9:15 AM - 9:30 AM
[SIT22-02] Towards constitutive equations for the deep Earth
Keywords:Deep Earth physical properties, Bulk modulus, Shear modulus
Currently a full treatment of both bulk- and shear properties at conditions of high pressure is only available for the Birch-Murnaghan formulation based on power series expansion of the strain energy. This representation is most suitable for extrapolation to mid-mantle conditions. Fits to experimental data for high pressures frequently favour the Vinet or Keane equations of state for bulk-modulus, but in neither case is there any connection to shear.
However, by working with invariants of the stretch tensor suitable isotropic constitutive equations can be found that add-in shear properties in a consistent way via local representations about a pre-stressed state. Such constitutive relations are particularly useful for high-pressure phases in the deep Earth, and make only slight modifications to popular representations for the bulk modulus.
However, by working with invariants of the stretch tensor suitable isotropic constitutive equations can be found that add-in shear properties in a consistent way via local representations about a pre-stressed state. Such constitutive relations are particularly useful for high-pressure phases in the deep Earth, and make only slight modifications to popular representations for the bulk modulus.