Brief Introduction to the speaker:
Dr. Rodrigue DESMORAT is a University Professor in the Laboratory of Mechanics at ENS Paris-Saclay. His research interests are: Damage, fatigue, failure of materials and structures.
Talk Abstract:
The seminar will begin with a short introduction to Continuum Damage Mechanics for modeling material degradation.
In the framework of thermodynamics, damage is a state variable, measured from stiffness loss. For quasi-brittle materials such as concrete, loading-induced damage is anisotropic. The question of the nature of the damage variable arises, strongly related to the proper definition of the damage variable itself. A scalar variable is commonly used [1,2], and a fourth-order tensor has been proposed in the general case [3]. We prefer a second-order tensor as a simpler but realistic approximation [4, 5], a choice that is assessed here for quasi-brittle materials.
Tensorial damage variables introduced phenomenologically (bearing in mind that a state potential exists and must be continuously differentiated) are not well suited for multiaxial loadings. Definitions of tensorial variables derived from theoretical micromechanics neglect branching and coalescence of microcracks [6,7]. Even when considered as fourth-order tensors, these variables are not accurate at high damage levels. To improve mechanical modeling, a new coupling between elasticity and damage is derived in 2D from cross-measurements with discrete element model [8], using an equivariant decomposition of the bidimensional effective orthotropic elasticity tensor [9]. This method has been shown to be accurate for multiaxial, proportional or non-proportional loading, up to high anisotropic damage of quasi-brittle materials.
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[3] Leckie F.A., Onat E.T., Tensorial nature of damage measuring internal variables. In: Physical Non-Linearities in Structural Analysis. Springer, Berlin, Heidelberg, pp.140-155, 1981.
[4] Cordebois J.-P., Sidoroff F., Anisotropic damage in elasticity and plasticity, Journal de Mécanique Théorique et Appliquée, Numéro Spécial 45-60, 1982.
[5] Lemaitre J., Desmorat R., Engineering damage mechanics: ductile, creep, fatigue and quasi-brittle failures, Springer, 2005.
[6] Kachanov, M., Effective elastic properties of cracked solids: critical review of some basic concepts. Appl. Mech. Reviews 45(8):304-335, 1992.
[7] Dormieux L., Kondo D., Stress-based estimates and bounds of effective elastic properties: the case of cracked media with unilateral effects, Computational Materials Science, 46(1):173-179, 2009.
[8] Loiseau F., Oliver-Leblond C., Verbeke T., Desmorat R., Anisotropic damage state modeling based on harmonic decomposition and discrete simulation of fracture, Engineering Fracture Mechanics, 293:109669, 2023.
[9] Oliver-Leblond C., Desmorat R., Kolev B. Continuous anisotropic damage as a twin modelling of discrete bi-dimensional fracture. Eur. J. Mech. A Solids, 89:104285, 2021.
