5.2.3 Rankine-Hill - Anisotropic

The plane stress anisotropic Rankine-Hill model provides for softening in the tensile (Rankine) regime and hardening, with subsequent softening in the compressive (Hill) regime. A typical application for this model is masonry. But please note that this model is not exclusive to masonry. The anisotropic Rankine-Hill criterion can also be applied to other orthotropic materials, like fiber reinforced composites, fractured rock and other layered or stacked materials. For theoretical backgrounds see §17.2.3.

    (syntax)

YIELD RANHIL

specifies that the Rankine-Hill criterion must be used.

YLDVAL

describes the yield surfaces: ftx is the tensile strength f_t.x in the x direction, fty is the tensile strength f_t.y in the y direction, alt is factor $\alpha_{{\tau}}^{}$ which determines the shear stress contribution to tensile failure ( $\alpha_{{\tau}}^{}$ = 1 is the standard Rankine value), alh is the factor $\alpha_{{h}}^{}$ (17.221). fcx is the compressive strength f_c.x in the x direction, fcy is the compressive strength f_c.y in the y direction, bet is factor $\beta$ which couples the normal compressive stresses (17.232), (typically $\beta$ = - 1.0 ), gam is factor $\gamma$ which controls shear stress contribution to compressive failure (17.235) ( $\gamma$ = 3.0 reproduces the isotropic Von Mises model).

HARVAL

defines the fracture energy G_ft for the Rankine model, or g_ft if you specify crack rate dependence crdep. Value gftx is the fracture energy in x direction, gfty in y direction.

CRACKB

h is the crack bandwidth h [§6.3]. In the compressive regime h is always used to regularize G_fc . In the tensile regime h is only used to regularize G_ft if you do not specify crack rate dependence crdep.

crdep

applies an optional crack rate dependence. If you do not specify crack rate dependence then DIANA will regularize G_ft with a crack bandwidth h .

CMORAT

applies the simple viscous cracking model (17.223). The two parameters define the contribution of the Crack Mouth Opening rate viscosity to the Rankine yield stress: mx is the dashpot viscosity m_x in x direction, and my is the dashpot viscosity m_y in y direction.

REFRAT

applies the model of Wu and Bazant (17.224). Parameters k0 k1 kapr respectively define the Crack Mouth Opening rate dependence parameters k₀ , k₁ , and $\dot{{\kappa}}_{{\mathrm{r}}}^{}$ .

CMPVAL

defines the fracture energy G_fc for the Hill model. Value gfcx is the fracture energy in x direction, gfcy in y direction.

TOPEPS

kap specifies the equivalent plastic strain $\kappa_{{\mathrm{p}}}^{}$ corresponding to the peak compressive stress.