Nonlinear behavior of reinforced concrete structures can be efficiently modeled through fiber discretization of the element sections, where each fiber follows its own uniaxial material law. Both concrete and steel constitute sources of material nonlinearities.

Although steel is typically modeled through constitutive laws combining simple elastic and isotropic or kinematic hardening behaviors, concrete requires more adept modeling. Due to its complex and non-homogeneous microstructure, concrete modeling has to combine the previous behaviors with softening and nonlinear unloading patterns that violate classic plasticity theory postulates. 

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Bouc-Wen hysteretic models enable us to capture such nonlinear behaviors, and obtain material laws or entire macro-element formulations with compact mathematical representations and smooth/differential transitions between different behavior branches. Such smooth models can be further equipped with damage considerations allowing us to efficiently describe the complexity of concrete's initial, post-peak, and cyclic characteristics. 

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Below follows the calibration of the above-described coupled plasticity-damage model for the concrete loading and unloading behavior based on experimental data.