Interviene
prof. Ariel Ramírez-Torres, University of Glasgow
Abstract
We propose a multiscale analytical framework aimed at deriving explicit expressions for the homogenised coefficients that characterise the mechanical response of composite materials experiencing structural transformations within their internal architecture [1,2]. We specifically address the case where the transformation is purely mechanical and confined to unresolved lower-scale interactions [3]. While the study is primarily theoretical, it is driven by biological motivations, particularly scenarios where tissues such as bone dynamically adapt their mechanical properties in response to internal and/or external stimuli [4]. A central challenge lies in overcoming the computational complexity involved in predicting the effective macroscopic behaviour of such evolving materials. To tackle this, we formulate the governing equations by considering the balance of linear momentum and the evolution law for inelastic distortions, both derived from the Principle of Virtual Work. Through the application of the asymptotic homogenisation method [5], we derive the local problems and their corresponding macroscopic counterparts. In particular, for fibre-reinforced and multilayered composites, we provide analytical solutions to the local problems, enabling the derivation of closed-form expressions for the homogenised mechanical properties which capture the dynamic evolution of the composite media under investigation.
References:
[1] Giammarini, A., Ramirez-Torres, A., Grillo, A. (2025). Effective elasto-(visco)plastic coefficients of a bi-phasic composite material with scale-dependent size effects. Mathematical Methods in the Applied Sciences, 48, 926–979.
[2] Ramirez-Torres, A., Roque-Piedra, A., Giammarini, A., Grillo, A., Rodriguez-Ramos, R. (2025). Analytical expressions for the effective coefficients of fibre-reinforced composite materials under the influence of inelastic distortions. Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM), 105, e70003.
[3] DiCarlo, A., Quiligotti, S. (2002). Growth and balance. Mechanics Research Communications, 29(6):449–456.
[4] Taber, L. (1995). Biomechanics of growth, remodeling and morphogenesis. Applied Mechanics Reviews, 48:487–545.
[5] Cioranescu, D., Donato, P. (1999). An Introduction To Homogenization. Oxford University Press Inc., New York.
