We study the reciprocity gap method [4] for the identification of planar cracks in the framework of three dimensional linear elasticity. In order to achieve better accuracy on thick domains, we propose to use polynomial test functions instead of Fourier series. We also propose to improve the solution by various regularization techniques that are tested and compared. Numerical assessments are provided in 2D and 3D.

This work proposes an estimation of the possible heat recovery of self-heating compost piles for building applications. The energy released during the aerobic composting of lignin and cellulose-based materials is computed by solving an inverse problem. The method consists first in an experimental phase with measurement of the temperature within the heap, then a numerical procedure allows for the inverse identification of the heat production due to the chemical reaction of composting. The simulation results show a good accordance with the experiments for the chosen source-term model. Comparing the results to the theoretical values for the energy released by aerobic composting provides an estimate for the efficiency of the reaction. The reached temperatures and recovered energy fit with the order of magnitude of building needs.

This study addresses the application of the modified Constitutive Relation Error to field identification problems in the framework of elastostatics. We show how relevant is the addition of a gradient-penalizing regularization term (in norm 1 or 2 ), and emphasize the role played by unreliable boundary conditions. This leads to the proposition of a method using two parameters, for which automatic determination is addressed. All theoretical assessments are illustrated on experimental data. The test-problem consists in the identification of the heterogeneous fiber-orientation in a woven fabric composite from a unique quasi-static tensile test with digital image correlation.

Summary This paper presents a study of primal and dual Steklov‐Poincaré approaches for the identification of unknown boundary conditions of elliptic problems. After giving elementary properties of the discretized operators, we investigate the numerical solution with Krylov solvers. Different preconditioning and acceleration strategies are evaluated. We show that costless filtering of the solution is possible by postprocessing Ritz elements. Assessments are provided on a 3D mechanical problem.