#### MAT_REBAR

###### Material properties
*MAT_REBAR
"Optional title"
mid, $\rho$, $E$
cid, $c$, $\dot{\varepsilon}_0$, $W_c$, $\tau_{max}$, bend, $r_{ref}$
##### Parameter definition
VariableDescription
mid Unique material identification number
$\rho$ Density
$E$ Young's modulus
cid ID of a CURVE or FUNCTION defining plastic flow stress versus plastic strain
$c$ Strain rate hardening parameter
default: 0
$\dot{\varepsilon}_0$ Reference strain rate
default: 1
$W_c$ Damage parameter
$\tau_{max}$ Maximum shear resistance between rebar and concrete
default: no slip
bend Flag to activate bending stiffness
options:
0 $\rightarrow$ no bending stiffness
1 $\rightarrow$ bending stiffness activated
$r_{ref}$ Ratio between rebar element length and rebar diameter at which the global ductility is correctly predicted
default: not used
##### Description

This material model can only be used for concrete reinforcement (see COMPONENT_REBAR, ELEMENT_REBAR). The plastic flow stress is defined as:

$\displaystyle{ \sigma_y = f(\varepsilon_{eff}^p) \cdot \left( 1 + \frac{\dot{\varepsilon}_{eff}^p}{\dot{\varepsilon}_0} \right)^c}$

where $f(\varepsilon_{eff}^p)$ is a user defined CURVE. Ductile failure is modeled with the Cockcroft-Latham failure criterion. A rebar element will be eroded once a damage parameter, $D$, has evolved from 0 to 1. The damage growth rate is defined as:

$\displaystyle{ \dot{D} = \frac{\mathrm{max}(0,\sigma) \cdot g(D)}{W_c} \cdot \dot{\varepsilon}_{eff}^p}$
$\displaystyle{ g(D) = \left\{ \begin{array}{ccc} 1 & : & D \leq D_{neck} \\ \frac{L_0}{D_0 r_{ref}} & : & D > D_{neck} \end{array} \right. }$

$\sigma$ is the tensile stress in the rebar. Note that damage only grows in tension (i.e. if $\sigma > 0$).

In uni-axial tension all deformations will be localized to a single element after onset of necking. This is a consequence of the one-dimensional stress formulation in ELEMENT_REBAR and it makes the global ductility element size dependent. $g(D)$ is a scale factor that is used to reduce this effect. Note that $g(D)$ is only used if $r_{ref} > 0$. The damage at onset of necking $D_{neck}$ is calculated automatically and it is based on $W_c$ and on the hardening curve. $L_0$ is the initial element length and $D_0$ is the initial rebar diameter.

$\tau_{max}$ is the maximum shear resistance between rebars and concrete. At shear stresses above $\tau_{max}$ the rebars begin to slide inside the concrete. In the current implementation, the shear resistance is maintained at $\tau_{max}$ even after initiation of sliding.