[MPM] RHT concrete material

[peterjwilson]

Hi @KratosMultiphysics/mpm , this PR brings in the Riedel-Hiermaier-Thoma (RHT) strain-rate sensitive plastic 3D law for concrete-like materials. A customized RHT Pressure-Alpha (compaction) Equation Of State (EOS) models the volumetric component of material response while the deviatoric portion is governed by a separate plastic strength model. The law has been checked against a separate Matlab model and aligns well with other published implementations.

Illustration of strength model under uniaxial compression

(* denotes normalized by compressive strength).

• Once the elastic limit is reached plastic strain accumulates.
• The new yield surface is interpolated between the elastic limit and the failure limit according to the hardening ratio (driven by plastic strain)
• Once the failure limit is reached (hardening ratio = 1.0), damage begins to accumulate.
• The new yield surface is interpolated between the failure limit and the residual limit according to the damage (driven by plastic strain)

Tests

5 tests are added, each considering many (>10) pressure states.

• Uniaxial compression
• Uniaxial tension
• Uniaxial compression/tension with strain rate effects
• Mixed shear compression
• Mixed shear tension

Other notes

• The original RHT softening law is mesh dependent. This is addressed with a linear softening law based of regularised fracture energy.
• The default material parameters correspond to standard (C30/37) 35MPa concrete.

References

[1] A general concrete model in hydrocodes: Verification and validation of the Riedel-Hiermaier-Thoma model in LS-DYNA https://doi.org/10.1177%2F2041419617695977

[2] Livermore Software Technology Corporation (2015) LS-DYNA Keyword User's Manual, vol. II (r. 6307).
http://ftp.lstc.com/anonymous/outgoing/jday/manuals/LS-DYNA_Manual_Volume_II_R8.0.pdf

[3] Nystrom, U. (2013). Modelling of concrete structures subjected to blast and fragment loading. Chalmers University of Technology.

[4] Pekmezi, G., Littlefield, D., and Martin, B. 'Implementation and Validation of the RHT Concrete Model', Proceedings of the 14th Annual Early Career Technical Conference, Birmingham, Alabama, November 2014.

[5] Christian Heckoetter, Juergen Sievers (2016). 'Weiterentwicklung der Analysemethodik zur Beruecksichtigung komplexer Last- annahmen bei hochdynamischen Einwirkungen auf Stahlbetonstrukturen.
https://www.grs.de/sites/default/files/pdf/grs-346.pdf