Ever since nuclear chain reactions were modelled at Los Alamos or since digital fluid mechanics was invented by NACA, the predecessors of NASA, back in the 1940s, to today’s systematic use of digital tools in industrial design work, computational mechanics has gone through all sorts of stages and phases, with the constant objective, however, of improving on the models to gain in time and precision. 

Through lack of time, numer­ous dif­fi­cul­ties to car­ry out scale-one exper­i­ments and the advent of the first gen­er­a­tion of dig­i­tal com­put­ers, the end of WWII and espe­cial­ly the after-effects of Project Man­hat­tan, sig­nal the birth of com­pu­ta­tion­al mod­el­ling. The ini­tial inves­ti­ga­tions con­sist­ed of sim­u­la­tion of nuclear chain reac­tion prop­a­ga­tion, which in turn led to the assem­bly of the first atom­ic bombs.

When we recall that the com­put­ers of that time took sev­er­al sec­ond stop car­ry out a mul­ti­pli­ca­tion, a major change came in the 1970s when pro­cess­ing pow­er of com­put­ers rose sig­nif­i­cant­ly. Mechan­i­cal engi­neer­ing mod­el­ling tools began to be used in indus­tri­al sec­tors. “At the CETIM [tech­ni­cal cen­tre for mechan­i­cal engi­neer­ing indus­tries] and at UTC, the first series of research work began in 1972–1975, lead­ing to the first soft­ware pack­ages used by indus­tri­al­ists in the 1980s”, explains Man­sour Afza­li, Senior Sci­ence Del­e­gate at CETIM.

Decomposing objects

One of the most com­mon­ly used meth­ods is that of “finite ele­ments” where space and objects are sub­di­vid­ed into ‘loops’ (or ele­ments) which are as sim­ple as pos­si­ble. The sys­tem of com­plex equa­tions that char­ac­ter­ize the com­plete sys­tem is obtained by assem­bling the data cal­cu­lat­ed for each loop. “In the ear­ly days of com­pu­ta­tion­al mechan­ics, the work con­sist­ed of mak­ing mod­els ‘char­ac­ter­iz­ing’ mechan­i­cal, phys­i­cal objects and to ensur­ing they were coher­ent with real­i­ty and the laws of mechan­i­cal engi­neer­ing”, adds Man­sour Afzali. 

The objec­tive is to mod­el the tire­some process of man­u­al design. It begins with a tech­ni­cal draw­ing, with which a series of cal­cu­la­tions is made to ensure com­pli­ance with the laws of physics. The next step is to assem­ble a phys­i­cal pro­to­type which under­goes a series of tests. Depend­ing on the results obtained, the process reit­er­ates, some­times form the start­ing point, so that errors detect­ed can be corrected. 

“The process can be reit­er­at­ed as many times as is nec­es­sary, until we obtain a pro­to­type that pass­es all the tests of the spec­i­fi­ca­tion”, under­lines Man­sour Afza­li, adding that mod­el­ling allows sci­en­tists to car­ry out a large num­ber of tests to avoid long and cost­ly iter­a­tions. Com­pu­ta­tion­al mechan­ics has led to a two-fold reduc­tion in the time need­ed to design a car and even design the Air­bus 380 sole­ly on the basis of com­put­er modelling. 

Improving the models and the software

As and when new com­pu­ta­tion­al mechan­ics tools became avail­able in the 1980s, numer­ous tests were car­ried out to detail the char­ac­ter­is­tics of mate­ri­als and to cer­ti­fy the results of the cal­cu­la­tions. Work like this enabled improve­ment to be m de on the mod­els as well as for the soft­ware. Sig­nif­i­cant test­ing was car­ried out on soft­ware in the 1990s to improve their reli­a­bil­i­ty and ‘robust­ness’.

Ever increas­ing num­bers of young engi­neers are being trained with these tools as they spread through indus­tri­al sec­tors. Com­put­er sci­ences devel­op rapid­ly and dig­i­tal mod­el­ling is now an inte­gral part of CAM soft­ware (com­put­er-aid­ed man­u­fac­tur­ing). “Progress like this, with increased mod­el robust­ness and homo­ge­neous mod­el­ling approach­es allow you to have sig­nif­i­cant time gains and also the num­ber of tests need­ed”, details Man­sour Afza­li. Com­pu­ta­tion­al mechan­ics tools are becom­ing more trust­wor­thy in the eyes of indus­tri­al­ists and have even become pri­or­i­ty tools. 

Numerous possible solutions

The pro­cess­ing pow­er of today’s com­put­ers grows con­stant­ly and it is hence­for­ward pos­si­ble to car­ry out com­plex cal­cu­la­tions to opti­mize prod­ucts. Giv­en a set of para­me­ters, con­straints and indus­tri­al objec­tives, the opti­miza­tion process con­sists of iden­ti­fy­ing the best solu­tions among numer­ous pos­si­ble solu­tions. “Opti­miza­tion is often due to the work of skilled engi­neers because it is nec­es­sary to make rel­e­vant deci­sions at var­i­ous design stages”, explains Man­sour Afza­li, for whom the con­tri­bu­tion of experts is nec­es­sary to cer­ti­fy the results of the computations. 

Faced with a true explo­sion of pro­cess­ing pow­er and with increas­ing­ly homoge­nous mod­els, mechan­i­cal engi­neer­ing research now inte­grates prob­a­bilis­tic approach­es to assess the life expectan­cy of com­po­nents that take into account the ‘vari­able’ fac­tors of the design para­me­ters and uses. They also explore increas­ing­ly com­plex mate­ri­als, such as the com­pos­ites. New meth­ods are com­ing on line, enabling sci­en­tists, for exam­ple, to take into account the speed of defor­ma­tion of mate­ri­als to mod­el mate­r­i­al reac­tions under crash-shock con­di­tions. Today, the tools can be used to design a hum­ble tin can or the mechan­i­cal response off the Eif­fel Tow­er to cli­mate or seis­mic events. 

“All the com­po­nent parts of a mechan­i­cal struc­ture can be mod­elled and com­put­ed and for this pur­pose, indus­tri­al­ists now use com­pu­ta­tion­al mechan­ics”, adds Man­sour Afza­li. This tool has become com­mon­place and young engi­neers often place a total yet blind trust in the method, esti­mat­ing that the results have the same lev­el of reli­a­bil­i­ty as would be obtained via full-scale test­ing. And Man­sour Afza­li insists on the role of the engi­neers “whose respon­si­bil­i­ty it is to ver­i­fy the hypothe­ses and the mod­els used and nev­er for­get to assess the qual­i­ty of the com­pu­ta­tion­al results”.