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Microplane Modeling for Inelastic Responses of Shape Memory Alloys

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Dynamics, Strength of Materials and Durability in Multiscale Mechanics

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 137))

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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 J2 or J2-J3 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.

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Authors and Affiliations

  1. Faculty of Mechanical and Materials Engineering, Graduate University of Advanced Technology, 76318-18356, Kerman, Iran

    Mohammad Reza Karamooz-Ravari

  2. Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, 84156-83111, Iran

    Mahmoud Kadkhodaei

  3. Department of Mechanical, Industrial, and Manufacturing Engineering, The University of Toledo, Toledo, OH, 43606, USA

    Mohammad Elahinia

Authors
  1. Mohammad Reza Karamooz-Ravari
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  2. Mahmoud Kadkhodaei
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  3. Mohammad Elahinia
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Correspondence to Mahmoud Kadkhodaei .

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Editors and Affiliations

  1. Dipartimento di Ingegneria Strutturale, Università degli Studi dell’Aquila MEMOCS, L’Aquila, Italy

    Francesco dell'Isola

  2. Research Institute for Mechanics, National Research Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia

    Leonid Igumnov

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Karamooz-Ravari, M.R., Kadkhodaei, M., Elahinia, M. (2021). Microplane Modeling for Inelastic Responses of Shape Memory Alloys. In: dell'Isola, F., Igumnov, L. (eds) Dynamics, Strength of Materials and Durability in Multiscale Mechanics. Advanced Structured Materials, vol 137. Springer, Cham. https://doi.org/10.1007/978-3-030-53755-5_17

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