## Abstract

In an earlier work, Elliott et al. [2006a, Stability of crystalline solids-II: application to temperature-induced martensitic phase transformations in bi-atomic crystals. Journal of the Mechanics and Physics of Solids 54(1), 193232], the authors used temperature-dependent atomic potentials and path-following bifurcation techniques to solve the nonlinear equilibrium equations and find the temperature-induced martensitic phase transformations in stress-free, perfect, equi-atomic binary B2 crystals. Using the same theoretical framework, the current work adds the influence of stress to study the model's stress-induced martensitic phase transformations. The imposition of a uniaxial Biot stress on the austenite (B2) crystal, lowers the symmetry of the problem, compared to the stress-free case, and leads to a large number of stable equilibrium paths. To determine which ones are possible reversible martensitic transformations, we use the (kinematic) concept of the maximal EricksenPitteri neighborhood (max EPN) to select those equilibrium paths with lattice deformations that are closest, with respect to lattice-invariant shear, to the austenite phase and thus capable of a reversible transformation. It turns out that for our chosen parameters only one stable structure (distorted αIrV) is found within the max EPN of the austenite in an appropriate stress window. The energy density of the corresponding configurations shows features of a stress-induced phase transformation between the higher symmetry austenite and lower symmetry martensite paths and suggests the existence of hysteretic stressstrain loops under isothermal loadunload conditions. Although the perfect crystal model developed in this work over-predicts many key material properties, such as the transformation stress and the ClausiousClapeyron slope, when compared to real experimental values (based on actual polycrystalline specimens with defects), it isto the authors knowledgethe first atomistic model that has been demonstrated to capture all essential trends and behavior observed in shape memory alloys.

Original language | English (US) |
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Pages (from-to) | 216-236 |

Number of pages | 21 |

Journal | Journal of the Mechanics and Physics of Solids |

Volume | 59 |

Issue number | 2 |

DOIs | |

State | Published - Feb 2011 |

### Bibliographical note

Funding Information:This work was supported by NSF grant—CMS 0409084 (Dr. Ken Chong, Program Director)—to the University of Michigan, by the NSF CAREER grant—CMMI- 0746628 (Dr. Shih-Chi Liu, Program Director)—to the University of Minnesota, and by The University of Minnesota Supercomputing Institute.

## Keywords

- Buckling
- Finite strain
- Phase transformation
- Stability and bifurcation
- Thermoelastic material