 0.27.

mat1:
    eos:
        name   : 'LiF'
        type   : 'MGR'
        rhoref : 2640.0
        c0     : 5144.0
        s1     : 1.355
        s2     : 0.0
        gamma0 : 1.6
        cv     : 1507.0
    str:
        type   : 'VM'
        gmod   : 55.14E9
        ys     : 0.2E9
    frac:
        pfrac   : 0.02E9
        nrhomin : 0.9

https://www.crystran.co.uk/optical-materials/lithium-fluoride-lif

Specific Heat Capacity : 1562 J Kg-1 K-1 Dielectric Constant : 0.1 Youngs Modulus (E) : 64.97 GPa (2) Shear Modulus (G) : 55.14 GPa (2) Bulk Modulus (K) : 62.03 GPa (2)