Implicit coupled constitutive relations and an energy-based method for material modelling

The contributions of this thesis are an implicit modelling method for the coupled constitutive relations and an energy-based method for material modelling. The two developed methods utilise implicit models to represent material constitutive relations without the requirement of physical parameters. The first method is developed to model coupled constitutive relations using state-space representation with neural networks. State-space representation is employed to express the desired relations in a compact fashion while simultaneously providing the capability of modelling rate- and/or path-dependent behaviour. The employment of neural networks with the generalised state-space representation results in a single implicit model that can be adapted for a broad range of constitutive behaviours. The performance and applicability of the method are highlighted through the applications for various constitutive behaviour of piezoelectric materials, including the effects of hysteresis and cyclic degradation. An energy-based method is subsequently developed for implicit constitutive modelling by utilising the energy principle on a deformed continuum. Two formulations of the proposed method are developed for the modelling of materials with varying nature in directional properties. The first formulation is based on an implicit strain energy density function, represented by a neural network with strain invariants as input, to derive the desired stress-strain relations. The second formulation consists of the derivation of an energy-based performance function for training a neural network that represents the stress-strain relations. The requirement of deriving stress is eliminated in both formulations and this facilitates the use of advanced experimental setup, such as multi-axial load tests or non-standard specimens, to produce the most information for constitutive modelling from a single experiment. A series of numerical studies -- including validation problems and practical cases with actual experimental setup -- have been conducted, the results of which demonstrate the applicability and effectiveness of the proposed method for constitutive modelling on a continuum basis.

Grantor dc:publisher

UNSW, Sydney

Year dc:date

2009

Author dc:creator

• Man, Hou Michael

• Composite characterisation.
• Material constitutive models.
• Piezoelectric materials.
• Artificial neural networks.

Statement dc:rights

• open access
• CC BY-NC-ND 3.0
• free_to_read

Licence

• https://purl.org/coar/access_right/c_abf2
• https://creativecommons.org/licenses/by-nc-nd/3.0/au/

Language dc:language

EN

Identifier

https://doi.org/10.26190/unsworks/20399

OAI identifier oai:identifier

oai:unsworks.library.unsw.edu.au:1959.4/43652