Data-Driven Constitutive Modeling via Conjugate Pairs and Response Functions

Abstract

Response functions completely define the constitutive equations for a hyperelastic material. A strain measure providing an orthogonal stress response, grants response functions directly from experimental curves. One of these strain measures is the Laplace stretch based on QR-decomposition of the deformation gradient. Such a recovery of response functions from experimental data fits the paradigm of data-driven modeling. The set of independent conjugate stress–strain base pairs were proposed as a simple alternative for constitutive modeling and thus might be efficient for data-driven modeling. In the present paper we explore applicability of the conjugate pairs approach for data-driven modeling. The analysis is based on representation of the conjugate pairs in terms of the response functions due to the Laplace stretch. Our analysis shows that one can not guarantee independence of these pairs except in the case of infinitesimal strain.

Keywords

• conjugate pairs
• QR decomposition
• isotropy
• hyperelasticity
• Laplace stretch