Premium
A constitutive model for shape memory alloy fibres and its applicability to prestressed composites
Author(s) -
Kohlhaas Benedikt,
Klinkel Sven
Publication year - 2011
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201110231
Subject(s) - constitutive equation , materials science , shape memory alloy , martensite , helmholtz free energy , state variable , mechanics , micromechanics , discretization , composite material , finite element method , thermodynamics , physics , mathematics , mathematical analysis , microstructure , composite number
This contribution is concerned with a constitutive model for shape memory fibres. The 1D‐constitutive model accounts for the pseudoplastic and shape memory effect (SME). The macroscopic answer of the material is determined by the evolution from a twinned martensitic lattice into a deformed and detwinned one. On the macroscopic scale these effects are responsible for the upper boundary of the hysteresis which is situated around the origin of the stress‐strain‐diagram. During the phase transition process inelastic strains arise. When the lattice is fully detwinned, a linear elastic branch at the end of the hysteresis is observed. The initial state of the material is recovered by unloading and heating the material subsequently. The constitutive model is derived from the Helmholtz' free energy and fulfils the 2nd law of thermodynamics. For the present model five internal state variables are employed. Two of them are used to describe the inelastic strain and a backstress. The others represent the martensitic volume fraction and are necessary to describe the SME. The latter variables are depending on the deformation state as well as on temperature. A change on temperature goes along with a reduction of the inelastic strain. The model is incorporated in a fibre matrix discretization to prestress the surrounding structure. The boundary value problem is solved for a truss element applying the finite element method. Examples will demonstrate the applicability in engineering structures. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)