SteelMPF - Menegotto and Pinto (1973) Model Extended by Filippou et al. (1983) - OpenSeesWiki

# SteelMPF - Menegotto and Pinto (1973) Model Extended by Filippou et al. (1983)

Developed and Implemented by:

Kristijan Kolozvari, California State University, Fullerton

Kutay Orakcal, Bogazici University, Istanbul, Turkey

John Wallace, Univeristy of California, Los Angeles

This command is used to construct a uniaxialMaterial SteelMPF (Kolozvari et al., 2015), which represents the well-known uniaxial constitutive nonlinear hysteretic material model for steel proposed by Menegotto and Pinto (1973), and extended by Filippou et al. (1983) to include isotropic strain hardening effects. The relationship is in the form of curved transitions (Figure 1), each from a straight-line asymptote with slope E0 (modulus of elasticity) to another straight-line asymptote with slope E1 = bE0 (yield modulus) where b is the strain hardening ratio. The curvature of the transition curve between the two asymptotes is governed by a cyclic curvature parameter R, which permits the Bauschinger effect to be represented, and is dependent on the absolute strain difference between the current asymptote intersection point and the previous maximum or minimum strain reversal point depending on whether the current strain is increasing or decreasing, respectively. The strain and stress pairs (εrr) and (ε00) shown on Figure 1 are updated after each strain reversal. The model allows calibration of isotropic hardening parameters in both compression and tension through optional input variables a1 and a2 for isotropic strain hardening in compression, and a3 and a4 for isotropic strain hardening tension, and uses default values of a1 = a3 = 0.0 and a2 = a4 = 1.0 that yield no isotropic strain hardening for either compression or tension. To incorporate isotropic strain hardening in compression, the recommended parameters are a1 = 0.01 and a2 = 7.0. To incorporate isotropic strain hardening in tension, the recommended parameters are a3 = 0.01 and a4 = 7.0.

Source: /usr/local/cvs/OpenSees/SRC/material/uniaxial/

Figure 1. Constitutive Model for Steel (Menegotto and Pinto, 1973)

Input Format:

 uniaxialMaterial SteelMPF \$mattag \$fyp \$fyn \$E0 \$bp \$bn \$R0 \$cR1 \$cR2 <\$a1 \$a2 \$a3 \$a4>
 \$mattag Unique uniaxialMaterial tag \$fyp Yield strength in tension (positive loading direction) \$fyn Yield strength in compression (negative loading direction) \$E0 Initial tangent modulus \$bp Strain hardening ratio in tension (positive loading direction) \$bn Strain hardening ratio in compression (negative loading direction) \$R0 Initial value of the curvature parameter R (R0 = 20 recommended) \$cR1 Curvature degradation parameter (a1 = 0.925 recommended) \$cR2 Curvature degradation parameter (a2 = 0.15 or 0.0015 recommended) \$a1 Isotropic hardening in compression parameter (optional, default = 0.0). Shifts compression yield envelope by a proportion of compressive yield strength after a maximum plastic tensile strain of \$a2(\$fyp/\$E0) \$a2 Isotropic hardening in compression parameter (optional, default = 1.0). See explanation of a1. \$a3 Isotropic hardening in tension parameter (optional, default = 0.0). Shifts tension yield envelope by a proportion of tensile yield strength after a maximum plastic compressive strain of \$a3(\$fyn/\$E0). \$a4 Isotropic hardening in tension parameter (optional, default = 1.0). See explanation of a3.

Example:

uniaxialMaterial SteelMPF 1 60 60 29000 0.02 0.02 20.0 0.925 0.15

Discussion:

Although the Menegotto-Pinto model is already available in OpenSees (e.g., Steel02), the formulation of SteelMPF introduces several distinctive features compared to existing models. For example, the model allows definition of different yield stress values and strain hardening ratios for tension and compression, and it considers degradation of cyclic curvature parameter R for strain reversals in both pre- and post- yielding regions, which could produce more accurate predictions of yield capacity for some RC wall specimens (element MVLEM, Example 1), whereas Steel02 considers the degradation in post-yielding region only. Strain-stress relationships obtained using SteelMPF and Steel02 are compared in Figure 2 for a strain history that includes strain reversals at strain values equal to one-half of the yield strain (i.e., εr = ±0.001 = εy/2).

Figure 2. Comparing the degradation of cyclic curvature in the pre-yielding region for Steel02 and SteelMPF