Abstract
The article describes the approach to modelling of single degree of freedom SMA oscillators by using rheological schemes. Certain sets of rheological components are presented and their influence on the oscillator response is examined. Regarding the field of civil engineering, the devices incorporating SMA elements mostly find applications in mitigation of natural disaster hazards, such as earthquakes. The promising results of applications are possible due to unique properties of SMA, such as shape memory effect (recovering of relatively high strains while material is heated) and superelasticity (recovering of strains upon load removal). The most common approach to the formulation of SMAs constitutive relations is a thermomechanical modelling, in which constitutive equations are dependent on internal state variables. One of the advantages of the phenomenological modelling approach presented in the article is a possibility of formulation of constitutive relationships as a set of explicit differential equations. Such system of equations can be easily implemented in mathematical software or in the commercial FEM codes as a user's subroutines. As an example of numerical application of presented approach, the simple one-dimensional oscillator is used in order to solve the case of forced vibrations of a cantilever with embedded SMA reinforcement.
Highlights
Main fields of the shape memory alloys (SMAs) application in civil engineering are oriented on mitigation of natural disaster hazards, such as significant ground motions related to earthquakes
In case of the shape memory effect phase transformation is a result of heating and in case of superelasticity it is induced by external stresses in isothermal conditions, above certain temperature ( Af )
It should be emphasised that the proposed methodology of the formulation of SMA constitutive equations is based on original rheological schemes
Summary
Main fields of the shape memory alloys (SMAs) application in civil engineering are oriented on mitigation of natural disaster hazards, such as significant ground motions related to earthquakes. It can be achieved due to unique characteristics of SMA such as shape memory effects and superelasticity. In case of the shape memory effect phase transformation is a result of heating and in case of superelasticity it is induced by external stresses in isothermal conditions, above certain temperature ( Af ). At the beginning of the test sample is in austenite phase ( A ) and the load application induces a transformation to the de-twined martensite ( M ). This phase transformation is illustrated as an arrow no. 2 in Fig. 1) occurs and the material is back in original austenite phase. The simple one-dimensional oscillator is used in order to solve the example of forced vibrations of a cantilever with embedded SMA reinforcement
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