Non-linearity and Stability in Continuous Media (NLS)
French side leader : Matthieu Mazière (matthieu.maziere@mines-paristech.fr)
Italian side leader : Angelo Luongo (angelo.luongo@ing.univaq.it)
Instabilities are ubiquitous in the behaviour of geomaterials, engineering materials and structures. Well–established methods are available to predict bifurcation points like buckling threshold, necking–barreling, strain localization phenomena including shear band or compaction band formation… One objective of the project is to address the post–bifurcation response which usually requires the introduction of structural or microstructural characteristic lengths. The microinertia terms which are inherent to higher order continuum theories can regularize further the ill–posedness of the underlined problems.
The LIA research will focus on some crucial problems in mechanics of reinforced composites and the related phenomena of modelling localization, boundary layers formation and consequent eventual loss of stability. In this context the experience of the Italian research leader in developing perturbative schemes will be complemented by the synergies with the group in Computational Mechanics.
The main objectives will be:
- modelling of fiber reinforced materials undergoing large deformations by means of discrete and continuous models; study of their equilibrium configuration and their loss of stability with analytical, semi-analytical and numerical methods,
- perturbative stability analyses of problems relevant for engineering applications,
- multiple scale stability analysis of micro-models for the development of suitably approximated
macro-models, - development of poromechanics which also involves various characteristic lengths playing a significant role in the instability modes
Elastoviscoplastic material instabilities belong to the most complex bifurcation modes and can hardly been predicted and simulated. Significant advances are expected in this field for instance in the field of strain ageing materials where combined material science based, mathematical and computational methods must be combined to predict the onset of instabilities like Portevin–Le Chatelier serrations.