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CONSTITUTIVE MODELING OF PRESTRESSED SHAPE MEMORY FIBER–MATRIX COMPOUNDS

Kohlhaas, B.; Klinkel, S.;

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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.

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Palavras-chave: shape memory fiber, composite, pseudoelasticity, pseudoplasticity, shape memory effect,

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DOI: 10.5151/meceng-wccm2012-18290

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Como citar:

Kohlhaas, B.; Klinkel, S.; "CONSTITUTIVE MODELING OF PRESTRESSED SHAPE MEMORY FIBER–MATRIX COMPOUNDS", p. 1139-1154 . In: In Proceedings of the 10th World Congress on Computational Mechanics [= Blucher Mechanical Engineering Proceedings, v. 1, n. 1]. São Paulo: Blucher, 2014.
ISSN 2358-0828, DOI 10.5151/meceng-wccm2012-18290

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