Thermomechanically coupled modelling of shape memory alloys in the framework of large strains

This contribution deals with a computational model for a shape memory alloy fiber composite. Three main topics have been considered within the presented model. First, a 1D fiber model is derived which accounts for all relevant nonlinear material phenomena of shape memory alloys. These are pseudoelasticity in the high temperature range and pseudoplasticity in the low temperature range. The latter is closely connected to the shape memory effect. The constrained and two-way shape memory effect are captured as well. Second, the shape memory fiber model is implemented into the finite element method. Two different structural elements are derived which lead to two different discretization schemes. A non-conform meshing concept and a conform meshing concept are presented. Randomly oriented and distributed fibers are considered. Both schemes are compared within the paper. Third, an FE 2 ansatz is presented. The computational homogenization process makes the detailed description of the complicated fiber-structure on macro-level dispensable. The micro-structure is considered in a representative volume element. It captures the main characteristics of the multi-functional composite. Finally, numerical examples present the capability of the formulation.

show abstract

“…In literature it is referred to as driving force ( [22,23]) or thermodynamic force ( [20,21]), for further explanation see Sect. 2.4.…”

Section: Constitutive Equationsmentioning

confidence: 99%

“…The finite element implementation considers pseudoelasticity. Christ and Reese [22][23][24] enhance the work for pseudoplasticity and the shape memory effect. An overview on existent models, their numerical treatment and further research topics on shape memory alloys may be found in Lagoudas [25].…”

Section: Introductionmentioning

confidence: 99%

An $$\hbox {FE}^{2}$$ FE 2 model for the analysis of shape memory alloy fiber-composites

Kohlhaas

Klinkel

2014

Comput Mech

View full text Add to dashboard Cite

show abstract

“…In literature it is referred to as driving force ( [8], [9]) or thermodynamic force ( [14], [15]), for further explanation see section 2.4.…”

Section: Constitutive Equationsmentioning

confidence: 99%

“…The finite element implementation was done for pseudoelasticity. Christ and Reese [8], [9], [10] improve the model of Helm and Haupt. They implement each material phenomenon into the finite element method.…”

Section: Introductionmentioning

confidence: 99%

Constitutive Modeling of Prestressed Shape Memory Fiber–matrix Compounds

Kohlhaas¹,

Klinkel²

2014

Proceedings of 10th World Congress on Computational Mechanics

View full text Add to dashboard Cite

Abstract. This contribution is concerned with a constitutive model for shape memory alloy (SMA) fibers. The model accounts for all material phenomena. It incorporates pseudoplasticity and the shape memory effect (SME). These phenomena occur in the low temperature range. For high temperature phase, the pseudoelastic behavior occurs. Additionally, the constrained SME (CSME) and the two-way SME are captured by the model. With respect to the assumption of small strains an additive split of the strain in an elastic and inelastic part is suggested. A free energy function is defined as a function of the elastic strain and an internal hardening variable. The constitutive equations for the stress and the conjugate hardening variable are derived from free energy. The elastic range is defined by two yield criteria, which are similar to kinematic hardening, known from classical plasticity theory. Here, the cases of loading and unloading are distinguished. These criteria are functions of the stress, the conjugate hardening variable and the energy difference between the austenitic and the martensitic phase, the so-called driving variable. The evolution equations for the inelastic state variables, namely the inelastic strain, the internal hardening variable and an inner variable, describing the martensitic volume evolution, are in accordance with the second law of thermodynamics. They are derived from the principle of maximum dissipation with the yield criteria as constraint. Following standard arguments, the martensite volume fraction is decomposed into twinned and oriented martensite. The first one is able to transform into austenite due to heating and vice versa. Just as well, it can change into the second one applying mechanical stress. The constitutive model is embedded in a one-dimensional truss formulation and implemented into a finite element analysis program. Numerical examples show the capability of the formulation. Simulations demonstrate the wide range of possible applications of SMA. A fiber-matrix composite is discussed, which allows for prestressing structures. This necessitates a precise description of the CSME. Likewise, this effect is used to prestress a representative volume element.

show abstract

Thermomechanically coupled modelling of shape memory alloys in the framework of large strains

Cited by 2 publications

References 36 publications

An $$\hbox {FE}^{2}$$ FE 2 model for the analysis of shape memory alloy fiber-composites

An $$\hbox {FE}^{2}$$ FE 2 model for the analysis of shape memory alloy fiber-composites

Constitutive Modeling of Prestressed Shape Memory Fiber–matrix Compounds

Contact Info

Product

Resources

About