Chapter 17
Microplane Modeling for Inelastic
Responses of Shape Memory Alloys
Mohammad Reza Karamooz-Ravari, Mahmoud Kadkhodaei,
and Mohammad Elahinia
Abstract Shape memory alloys (SMAs) are a class of smart materials. In these
alloys, an inelastically deformed configuration can recover to their original shape
upon heating to a specific temperature. One of the main challenges in modeling
these materials under multiaxial loadings is that the so-called normality rule does not
necessarily hold true as the direction of inelastic strain rate vector does not coincide
with the deviatoric stress vector for nonproportional loadings. Therefore, any generalization of 1-D constitutive equations to 3-D cases based on J 2 or J 2 -J 3 plasticity is
valid only for proportional loadings. Microplane modeling approach is a promising
candidate for overcoming this challenge since 1-D constitutive models in this method
are generalized to 3-D through a particular homogenization technique. All the material parameters can be obtained using uniaxial tension–compression tests. These
features make microplane theory an efficient approach in constitutive modeling of
shape memory alloys. In this chapter, first, the basic concepts of microplane theory
are reviewed. Then, a microplane model for SMAs along with an efficient technique
in numerical implementation of the constitutive equations is presented. Introduction of tension–compression asymmetry is further discussed and verified. Finally,
modeling of plastic and cyclic response is explained, and the theoretical results are
validated against experimental findings.
Keywords Microplane theory · Shap memory alloy · SMA · Tension-compression
asymmetry · Residual strain · Cyclic loading · Strain accumulation · Numerical
implementation
M. R. Karamooz-Ravari
Faculty of Mechanical and Materials Engineering, Graduate University of Advanced Technology,
76318-18356 Kerman, Iran
M. Kadkhodaei (B)
Department of Mechanical Engineering, Isfahan University of Technology, Isfahan 84156-83111,
Iran
e-mail: kadkhodaei@iut.ac.ir
M. Elahinia
Department of Mechanical, Industrial, and Manufacturing Engineering, The University of Toledo,
Toledo, OH 43606, USA
© Springer Nature Switzerland AG 2021
F. dell’Isola and L. Igumnov (eds.), Dynamics, Strength of Materials and Durability
in Multiscale Mechanics, Advanced Structured Materials 137,
https://doi.org/10.1007/978-3-030-53755-5_17
303
Microplane Modeling for Inelastic
Responses of Shape Memory Alloys
Mohammad Reza Karamooz-Ravari, Mahmoud Kadkhodaei,
and Mohammad Elahinia
Abstract Shape memory alloys (SMAs) are a class of smart materials. In these
alloys, an inelastically deformed configuration can recover to their original shape
upon heating to a specific temperature. One of the main challenges in modeling
these materials under multiaxial loadings is that the so-called normality rule does not
necessarily hold true as the direction of inelastic strain rate vector does not coincide
with the deviatoric stress vector for nonproportional loadings. Therefore, any generalization of 1-D constitutive equations to 3-D cases based on J 2 or J 2 -J 3 plasticity is
valid only for proportional loadings. Microplane modeling approach is a promising
candidate for overcoming this challenge since 1-D constitutive models in this method
are generalized to 3-D through a particular homogenization technique. All the material parameters can be obtained using uniaxial tension–compression tests. These
features make microplane theory an efficient approach in constitutive modeling of
shape memory alloys. In this chapter, first, the basic concepts of microplane theory
are reviewed. Then, a microplane model for SMAs along with an efficient technique
in numerical implementation of the constitutive equations is presented. Introduction of tension–compression asymmetry is further discussed and verified. Finally,
modeling of plastic and cyclic response is explained, and the theoretical results are
validated against experimental findings.
Keywords Microplane theory · Shap memory alloy · SMA · Tension-compression
asymmetry · Residual strain · Cyclic loading · Strain accumulation · Numerical
implementation
M. R. Karamooz-Ravari
Faculty of Mechanical and Materials Engineering, Graduate University of Advanced Technology,
76318-18356 Kerman, Iran
M. Kadkhodaei (B)
Department of Mechanical Engineering, Isfahan University of Technology, Isfahan 84156-83111,
Iran
e-mail: kadkhodaei@iut.ac.ir
M. Elahinia
Department of Mechanical, Industrial, and Manufacturing Engineering, The University of Toledo,
Toledo, OH 43606, USA
© Springer Nature Switzerland AG 2021
F. dell’Isola and L. Igumnov (eds.), Dynamics, Strength of Materials and Durability
in Multiscale Mechanics, Advanced Structured Materials 137,
https://doi.org/10.1007/978-3-030-53755-5_17
303