Solution of nonlinear Cauchy problem for hyperelastic solids

DOI10.1088/0266-5611/31/11/115003zbMath1333.35269OpenAlexW2345605441MaRDI QIDQ3458213

Stéphane Andrieux, Thouraya Nouri Baranger

Publication date: 18 December 2015

Published in: Inverse Problems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/0266-5611/31/11/115003

zbMATH Keywords

Cauchy problemconvexityhyperelasticitydata completionboundary data identification

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) PDEs in connection with mechanics of deformable solids (35Q74)

Related Items (5)

Convergence study and regularizing property of a modified Robin–Robin method for the Cauchy problem in linear elasticity ⋮ Identification of injection and extraction wells from overspecified boundary data ⋮ On the determination of missing boundary data for solids with nonlinear material behaviors, using displacement fields measured on a part of their boundaries ⋮ Nonlinear Cauchy problem and identification in contact mechanics: a solving method based on Bregman-gap ⋮ Numerical solution of an ill-posed Cauchy problem for a quasilinear parabolic equation using a Carleman weight function

Uses Software

• Matlab
• SciPy
• Optimization Toolbox

Cites Work

• Unnamed Item
• Unnamed Item
• An optimization approach for the Cauchy problem in linear elasticity
• The method of fundamental solutions for the Cauchy problem in two-dimensional linear elasticity
• Constitutive law gap functionals for solving the Cauchy problem for linear elliptic PDE
• An energy error-based method for the resolution of the Cauchy problem in 3D linear elasticity
• The method of fundamental solutions and condition number analysis for inverse problems of Laplace equation
• Boundary element solution for the Cauchy problem in linear elasticity using singular value decomposition
• The unique continuation property of an elliptic system. The Lamé system
• Identification of nonlinear elliptic equations
• Carleman estimates for the regularization of ill-posed Cauchy problems
• Application of some anisotropic damage model to the prediction of the failure of some complex industrial concrete structure
• Numerical analysis of an energy-like minimization method to solve a parabolic Cauchy problem with noisy data
• On iterative methods for solving ill-posed problems modeled by partial differential equations
• Solution of the Cauchy problem using iterated Tikhonov regularization
• Global Carleman Estimates for Waves and Applications
• On the Alternating Method for Cauchy Problems and Its Finite Element Discretisation
• Regularization of the noisy Cauchy problem solution approximated by an energy-like method
• Uniqueness in the Cauchy Problem for Partial Differential Equations
• Solving Cauchy problems by minimizing an energy-like functional
• Error Estimate Procedure in the Finite Element Method and Applications
• Application of a posteriori error estimation for structural model updating
• Proximal Minimization Methods with Generalized Bregman Functions
• An iterative method for solving elliptic cauchy problems
• A mixed formulation of quasi-reversibility to solve the Cauchy problem for Laplace's equation
• On Cauchy's problem: II. Completion, regularization and approximation
• Combined energy method and regularization to solve the Cauchy problem for the heat equation
• Numerical implementation of a variational method for electrical impedance tomography

This page was built for publication: Solution of nonlinear Cauchy problem for hyperelastic solids