Fracture & Damage Mechanics
My work in fracture and damage mechanics focuses on variational and computational approaches to model crack initiation and propagation in brittle materials. This includes the use of shape optimization and topological derivatives to predict material failure.
A significant part of this research was developed during my postdoctoral work at École Polytechnique in collaboration with G. Allaire and F. Jouve, and published in the paper
Damage and crack evolution by shape optimization methods.
The methodology was later extended to hydro-mechanical fracture modeling, in collaboration with A. Novotny (LNCC, Brazil). Here, our approach was to consider and use only the topological derivative to predict
crack initiation and propagation (see the papers Crack Nucleation Sensitivity Analysis, conceived after but published before JCP paper). Our work on hydraulic fracture was published in Hydro-mechanical fracture modelling governed by topological derivatives
In parallel, I have collaborated with engineers, such as P. Areias (Instituto Superior Tecnico, Lisbon), on computational approaches to fracture and damage, which are more applied and engineering-focused.
Some related Publications
Brittle fracture on plates governed by topological derivatives
M. Xavier, N. Van Goethem
Eng. Comput., 39(1), 421-437, 2021
Hydro-mechanical fracture modelling governed by topological derivatives
M. Xavier, N. Van Goethem, A. Novotny
Comp. Meth. Appl. Mech. Eng. (CMAME), 2019
A simplified model of fracking based on the topological derivative concept
M. Xavier, N. Van Goethem, A. Novotny
Int. J. Sol. Struct., , 2018
Topological Derivative-Based Fracture Modelling in Brittle Materials: A Phenomenological Approach
M. Xavier, N. Van Goethem, A. Novotny, J.-M. Faria, E. Fancello
Eng. Fract. Mech., 2017
Damage-based fracture with electromagnetic coupling
H.G. Silva, P. Areias, N. Van Goethem, M. Bezzeghoud
Comput. Mech., 2013
A finite-strain temperature-dependent ductile fracture model with configurational forces
P. Areias, N. Van Goethem
Int. J. Fract., 2013
A damage model for ductile crack initiation and propagation
P. Areias, N. Van Goethem, E. B. Pires
Comput. Mech., 2011
Damage and crack evolution by shape optimization methods
G. Allaire, F. Jouve, N. Van Goethem
J. Comput. Phys. (JCP), 2011