# Data-driven Nonlinear Plate Theory

Project: Research

## Description

The emergence of Big Data and Data Science has the potential to revolutionise the mathematical modelling of complex physical phenomena. This project aims at contributing to realise this potential in Elasticity Theory in general, and in Plate Theoryin particular. Elasticity theory predicts the displacements and stresses in elastic bodies subjected to external forces by means of mathematical models such us optimisation problems or boundary value problems of systems of nonlinear partial differential equations. Platetheory is the theory of elasticity applied to thin elastic plates that can be approximated by two-dimensional planar bodies (such as, e.g., steel sheets). All these models are built from two types of information:(1) absolute laws of physics (which apply to all bodies irrespective of the their specific nature).(2) empirical and observational data (which are specific to the elastic material of which the bodies are made). Classical Elasticity uses the empirical and observational data of (2) to define a ``constitutive law'' for the elastic material from which the body is made, then combines this constitutive law with the ``absolute laws'' of 1) to build one mathematical model foreach elastic material. This freezes the model to a given set of data, in the sense that new data or new elastic materials cannot be included in the model. By contrast, the emerging new theory of ``Data-driven Elasticity'' directly combines (1)and (2) to build a mathematical model, thus skipping the intermediate step of defining a``constitutive law'' in classical elasticity. This completely eliminates the errors ofmodelling the elastic material by means of a ``constitutive law''. Besides, by keeping the empirical and observational data in a separate set of ``big data",the mathematical model can be updated whenever new empirical and observational databecome available. In addition, this new approach makes the model adaptable to newelastic materials, such that those created by new technologies for specific purposes. But to realise this potential, the new theory of Data-driven Elasticity has to be put onfirm theoretical and computational bases, and show how the enormous knowledgeacquired in classical elasticity, both qualitative and quantitative, can be incorporated inthe new theory in a systematic way. This is the ultimate aim of this proposal.

## Detail(s)

Project number 9043404 GRF Not started 1/01/23 → …