# Three-Dimensional Yielding in Anisotropic Materials: Validation of Hill Criterion

## TL;DR

This study demonstrates that the Hill yielding criterion accurately predicts the yielding behavior of anisotropic electrorheological fluids under combined stress fields, extending its applicability beyond metallic systems.

## Contribution

The paper validates the Hill criterion for anisotropic soft materials, specifically ER fluids, under orthogonal stress superposition, showing its universal relevance.

## Key findings

- Hill criterion accurately predicts yield in ER fluids
- Yield state diagram aligns with Hill model predictions
- Supports universality of Hill criterion for anisotropic materials

## Abstract

Yielding transition in isotropic soft materials under superposition of orthogonal deformation fields is known to follow von Mises criterion. However, in anisotropic soft materials von Mises criterion fails owing to preferred directions associated with the system. In this work we study a model anisotropic yield stress system: electrorheological (ER) fluids that show structure formation in the direction of electric field. We subject the ER fluids to superposition of orthogonal stress fields that leads to different yield stress values. We obtain a yielding state diagram by plotting normalized rotational shear stress against normalized radial shear stress corresponding to yield point for a given electric field. Remarkably, the state diagram validates the Hill yielding criterion, which is a general yielding criterion for materials having anisotropy along three orthogonal directions, originally developed for metallic systems. Validation of Hill criterion suggests the universality of its application to anisotropic systems including conventional anisotropic soft materials having yield stress.

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Source: https://tomesphere.com/paper/1906.03800