Synergies between the constitutive relation error concept and PGD model reduction for simplified V&amp;V procedures

Ludovic Chamoin,Basile Marchand,Pierre-Eric Allier

doi:10.1186/s40323-016-0073-9

Abstract

The paper deals with the constitutive relation error (CRE) concept which has been widely used over the last 40 years for verification and validation of computational mechanics models. It more specifically focuses on the beneficial use of model reduction based on proper generalized decomposition (PGD) into this CRE concept. Indeed, it is shown that a PGD formulation can facilitate the construction of so-called admissible fields which is a technical key-point of CRE. Numerical illustrations, addressing both model verification and model updating, are presented to assess the performances of the proposed approach.

Highlights

Mathematical models and their solutions, either analytical or numerical, are fundamental in science and engineering activities as they constitute the basic ingredient of simulations that enable to predict the behavior of physical phenomena
To solve the associated ill-posed inverse problem, we introduce the energy-based concept of modified constitutive relation error [28,45], which can be seen as a direct extension of the CRE concept developed in the previous section
“Example 1: a posteriori error estimation on a 2D structure” section deals with model verification using a CRE error estimate coupled with proper generalized decomposition (PGD), whereas

Summary

Introduction

Mathematical models and their solutions, either analytical or numerical, are fundamental in science and engineering activities as they constitute the basic ingredient of simulations that enable to predict the behavior of physical phenomena. Verification deals with the assessment of the numerical (FE) model with respect to initial mathematical model, and implies the estimation of discretization error in order to control the quality of the approximate numerical solution In this context, a large set of a posteriori error estimates has appeared over the last thirty years (see [1,2,3] for an overview). Validation addresses the capability of mathematical models to represent a faithful abstraction of the real (physical) world It aims at identifying or updating model parameters in order to minimize the discrepancy between numerical predictions and experimental measurements, and leads to the solution of inverse problems [4]. The CRE concept was first introduced as a robust a posteriori

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