# Inelastic Deformation of Coronary Stents: Two-Level Model

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

**b**in the slip direction and the slip plane’s normal

**n**. Assuming a uniform dislocation distribution in grains, the inelastic component of the strain rate measure can be calculated [29,53]:

_{0}and a are the hardening-law parameters.

## 3. Results and Discussion

**k**

_{i}of the deformation tensor in pressure. This was necessary to determine the deformed state of the structure and the deformation directions in the principal stress space to use the developed model (1)–(12).

**k**

_{i}are the orthogonal unit vectors along the corresponding xi-axes.

- Angle φ between the deformation direction and the projection of the X-axis of principal deformation E
_{1}on a given plane; - The radius vector drawn from the origin to the considered point, which is equal to the yield strength of the material.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 5.**Numerical and experimental results for stress-strain diagram of polycrystalline aggregate in uniaxial tension.

**Figure 6.**Dependence of yield strength on parameters of lognormal law of grain-size distribution in polycrystal.

**Figure 7.**Histograms of grain-size distribution in polycrystal for different parameters: (

**a**) μ = 3.5, σ = 0.5; (

**b**) μ = 3.5, σ = 0.2; and (

**c**) μ = 4.5, σ = 0.5.

**Figure 9.**Dependence of yield strength on deformation direction in most dangerous stress state (deformation directions with minimum yield strength are highlighted with red arrows).

Material Parameters | Notation | Value |
---|---|---|

Poisson’s ratio | $\nu $ | 0.27 |

Young’s modulus | $E$ | 197 GPa |

Density | $\rho $ | 7000 kg m^{−3} |

Initial shear stresses | ${\sigma}_{gs}$ | 101 MPa |

Material Parameters | Notation | Value |
---|---|---|

Grain count | N | 350 |

Elastic constant | ${C}_{iiii},i,j=\overline{1,3}$ | 163 GPa |

Elastic constant | ${C}_{iijj},i,j=\overline{1,3}$ | 110 GPa |

Elastic constant | ${C}_{ijij},i,j=\overline{1,3}$ | 101 GPa |

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**MDPI and ACS Style**

Volegov, P.S.; Knyazev, N.A.; Gerasimov, R.M.; Silberschmidt, V.V. Inelastic Deformation of Coronary Stents: Two-Level Model. *Materials* **2022**, *15*, 6948.
https://doi.org/10.3390/ma15196948

**AMA Style**

Volegov PS, Knyazev NA, Gerasimov RM, Silberschmidt VV. Inelastic Deformation of Coronary Stents: Two-Level Model. *Materials*. 2022; 15(19):6948.
https://doi.org/10.3390/ma15196948

**Chicago/Turabian Style**

Volegov, Pavel S., Nikita A. Knyazev, Roman M. Gerasimov, and Vadim V. Silberschmidt. 2022. "Inelastic Deformation of Coronary Stents: Two-Level Model" *Materials* 15, no. 19: 6948.
https://doi.org/10.3390/ma15196948