# Equation-Based Modeling of Shape Memory Alloys for Reinforcement of Masonry Structures Against Out-of-Plane Excitation

## TL;DR

This paper introduces a new equation-based model for shape memory alloys to improve the seismic resistance of masonry structures.

## Contribution

A novel equation-based model for SMA superelasticity is proposed, with parameters directly tied to experimental data.

## Key findings

- The proposed model accurately captures SMA superelasticity under isothermal conditions.
- SMA-based ties outperform traditional steel ties in reducing damage and improving structural performance during seismic events.

## Abstract

The incorporation of advanced smart materials, such as shape memory alloys (SMAs), in civil engineering presents significant challenges, particularly in modeling their complex behavior. Traditional numerical SMA models often require material parameters that are difficult to estimate and validate. The objective of this paper is to introduce an equation-based approach to modeling the superelastic behavior of SMAs based on rheological models. The proposed phenomenological model accurately captures SMA superelasticity under isothermal conditions, with each material parameter directly correlated to data from standard mechanical experiments. Four modifications to the baseline rheological model are proposed, highlighting their impact on superelastic characteristics. The resulting constitutive relationships are expressed as non-linear ordinary differential equations, making them compatible with commercial finite element method (FEM) software through user-defined subroutines. The practical application of this modeling approach is demonstrated through the strengthening of a historical masonry wall subjected to seismic activity. Comparative analysis shows that ties incorporating SMA segments outperform traditional steel ties by reducing the potential damage and enhancing the structural performance. Additionally, the energy dissipation during the SMA phase transformation improves the damping of vibrations, further contributing to the stability of the structure. This study underscores the potential of SMA-based solutions in seismic retrofitting and highlights the advantages of equation-based modeling for practical engineering applications.