Logo image
Back
A force–displacement formulation of constitutive-relation-error at finite strain
Journal article   Peer reviewed

A force–displacement formulation of constitutive-relation-error at finite strain

Farshid Masoumi and Jia Lu
International journal of solids and structures, Vol.340( 1 November 2026), 114278
08/24/2026
DOI: 10.1016/j.ijsolstr.2026.114278

View Online

Abstract

This article presents a new finite strain constitutive-relation-error (CRE) formulation for inverse characterization of hyperelastic materials. The proposed formulation builds on an alternative representation of the classical constitutive error functional, which expresses the constitutive error directly through residual work. This representation naturally extends the classical CRE formulation to finite strain. After finite element discretization, the functional reduces to the inner product between force and displacement vectors. The computational structure is remarkable simple. The first order sensitivities of the loss function can be computed analytically. A modified formulation which augments the loss with a displacement term is also presented. The method naturally accommodates incomplete displacement measurements; here the notion of missing displacement is extended to unknown stress-free configuration. Contour plots are used to compare the proposed formulation with two fundamental loss functions, providing insight into their intrinsic conditioning and noise sensitivity. Numerical examples are presented to examine the conditioning, robustness, scalability, and statistical behavior of the proposed formulation. •A new finite strain constitutive-relation-error formulation is proposed.•The computation structure is remarkably simple, involving FEM vector operations.•An example is presented to demonstrate the application with missing reference configuration.•Scalability is tested using an example involving 10,000 unknown parameters.•The intrinsic property is compared with two fundamental formulations via contour plots.
 Constitutive-relation-error Finite strain Hyperelastic material characterization Inverse method Partial field problem

Details

Metrics

4 Record Views
Logo image