A mesoscopic thermomechanically coupled model for thin-film shape-memory alloys by dimension reduction and scale transition

Benešová, Barbora; Kružík, Martin; Pathó, Gabriel

doi:10.1007/s00161-013-0323-8

Continuum Mech. Thermodyn.

2013

DOI: 10.1007/s00161-013-0323-8

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A mesoscopic thermomechanically coupled model for thin-film shape-memory alloys by dimension reduction and scale transition

Barbora Benešová

Martin Kružík

Gabriel Pathó

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Cited by 2 publications

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“…Babadjian obtained in [2] via dimension reduction the existence of a quasistatic evolution for a free crack in an elastic brittle thin film. Dimension reduction in a delamination context is addressed in [17,18] whereas an application to shape-memory thin films is described in [3].…”

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Quasistatic evolution of magnetoelastic plates via dimension reduction

Kružík¹,

Stefanelli²,

Zanini³

2015

DCDS-A

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A rate-independent model for the quasistatic evolution of a magnetoelastic plate is advanced and analyzed. Starting from the three-dimensional setting, we present an evolutionary Γ-convergence argument in order to pass to the limit in one of the material dimensions. By taking into account both conservative and dissipative actions, a nonlinear evolution system of rateindependent type is obtained. The existence of so-called energetic solutions to such system is proved via approximation.2010 Mathematics Subject Classification. Primary: 74F15, 74N30, 35K55.

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mentioning

confidence: 99%

Quasistatic evolution of magnetoelastic plates via dimension reduction

Kružík¹,

Stefanelli²,

Zanini³

2015

DCDS-A

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On the strain differential effect in the theory of shape memory membranes

Kurbatov,

Zhavoronok

2024

E3S Web Conf.

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A theory of thin shells made of shape memory alloys is developed. Such thin-walled elements could be used in various structures as sensors, actuators, vibration dampers, etc. The new incremental constitutive equations for a thin shape memory membrane shell are derived accounting for the strain differential effect taking the once coupled phenomenological model of thermoelastic phase transitions as a background. The solutions for spherical and cylindrical shape memory alloy shells loaded by the internal or external pressure and axial loads are obtained. It is shown that the ratio of second invariant of the deviatoric stress and the stress intensity impacts significantly on the strains accumulated by the shell during martensite phase transitions, as well as on the temperature ranges of phase transforms.

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A mesoscopic thermomechanically coupled model for thin-film shape-memory alloys by dimension reduction and scale transition

Cited by 2 publications

References 39 publications

Quasistatic evolution of magnetoelastic plates via dimension reduction

Quasistatic evolution of magnetoelastic plates via dimension reduction

On the strain differential effect in the theory of shape memory membranes

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