Responses of any arbitrary initially stressed reference and the stress-free reference

TL;DR

This paper introduces three novel methods to determine the response of stress-free or arbitrarily stressed references from known stressed states, bypassing the need for destructive testing and known stress-free configurations.

Contribution

It develops three approaches for deriving constitutive relations of stress-free or arbitrarily stressed references from known stressed responses, extending beyond standard practices.

Findings

The approaches can derive stress-free responses without destructive tests.

Even Green elastic states can exhibit implicit elasticity in stressed references.

The methods are applicable to various constitutive relations and stress states.

Abstract

The constitutive relation for an initially stressed reference is often determined by using the response of a virtual stress-free reference. However, identifying the constitutive relation of the original stress-free body can be challenging without conducting destructive tests. This paper presents three approaches for determining the response of a stress-free reference -- or any arbitrary initially stressed reference -- when the response of a particular initially stressed reference is known. Unlike standard practice, these approaches of changing reference configurations do not begin with a known stress-free state. The first and third approaches directly derive the constitutive relations of one stressed reference from another. {The first approach is applicable to a specific constitutive relation of the known initially stressed state,} while the third approach extends the first and is applicable to any constitutive form. The second approach uses any general response of a given stressed reference to identify the stress-free material. The response of the stress-free material is further analyzed and processed to determine the response of any stressed reference. We observe that even when the known initially stressed state is Green elastic, the arbitrarily stressed or stress-free references may exhibit implicit elasticity. (complete abstract is available in the published version)