Finite element simulations of poly-crystalline shape memory alloys based on a micromechanical model

Junker, Philipp; Hackl, Klaus

doi:10.1007/s00466-010-0555-4

Cited by 18 publications

(9 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the present work, the material model developed by is used which is a mathematically condensed version of the micromechanical models introduced in Hackl et al (2004), Hackl and Heinen (2008), and Junker and Hackl (2011). Due to a simplified description of the polycrystalline orientation distribution function of the martensitic strain (which must not be confused with an orientation distribution function for the grains or texture), this model proves to be numerically very efficient.…”

Section: Model For Polycrystalline Shape Memory Alloysmentioning

confidence: 98%

See 1 more Smart Citation

Variational prediction of the mechanical behavior of shape memory alloys based on thermal experiments

Junker

Jaeger

Kastner

et al. 2015

Journal of the Mechanics and Physics of Solids

Self Cite

View full text Add to dashboard Cite

Section: Model For Polycrystalline Shape Memory Alloysmentioning

confidence: 98%

“…A detailed excursion into implementation issues for polycrystalline shape memory can be found in Junker and Hackl (2011). Let us mention that the result of any finite element calculation is an approximation of the minimizer of the Gibbs free energy , defined as…”

Section: Finite Element Simulations Of Tension Testsmentioning

confidence: 99%

Variational prediction of the mechanical behavior of shape memory alloys based on thermal experiments

Junker

Jaeger

Kastner

et al. 2015

Journal of the Mechanics and Physics of Solids

Self Cite

View full text Add to dashboard Cite

“…While phase transformation is proceeding, other grains may become active until (nearly) the entire material has transformed. However, implementation of such a model into a finite element code reveals that such a model is very time consuming and thus not appropriate for an industrial use (see [15]). Therefore, the polycrystalline character is condensed to a modeling approach in which a dynamically evolving orientation distribution function is considered and parameterized by Euler angles.…”

Section: Materials Modelmentioning

confidence: 99%

Calibration and Finite Element Implementation of an Energy-Based Material Model for Shape Memory Alloys

Junker

Hackl

2016

Shap. Mem. Superelasticity

Self Cite

View full text Add to dashboard Cite

Numerical simulations are a powerful tool to analyze the complex thermo-mechanically coupled material behavior of shape memory alloys during product engineering. The benefit of the simulations strongly depends on the quality of the underlying material model. In this contribution, we discuss a variational approach which is based solely on energetic considerations and demonstrate that unique calibration of such a model is sufficient to predict the material behavior at varying ambient temperature. In the beginning, we recall the necessary equations of the material model and explain the fundamental idea. Afterwards, we focus on the numerical implementation and provide all information that is needed for programing. Then, we show two different ways to calibrate the model and discuss the results. Furthermore, we show how this model is used during real-life industrial product engineering.

show abstract

“…In addition to the energy, we need to make assumptions concerning the dissipation functional. As in previous works, for example, , we chose the dissipation functional to consist of the norm of the rate of the volume fractions

\overset{bold-italicλ}{true}

, and newly of the skew symmetric matrix of angular velocities

bold-italicΩ MathClass-punc: MathClass-rel= \overset{bold-italicQ}{true} MathClass-bin\cdot Q^{MathClass-bin- 1}

, weighted with some parameters r λ and r α , thus,

scriptD MathClass-rel= r_{λ} MathClass-rel| \overset{bold-italicλ}{true} MathClass-rel| MathClass-bin+ r_{α} MathClass-rel| MathClass-rel| bold-italicΩ MathClass-rel| MathClass-rel| MathClass-rel= r_{λ} MathClass-rel| \overset{bold-italicλ}{true} MathClass-rel| MathClass-bin+ \sqrt{2} r_{α} {((), {\overset{ϕ}{true}}^{2} MathClass-bin+ {\overset{ν}{true}}^{2} MathClass-bin+ 2 \overset{ϕ}{true} \overset{ω}{true} normalcos ν MathClass-bin+ {\overset{ω}{true}}^{2})}^{1 MathClass-bin∕ 2}

The use of Ω , instead of

\overset{bold-italicα}{true}

for instance, ensures frame‐independence. The respective derivatives then yield

\frac{\partial scriptD}{\partial \overset{bold-italicλ}{true}} MathClass-rel= r_{λ} \frac{\overset{bold-italicλ}{true}}{MathClass-rel| \overset{bold-italicλ}{true} MathClass-rel|} and \frac{\partial scriptD}{\partial \overset{bold-italicα}{true}} MathClass-rel= \sqrt{2} \frac{r_{α}}{MathClass-rel| MathClass-rel| bold-italicΩ MathClass-rel| MathClass-rel|}

…”

Section: Materials Modelmentioning

confidence: 99%

“…In addition to the energy, we need to make assumptions concerning the dissipation functional. As in previous works, for example, [11,17,26], we chose the dissipation functional to consist of the norm of the rate of the volume fractions P , and newly of the skew symmetric matrix of angular velocities WD P Q Q 1 , weighted with some parameters r and r˛, thus,…”

Section: Dissipation Functionalmentioning

confidence: 99%

A novel approach to representative orientation distribution functions for modeling and simulation of polycrystalline shape memory alloys

Junker

2014

Numerical Meth Engineering

View full text Add to dashboard Cite

SUMMARYA micromechanical model for polycrystalline shape memory alloys (SMAs) was introduced in a series of papers by Hackl and coauthors. In order to model the polycrystalline aspect, they assumed a specific set of orientation distribution functions that had to be resolved with high numerical effort. Although this model displays interesting aspects, its use to simulate macroscopic specimens is problematic due to the long calculation time.In this paper, we present a new approach to modeling and simulation of polycrystalline SMAs that is based on parameterization of a class of orientation distribution functions by using only a few parameters. A variational concept is applied to derive evolution equations for these parameters. The resultant material model drastically reduces the calculation time and may thus provide an approach to efficient micromechanical simulation of specimens that are of engineering interest.This study presents a variety of different numerical examples, such as pseudoelastic and pseudoplastic material behavior for CuAlNi and NiTi SMAs, to demonstrate the broad applicability of the material model. The numerical benefit of the presented modeling approach is demonstrated by comparative calculations of the new model versus the previous model. Copyright © 2014 John Wiley & Sons, Ltd.

show abstract

Finite element simulations of poly-crystalline shape memory alloys based on a micromechanical model

Cited by 18 publications

References 24 publications

Variational prediction of the mechanical behavior of shape memory alloys based on thermal experiments

Variational prediction of the mechanical behavior of shape memory alloys based on thermal experiments

Calibration and Finite Element Implementation of an Energy-Based Material Model for Shape Memory Alloys

A novel approach to representative orientation distribution functions for modeling and simulation of polycrystalline shape memory alloys

Contact Info

Product

Resources

About