Is the finite element method eligible to manipulate problems in molecular up to nano scales? if yes How and what's your suggested procedure?
Can downscaling used in FEM?
Dear Sadeem,
FEM works well at the macro-microscale. But, since FEM needs the definition of a constitutive law, it does not able to simulate directly effects strictly associated to attractive/repulsive forces related to energetic inter-atomic potentials or related to entropic thermal-related fluctuations, that instead are fundamental for simulating molcular and/or atomic interactions at the nanoscale.
Accordingly, FEM can not directly employed to simulate a nanoscale problem. Nevertheless, FEM can be suitably formulated in order to account at the microscale or at the macroscale for effects deriving by nanoscale processes and mechanisms. In other words, by employing suitable homogenization approaches, you can define constitutive relationships at the micro/macroscale that include the influence of subscale phenomena. This is the "multiscale" universe. For instance, you can refer to several multiscale approaches available in the literature. I have published something on this matter for what concerns mechanical response of soft tissues. You find my main publications on this topic in my researchgate profile.
I hope that my answer can be useful for you. Let me know
Regards
Giuseppe
Dear colleague
FEM seems not to be a proper utensil in media without continuity assumption.There are now kind of mesh generating algorithms that they use a cloud of nodes instead of a network.(in my humble opinion)
search this algorithms
Dear Andrew
Thanks for your participation. Can't we take the non nearest neighborhood into account by modifying the code and assume the mesh points can interact farther than the nearest neighborhood?
Dear Andrew
I understand what you mean, I think the solution lies in multiscale model. If such model is reached that can work on different scales, then other steps are only conversion steps of this model to simulation. So we need the model first after that its only a matter of conversion the scale to other scale which a process that can be done in FEM as far as I know. What do you think?
Dear Sadeem,
FEM works well at the macro-microscale. But, since FEM needs the definition of a constitutive law, it does not able to simulate directly effects strictly associated to attractive/repulsive forces related to energetic inter-atomic potentials or related to entropic thermal-related fluctuations, that instead are fundamental for simulating molcular and/or atomic interactions at the nanoscale.
Accordingly, FEM can not directly employed to simulate a nanoscale problem. Nevertheless, FEM can be suitably formulated in order to account at the microscale or at the macroscale for effects deriving by nanoscale processes and mechanisms. In other words, by employing suitable homogenization approaches, you can define constitutive relationships at the micro/macroscale that include the influence of subscale phenomena. This is the "multiscale" universe. For instance, you can refer to several multiscale approaches available in the literature. I have published something on this matter for what concerns mechanical response of soft tissues. You find my main publications on this topic in my researchgate profile.
I hope that my answer can be useful for you. Let me know
Regards
Giuseppe
Dear Prof. Giuseppe Vairo
Thank you for your answer, But how about using micromechanics in some projects that depends on assuming unit cells interaction. Can these cells assumed to be down to nanoscale?
Dear Sadeem, please give some more details...
what do you mean "unit cell interaction"?
Dear Giuseppe Vairo
if you have an account on DS see the following link
https://swym.3ds.com/#post:34107
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