Numerical Methods Across Scales

The traditional analytical framework in engineering mechanics has been that of a continuum. However, the mechanical deformation and failure of many engineering materials are inherently multi-scale. Indeed, the observed homogeneous macroscopic (continuum scale) behavior of the material is governed by physical processes that occur at a heterogeneous microscopic fine scale. The current challenge in several solid mechanics applications is to incorporate micro-structural and/or atomic details to improve model predictions. However, approximations need to be done since the explicit representation of billions of atoms is out of reach even for the largest computer ever built.

At LSMS we develop and implement such multi-scale approaches. We put particular emphasis on direct concurrent coupling between discrete and continuum models. Our main current efforts are directed towards finite temperature and dislocation defects management when coupling molecular dynamics, dislocation dynamics and continuum mechanics. These multi-scale methods find direct applications in fracture (e.g. fatigue) and contact mechanics, where dislocations originate at atoms (discrete representation) whereas bulk behavior is best described by continuum approaches.



Selected Publications

Mobility law of dislocations with several character angles and temperatures in FCC Aluminum

J. Cho; J-F. Molinari; G. Anciaux 

International Journal of Plasticity. 2017. Vol. 90, p. 66-75. DOI : 10.1016/j.ijplas.2016.12.004.

Toward a 3D coupled atomistic and discrete dislocation dynamics simulation: dislocation core structures and Peierls stresses with several character angles in FCC aluminum

J. Cho; T. Junge; J-F. Molinari; G. Anciaux 

Advanced Modeling and Simulation in Engineering Sciences. 2015. Vol. 2, num. 1, p. 1-17. DOI : 10.1186/s40323-015-0028-6.

Implementation of a parallel finite-element library: test case on a non-local continuum damage model

N. Richart; J-F. Molinari 

Finite Elements in Analysis & Design. 2015. Vol. 100, p. 41-46. DOI : 10.1016/j.finel.2015.02.003.

A concurrent atomistic and continuum coupling method with applications to thermo-mechanical problems

S. B. Ramisetti; G. Anciaux; J. F. Molinari 

International Journal For Numerical Methods In Engineering. 2014. Vol. 97, num. 10, p. 707-738. DOI : 10.1002/nme.4606.

A molecular dynamics and finite element study of the nanoscale thermal contact conductance

G. Anciaux; J-F. Molinari 

International Journal of Heat and Mass Transfer. 2013. Vol. 59, p. 384-392. DOI : 10.1016/j.ijheatmasstransfer.2012.12.003.