We implemented the strength model described by Collins et al. ; precursor work to their model was conducted by Ivanov et al. . A detailed description of the model can be found in these papers; however, for the purpose of discussing specific model parameters, we reproduce the equations here. In CTH, the model is named the ROCK model to distinguish it from other existing models in the code.
 The strength model takes the current state (temperature, pressure, stress, and strain rate) of the material in a computational cell and returns the updated deviatoric stress tensor. The computational steps are as follows:
 1. Calculate the limiting tensile strength of the cell according to
where Yt is the limiting tensile strength, Yto is the maximum tensile strength, Ftherm is a thermal degradation factor, Dtot is the total damage, ξ is a material constant, Tm is the melting temperature, and T is the temperature. Note that the tensile strength decreases with increasing temperature and total damage; the hyperbolic tangent form for the reduction in strength due to temperature was determined experimentally by Ohnaka . Yt is the minimum principal stress (where Yt is negative) that the cell is allowed to have.
 In this paper, we demonstrate that a single material constant value for Yto is not appropriate for all applications, and that Yto should be replaced with a function of the length scale and strain rate. In addition, we note that for planetary-scale applications, the pressure dependence upon melting should be accounted for by replacing the single value for Tm with a melting curve.
 2. If there is no acoustic fluidization, then calculate the limiting shear strength of the cell according to
where Yi is the shear strength of the intact (total damage equal to zero) rock, Yo is the shear strength of the intact rock at zero pressure, μi is the coefficient of internal friction of the intact rock, P is the pressure, Ym is the limiting strength as pressure increases (the von Mises strength), Yd is the shear strength of the completely fragmented (total damage equal to one) rock, Yc is the zero-pressure cohesion, μd is the coefficient of friction of the completely fragmented rock, and Ys is the shear strength. Note that the shear strength is given as a linear combination of the shear strength of the completely intact and completely damaged rock (depending on the amount of damage), and includes thermal degradation effects. If Yd > Yi(which occurs when the pressure is sufficiently high), then these equations no longer hold and the shear stress is assumed to follow the thermally degraded intact shear strength, regardless of damage. This is based on the idea that at sufficiently high pressures, damaged rock is thought to behave like intact rock because the boundaries between fragments are so compressed that they behave like grain boundaries. The form of equation (A3) was determined experimentally by Lundborg .
 In this work, we demonstrate that Yd should be replaced by a function of strain rate and scale. Additionally, Ym is strain rate dependent, but probably not scale dependent.
 3. If there is acoustic fluidization [Collins, 2002; Collins et al., 2004; Melosh and Ivanov, 1999; Wunnemann and Ivanov, 2003], then calculate the limiting shear strength of the cell according to
where Yb is known as the Bingham yield strength. This is the yield strength if the pressure were equal to the local pressure minus the vibrational pressure (Pvib) (equations (A3) through (A5) where Yb is substituted for Ys and P − Pvib is substituted for P). ρ is the density, η is the acoustic fluidization viscosity, ɛrate is an invariant measure of the strain rate (specifically, the square root of the second invariant of the deviatoric strain rate tensor; this is chosen to correspond with the yield strength criteria), Cs is the sound speed, and vg is the vibrational particle velocity. The maximum vibrational particle velocity is assumed to be some fraction (Cvib) of the maximum cell velocity (Vg,max) and to decay exponentially with time (t) according to
where τ the acoustic fluidization decay constant. Looking at equation (A6), it is seen that acoustic fluidization will not cause failure of the target material unless the shear stresses exceed Yb (also known as the Bingham yield stress); above that, the material will flow with an effective viscosity of η.
 Note that the four acoustic fluidization parameters are validated through a combination of impact crater scaling laws for the sizes of transient and final crater cavities and observations of final crater shapes. These parameters are dependent on the assumed strength model and must be adjusted when the strength model parameters change.
 4. Calculate the trial deviatoric stresses, assuming that all of the deformation can be accommodated elastically. The shear modulus is degraded according to the same factor (Ftherm) used to degrade the shear and tensile strength.
 5. Calculate the second invariant, J2, of the trial deviatoric stress tensor.
 6. Apply the shear failure criteria. If J2 > Ys2, then the cell is failing in shear and the deviatoric stresses need to be decremented by a factor of Ys/.
 7. Apply the tensile failure criterion. If the greatest principal stress of the stress tensor is larger than the tensile yield strength (where tensile stresses are positive), then the cell is failing in tension. In CTH, void space is iteratively added to simulate fracture until the averaged principal tensile stress of the cell is equal to the tensile strength. Note that the model implementation by Collins et al.  does not add void upon tensile failure.
 8. Update the total plastic strain in the cell. If the cell is currently failing (in shear, tension, or both), then
where ɛtot is the total plastic strain in the cell, ɛrate is an invariant measure of the strain rate in the cell, and dt is the time step.
 9. Increment the shear damage (if the cell is failing in shear) using
where Ds is the shear damage, and ɛf is the equivalent plastic strain at failure. ɛf is an increasing function of pressure, such that at low pressures damage will accumulate quickly and the material will behave in a more brittle manner, while at high pressures damage will accumulate slowly and the material will behave in a more ductile manner. The input parameters Pbd (brittle ductile transition pressure) and Pbp (brittle plastic transition pressure) govern the pressures at which the transitions between these behaviors (brittle, semi-brittle, and ductile) occur for a given material. The shear damage is limited to one. Pbd can be calculated as the intersection of the intact yield surface and the damaged yield surface, while Pbp can be calculated as where the pressure is equal to twice the yield strength [Collins et al., 2004; Evans and Kohlstedt, 1995; Goetze, 1978].
 10. Increment the tensile damage (if the cell is failing in tension) using
where Dten is the tensile damage, Cs is the sound speed, and dmin is the minimum dimension of the cell. Essentially, equation (A11) can be thought of as simple crack growth model, where the crack growth speed is 0.4Cs (this is the maximum crack growth speed which is asymptotically approached as the crack grows [see Myers, 1994]) and the growth is limited to dmin in a given time step. The tensile damage is limited to one. From this work and Collins et al. , it is clear that the shear and tensile damage variables are nearly equal; thus having two damage variables may be unnecessary.
 11. Increment the total damage using
where the total damage is limited to a maximum value of one.