Defects & Dislocation Theory
My research in dislocation theory focuses on the geometric and analytical descriptions of defects in crystalline solids. I explore variational methods to model the evolution of dislocations in single crystals, using tools like Cartesian currents to derive rigorous mathematical frameworks.
A key focus is on the variational evolution of dislocations, where the interplay between energy minimization and dissipation is critical. This includes the homogenization of dislocation clusters into elastoplasticity, which remains an open challenge.
Defects in Non-Riemannian Geometry
My work in geometric analysis focuses on the mathematical foundations of defects in solids, including the study of bounded deformation, incompatibility operators, and geometric measure theory. This also extends to the non-Riemannian geometry of crystals with defects.
Key Publications
A new approach to topological singularities via a weak notion of Jacobian for functions of bounded variation
L. De Luca, R. Scala, N. Van Goethem
Indiana Univ. Math. J., 73(2), 723-779, 2024
Analytic and geometric properties of dislocation singularities
R. Scala, N. Van Goethem
Proc. R. Soc. Edinburgh: Section A Math., 2020
Variational evolution of dislocations in single crystals
R. Scala, N. Van Goethem
J. Nonlinear Sci., 2019
A variational approach to single crystals with dislocations
R. Scala, N. Van Goethem
SIAM J. Math. Anal. (SIMA), 2019
Front migration for the dislocation strain in single crystals
N. Van Goethem
Communications in Mathematical Sciences, 2017
Incompatibility-governed singularities in linear elasticity with dislocations
N. Van Goethem
Math. Mech. Solids, 22(8), 2017
Constraint reaction and the Peach-Koehler force for dislocation networks
N. Van Goethem
Math. Mech. Complex. Syst., 2016
Currents and dislocations at the continuum scale
R. Scala, N. Van Goethem
Meth. Appl. Analysis, 2016
Dislocation-induced linear-elastic strain dynamics by Cahn-Hilliard-type equations
N. Van Goethem
Math. Mech. Complex. Syst., 2016
The Frank tensor as a boundary condition in intrinsic linearized elasticity
N. Van Goethem
J. Geom. Mech., 2016
A compatible-incompatible decomposition of symmetric tensors in Lp with application to elasticity
G. Maggiani, R. Scala, N. Van Goethem
Math. Meth. Appl. Sc., 2015
Cauchy elasticity with dislocations in the small strain assumption
N. Van Goethem
Applied Mathematics Letters, 2015
Strain incompatibility in single crystals: Kröner's formula revisited
N. Van Goethem
Journal of Elasticity, 2011
A distributional approach to the geometry of 2D dislocations at the continuum scale
Ann. Univ. Ferrara, 2012
A distributional approach to 2D Volterra dislocations at the continuum scale
Europ. Jnl. Applied Math., 2012
The non-Riemannian dislocated crystal: a tribute to Ekkehart Kröner
J. Geom. Mech., 2010
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