Numerical Mechanics Team

Development of predictive simulation tools and solving methods for multiphysical problems

One of the chal­lenges is to pro­pose strate­gies, meth­ods and numer­i­cal mod­els con­tribut­ing not only to the pre­dic­tion of the behav­iour of mate­ri­als and struc­tures, pos­si­bly up to their rup­ture, but also to the under­stand­ing of the mech­a­nisms at play in a con­text includ­ing, where appro­pri­ate, sev­er­al physics. In this con­text where exper­i­men­ta­tion is dif­fi­cult, the numer­i­cal tool then becomes a means of reach­ing mea­sure­ments not acces­si­ble by phys­i­cal means. In this con­text, the team’s work focus­es on:

• the descrip­tion of the frac­ture in a pos­si­bly mul­ti-phys­i­cal con­text but also,
• stak­ing into account the effect of archi­tec­ture or the micro (or even nano) struc­ture of mate­ri­als on the behav­iour at high­er scales.

Management and propagation of uncertainties

The man­age­ment, quan­tifi­ca­tion and prop­a­ga­tion of uncer­tain­ties appear to be essen­tial at dif­fer­ent lev­els of mod­el­ling and con­sti­tute a trans­ver­sal axis of the team’s activ­i­ties. The improve­ment of mechan­i­cal and numer­i­cal mod­els based on mul­ti-modal mea­sure­ments can­not be envis­aged with­out con­sid­er­ing the ques­tion of the man­age­ment of uncer­tain­ties, linked both to the intrin­sic nature of the mea­sure­ments and to their exploita­tion (ran­dom uncer­tain­ties / epis­temic uncertainties).

On the basis of the tools devel­oped by the team which are based on prob­a­bilis­tic but also non-sto­chas­tic approach­es, the tools nec­es­sary to meet the chal­lenges of pre­dic­tive mod­el­ling and the rel­e­vant use of mea­sure­ments are devel­oped. The work car­ried out so far on the assess­ment of vari­abil­i­ty has focused on the scale of the struc­ture.

One per­spec­tive is to devel­op a strat­e­gy to prop­a­gate uncer­tain­ty and vari­abil­i­ty across scales by tak­ing into account vari­abil­i­ty at the micro and/or meso scales in the assess­ment of vari­abil­i­ty at the macro scale of the structure.

Model reduction and rich data management

The study of com­plex sys­tems involv­ing mul­ti­ple physics leads to sim­u­la­tions gen­er­at­ing large vol­umes of data. The con­struc­tion and iden­ti­fi­ca­tion of the mod­els involved pre­sup­pose the use of com­plex tests (mul­ti-instru­men­tal) gen­er­at­ing rich and het­ero­ge­neous mea­sure­ments (mul­ti-modal).

The man­age­ment and con­struc­tion of these large quan­ti­ties of data of a het­ero­ge­neous nature rais­es the prob­lem of find­ing rel­e­vant infor­ma­tion, cou­pling these data, merg­ing them and man­ag­ing uncer­tain­ties. In this con­text emerge

• the need for mod­el reduc­tion tech­niques to deal with, under­stand and con­trol prob­lems involv­ing dimen­sion­al­i­ty that is incom­pat­i­ble with the pos­si­bil­i­ties of struc­tur­al cal­cu­la­tion, but also,
• the need for data com­pres­sion tools to man­age and exploit the vol­umes of data result­ing from the tests.

The con­clu­sion is that mod­el reduc­tion tech­niques are based on a math­e­mat­i­cal frame­work com­mon to data com­pres­sion and « machine learn­ing » tech­niques devel­oped main­ly by com­put­er scientists. 

The objec­tive, on the basis of the team’s exper­tise in opti­mi­sa­tion and mod­el reduction/simplification tech­niques, and more par­tic­u­lar­ly « man­i­fold learn­ing », is there­fore to pro­pose a uni­fied approach that makes it pos­si­ble to com­bine mod­el reduc­tion, learn­ing and cal­cu­la­tion of struc­tures and opti­mi­sa­tion with a view to trans­for­ma­tion: data -> infor­ma­tion -> knowl­edge -> decision-making.