Dear Quy Dong,

these are very good points! I personally think that the goal is not to reproduce all MD results in a continuum theory.
I see MD more as an inspiration to which mechanisms might be important and should not be neglected as they might have a strong influence on the macroscopic fracture behavior. I agreen that heat transfer and wave propagation might also important.
So I think that in order to decide what to include in a model or not we would need to in some way extract information on which aspects contribute how much to energy dissipation, and which mechanisms change the behavior of cracks. This will be different for different types of materials and microstructures. MD might help here, as we have all the information from all the atoms, but the gold standard would be experimental methods...

Indeed, if one want to reproduce MD results by a continuum theory, plasticity can not be neglected. Sometimes, plasticity may not be enough. Many ssues can intervene in the MD process for example heat transfer, wave propagation, etc..., which will render the continuum method quite complicated.

Thanks for your interest in such kind of work! From my perspective, however, there are already pretty good, atomistically-informed crystal plasticity models for semi-brittle materials out there (e.g., http://www.sciencedirect.com/science/article/pii/S0749641912000526 , http://www.sciencedirect.com/science/article/pii/S1359645412002431 , http://www.sciencedirect.com/science/article/pii/S0749641915001485 ,http://www.annualreviews.org/doi/pdf/10.1146/annurev-matsci-070214-020852). The challenge seems to lie more in how to couple/implement the crack tip plasticity in such models, e.g., through appropriate source and sink terms. I would be interested in collaborations along such lines!

This is a very interesting topic. Molecular Dynamics is a powerful method that can provide information about what happened at the atomic scale when a crack propagates. However, as you already mentionned, we are lacking a theory/a model that can capture those things. In my opinion, we must understanding completely the plasticity problem from the atomic scale first (crystal plasticity for example) before dealing with cracks. As seen in the figures, the distribution of dislocation and plastic events are very complicated.

Dear Erik Bitzek,

Well for the atomic scale effects. I am convinced that modelling random cracks is not a solution since they can occur at arbitrary locations but it is efficient to do that for fractured parts like hydraulic turbine big rotors which need to be kept operating until they will be replaced.

I have analysed a coarse composite mixture made of cement, sands and gravels : the dynamic FEM analysis computes the stresses and strains inside the mesh elements at each time step iteration with efficient finite element formulas. It is then possible to check if these values satisfy the strength bounds of the material at exact locations of the finite element mesh. A suitable modelling of the structure (or mechanism) is required for the analysis. You can see that this is an obvious method which can be applied to other materials like composite laminates where the stresses and strains need careful formulations to consider the plies effects or the possible dislocations for general anisotropic materials.

Dear Mohamaed Lamine,

the finite Element method is very useful for many engineering problems. However, it requires constitutive relations and in the case of fracture also criteria for decohesion. I.e. without such information, FEM can not "predict" fracture. Furthermore, it is well know, that
the usual continuum description of materials break down at small scales (e.g., the famous "smaller is stronger", or changes in elastic constants with size). Continuum mechanics description of fracture and failure thus require information from underlying scales, and this is where atomistic simulations come in. They can e.g. show that small cracks behave differently than larger cracks, that crack pinning leads to crack front deviation and dislocation nucleation, that there is stimulated dislocation nucleation and avalanche multiplication, etc. and they were also able to explain experimental findings. As brittle and semi-brittle fracture ultimatively involves breaking of atomic bonds, atomistic simulations are ultimatily required for a fundamental understanding of the fracture process and accompanying mechanisms. They will however not by themselfes be useful to solve engineering fracture problems. I think there is still lot of work to be done to include atomic scale mechanisms and mesoscale effects in the continuum descriptions of fracture, and these are very exiting times for fracture mechanics!

Maybe someone else might want to chime in on the use of FEM in modeling fracture and the current limitations and challenges, and where multiscale modeling approaches might be helpful?

Dear Erik Bitzek,

The finite element method up to the three dimensional case can predict the exact behaviour of several materials. It is also able to model cracks zones or to detect their locations. Is this widely used in practice and what are the assessment methods?

You might be interested in a Symposium on

Atomistic and Mesoscale Aspects of Fracture and Fatigue

at the 14th International Conference of Fracture” (ICF14) in Rhodes, Greece, June 18-23, 2017, see http://www.icf14.org for information on the conference and https://dl.dropboxusercontent.com/u/41288223/ICF14/Symposia/Gumbsch.pdf for information on the symposium.

The deadline for abstract submission has been postponed to November 30, 2016.