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Constitutive Modelling and Numerical Implementation of SMA Material with Internal Loops

Abstract The article presents a constitutive model for Shape Memory Alloys (SMA) along with result of dynamic simulations of SMA model. The applications of devices incorporating SMA in civil engineering focus mostly on mitigation of the seismic hazard effects in new-build and historical buildings or improvement of fatigue resilience. The unique properties of SMA, such as shape memory effect and superelasticity give promising results for such applications. The presented model includes additional phenomenon of SMA – internal loops. The paper shows the method of formulation of physical relations of SMA based on special rheological structure, which includes modified Kepes’s model. This rheological element, introduced as dual-phase plasticity body, is given in the context of martensite phase transformation. One of the advantages of such an approach is a possibility of formulation of constitutive relationships as a set of explicit differential equations. The application of the model is demonstrated on example of dynamic simulations of three dimensional finite element subjected to dynamic excitation.