Dilatational plastic equations, which can include the effects of ductile damage, are derived based on the equivalency in expressions for dissipated plastic work. Void damage developed internally at the large-strain stage is represented by an effective continuum being strain-softened and plastically dilated. Accumulation of this local damage leads to progressive failure in materials. With regard to this microstructural background, the constitutive parameters included for characterizing material behaviour have the sense of internal variables. They are not able to be determined explicitly by macroscopic testing but rather through computer simulation of experimental curves and data. Application of this constitutive model to mode-I cracking examples demonstrates that a huge strain concentration accompanied by a substantial drop of stress does occur near the crack tip. Eventually, crack propagation is simulated by using finite elements in computations. Two numerical examples show good accordance with experimental data. The whole procedure of study serves as a justification of the constitutive formulation proposed in the text. NOMENCLATURE 7 ' ' = Kirchhoff stress (contravariant tensor) 0'' = Cauchy (true) stress (contravariant tensor) DI;"' = plastic deformation rate (covariant tensor) urn = mean stress 0 : ) = plastic mean deformation rate a, = equivalent stress Dip) = plastic equivalent deformation rate D, =total equivalent deformation rate S' -deviatoric stress (mixed tensor) 4 plastic deviatoric deformation rate (mixed tensor) 6, = lo' D, dr 6:) = f D!$dt Or g" = metric tensor E t ) = deviatoric plastic tangent modulus E$$ = volumetric plastic tangent modulus -= ' Jaumann rate E = Young's modulus v = Poisson's ratio V,,, = covariant derivative of velocity

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In the present paper, numerical study of flow and heat transfer properties of RP-3 kerosene at supercritical conditions in an impingement model are conducted with SST k-? turbulence model and a 10-species surrogate of kerosene. The independence of grids is first studied and the numerical results are compared with experimental data for validation. Characteristics of flow and heat transfer of kerosene flow in the impingement model are studied with different inlet temperatures, different dimensionless open areas, and different separation distances. The heat transfer coefficients and pressure losses increase with decreasing dimensionless open areas. The separation distance H/d=2 gets the best heat transfer performance and the separation distance H/d=3 gets the best heat transfer uniformity on the target plate. Higher inlet temperature gets a higher heat transfer performance and heat transfer uniformity on the target plate.