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A structured continuum modelling framework for martensitic transformation and reorientation in shape memory

Davide Bernardini¹, Thomas J Pence²

¹Department of Structural and Geotechnical Engineering, University of Rome Sapienza, Via Antonio Gramsci 53, 00197 Rome, Italy davide.bernardini@uniroma1.it.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences

|March 23, 2016

Summary

This study presents a structured continuum theory for shape memory materials, detailing microstructure with phase fraction and martensite reorientation fields. It enables modeling of localized phase transformations under finite strains.

Keywords:

martensite transformation multi-field theory reorientation plasticity shape memory material thermomechanics

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Area of Science:

Continuum Mechanics
Materials Science
Solid Mechanics

Background:

Shape memory materials exhibit complex behaviors driven by microstructural changes.
Existing models often simplify the description of phase transformations and reorientation.
Finite strain analysis is crucial for accurately modeling material deformation.

Purpose of the Study:

To develop a structured continuum theory for shape memory material behavior.
To incorporate microstructural descriptors like phase fraction and martensite reorientation.
To enable the modeling of phase transformation localizations under finite strains.

Main Methods:

Formulation of a constitutive theory based on free energy and dissipation functions.
Inclusion of microstructural descriptor gradients to capture local phenomena.
Derivation of balance laws with bulk and surface terms, considering material objectivity.

Main Results:

A comprehensive constitutive framework for shape memory materials is established.
The theory naturally incorporates microstructural descriptors and their gradients.
Balance laws are derived, including reactive fields arising from constraints on martensite reorientation.

Conclusions:

The proposed theory provides a robust framework for modeling shape memory material behavior.
It offers enhanced capabilities for describing phase transformation localizations.
The model is consistent with established principles of continuum mechanics and objectivity.