A one-dimensional model for superelastic shape-memory alloys with different elastic properties between austenite and martensite.

*(English)*Zbl 0906.73006The authors present a rational one-dimensional model for the superelastic behavior of shape-memory alloys (SMA). A single scalar internal variable, the volume fraction of martensite, is considered for which an evolution equation in rate form is proposed. The simplicity of the modeling is rewarded by its efficiency, because various homogenization techniques (Voigt scheme (law of mixtures), Mori-Tanaka scheme, Reuss scheme, time-discrete model) allow the authors to determine the dependency of the elasticity coefficient upon the martensite contents. A numerical technique using a return-map algorithm is exploited to find sensible solutions of the time-discrete model. Simulations of the modeling for typical SMA superelastic stress-strain responses demonstrate excellent agreement with experimentally recorded stress-strain curves including hysteresis (Ni-Ti straight wires). The paper is well documented and proves that rather simple modelings completed by good applied mathematics and a safe numerical algorithm can provide a mathematically efficient and physically sound approach to a difficult problem.

Reviewer: G.A.Maugin (Paris)

##### MSC:

74A15 | Thermodynamics in solid mechanics |

74S30 | Other numerical methods in solid mechanics (MSC2010) |

80A22 | Stefan problems, phase changes, etc. |