ENSAM ParisTech answers some questions about Model Order Reduction and its application and implications in the project. Continue reading!
Model Order Reduction is experiencing continuous advances for becoming more efficient, how the UPSCALE project will foster this trend?
Nowadays, general purpose tools are being replaced by personalized solutions. Medicine is becoming patient specific, digital twins and other kind of “avatars” are expected replicating and adapting to each individuality … and simulation cannot be the exception. Model Order Reduction -MOR- is a general methodology (even if there exist several techniques for performing such reduction) that becomes optimal in each particular application context.
MOR is based on the fact that even if a model is expected accommodating any action, to infer its associate reaction, in fact “any” is too rich, and in general actions (and consequently their associated reactions) are living in a small subset of the set of all the possible. Life, in its general sense, is finally not so rich in practice, even if the space of possible is almost infinite, we are finally quite sedentary, and it that case reduced models work!
MOR experienced major achievements in the last years, and many technologies still under construction few years ago, are nowadays proven and industrially applied. Parametric solutions, that is, the solution of a given physics for any parameter defining the geometry of the domain in which it is defied, any parameter associated to the given physics (e.g. material parameters) or any parameters describing the loading (in its most general sense) … are of major interest in both, the design, and also for accompanying the component in operation all along its life.
These parametric solutions (at the heart of the so-called PGD – Proper Generalized Decomposition -) make possible simulation (i.e. predicting responses), optimization, inverse analysis, uncertainty propagation and control, all them under the stringent real-time constraint.
However, when addressing very large thermomechanical transformations, with localized behaviours (in space – e.g. fracture – and time – e.g. impact -), strong non-linearities exhibiting bifurcations, involving numerous parameters, … MOR remains today a challenging issue, where two main approaches are being pushed forward: the intrusive and the non-intrusive ones.
UPSCALE is precisely on the border of the comfort (proven) zone, and needs addressing scenarios beyond the state-of-the-art. In a crash, all the ingredient just mentioned are present. UPSCALE will serve to validate the existing techniques and methodologies, and propose and explore new routes to improve existing solutions.
Which are the main characteristics of the reduction techniques for contact modelling?
The main characteristic of contact mechanics from the point of view of MOR is not its unilateral no-linearity, its main concern is its intrinsic richness: in very complex and parametric settings (the impactor producing the crash can act from different directions, having different velocities, area, mass, …) the number of contacts, their location (in space and time), … explore a too vast region of the parametric space and consequently the extraction of a reduced basis for the solution representation is no more possible at a global scale.
At the local scale, when addressing a particular contact, some reduction can be accomplished in both the intrusive and the non-intrusive settings: at that scale a reduced basis exist or a parametric solution can be constructed respectively, but its connexion with the global scale (structure) becomes a tricky issue because both approaches become too intrusive at the structural level.
Are there big differences when applied at the micro, macro and meso scale?
In the context of UPSCALE we defined a three scales approach.
First a region of interest is defined (a patch). The patch parametric deformation is the finely analysed (micro description and its high-fidelity simulation, extremely expensive from the computational point of view despite the small patch size) and an effective reduced parametric model elaborated to coarsely represent the patch behaviour. For that purpose, kinematics and internal forces on the patch boundary are associated by learning the reduced model relating both. However, as the model depends on the deformation history, some state variable must be introduced describing the impact of the past deformation on the present mechanical behaviour. Thus, another model must be learned or analytically derived for evolving those state variables representing the material integrity within the patch.
This patch-model constitutes the meso-level that encapsulates in a transparent way for the user all the internal richness into a model describing the relation between the kinematics and dynamic variables on the patch boundary.
Then the meso-model is coupled to the macro-one (the car) in an almost standard way.