Menegotto-Pinto steel model - stl_mp

This is a uniaxial steel model initially programmed by Yassin [1994] based on a simple, yet efficient, stress-strain relationship proposed by Menegotto and Pinto [1973], coupled with the isotropic hardening rules proposed by Filippou et al. [1983]. The current implementation follows that carried out by Monti et al. [1996]. 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 structures, particularly those subjected to complex loading histories, where significant load reversals might occur. 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.

Isotropic hardening calibrating coefficients - a3 & a4
These are the two coefficients used to define the degree to which isotropic hardening is introduced in the stress-strain cyclic response characteristics of the material. In the case of a3, a variation between 0.01 and 0.025 can usually be found in practice, whilst for coefficient a4 oscillations between 2 and 7 are commonly observed. It is noted, however, that since the contribution of isotropic hardening is usually considerably smaller than its kinematic counterpart, variation of these parameters does not affect noticeably the cyclic response characteristics of the material. However, when large cyclic straining takes place, isotropic hardening may lead to unrealistically large member capacities (especially if no facture/buckling strain has been set). For this reason, by default, isotropic hardening is  disabled, and hence the default values are 0 and 1 for coefficients a3 and a4, respectively.

Note: It is possible to assign a negative value to parameter a3 in order to artificially introduce softening in the response of a structural element featuring this material model. In such cases, however, users should check the results carefully, since this material model was not initially devised with such feature in mind.

Fracture/buckling strain -
This is the strain at which fracture or buckling occurs. The default value is 0.1 (this may be a reasonable value for steel rebars in reinforced concrete sections, but rather inappropriate for steel profiles - users should thus set it with care (even using an infinitely large value when no fracture/buckling modelling is desired)).

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