Monti-Nuti steel model - stl_mn

This is a uniaxial steel model initially programmed by Monti et al. [1996], which is able to describe the post-elastic buckling behaviour of reinforcing bars under compression. It uses the Menegotto and Pinto [1973] stress-strain relationship together with the isotropic hardening rules proposed by Filippou et al. [1983] and the buckling rules proposed by Monti and Nuti [1992]. An additional memory rule proposed by Fragiadakis et al. [2008] is also introduced, for higher numerical stability/accuracy under transient seismic loading. Its employment should be confined to the modelling of reinforced concrete members where buckling of reinforcement might occur (e.g. columns under severe cyclic loading). Further, as discussed by Prota et al. [2009], with the correct calibration, this model, initially developed with ribbed reinforcement bars in mind, can also be employed for the modelling of smooth rebars, often found in existing structures.

Ten model calibrating parameters must be defined in order to fully describe the mechanical characteristics of the material:

Modulus of elasticity - Es
This is the initial elastic stiffness of the material. Its value usually oscillates between 200 and 210 GPa. The default value is 200 GPa.

Yield strength - fy
This is the stress at yield. Its value typically varies from 230 MPa up to 650 MPa. The default value is 500 MPa.

Strain hardening parameter -
This is the ratio between the post-yield stiffness (Esp) and the initial elastic stiffness (Es) of the material. The former is defined as Esp=(fult-fy)/(-fy/Es), where fult and represent the ultimate or maximum stress and strain capacity of the material, respectively. Its value commonly ranges from 0.005 to 0.015. The default value is 0.005.

Transition curve initial shape parameter - R0
This is the initial (first loading cycle) value of the parameter R, that controls the shape of the transition curve between initial and post-yield stiffness, necessary to accurately represent Baushinger effects and pinching of the hysteretic loops. The default value is 20.

Transition curve shape calibrating coefficients - a1 & a2
These are the two coefficients used to calibrate the changes that must be applied to parameter R0 in order to obtain the updated transition curve shape parameter Rn. Whilst a1 is usually adopted with an invariable value of 18.5, a2 might range between 0.05 and 0.15. The default values are 18.5 and 0.15 for coefficients a1 and a2, respectively.

Kinematic/isotropic weighting coefficient - P
This is the weighting coefficient used in this model to define the degree to which kinematic and isotropic hardening are introduced in the stress-strain cyclic response characteristics of the material. A value close to unity implies a kinematic-dominated hardening behaviour, whilst a value close to zero is employed when isotropic hardening controls the response of the material. Monti and Nuti [1992] suggest the use of single-cycle tests to define the value of P, indicating also that values close to 0.9 are usually found. The default value is thus 0.9.

Spurious unloading corrective parameter - r
This is the threshold for small strain reversals, defined as a percentage of the strain measured at the end of a loading cycle, used to prevent the occurrence of spurious strain unloading cycles. Typical values of r vary between 2.5 and 5 percent. The default value is 2.5%.

Fracture strain -
This is the strain at which fracture occurs. The default value is 0.1.

Specific weight -
This is the specific weight of the material. The default value is 78 kN/m3.