A two-parameter strain energy function for brain matter: An extension of the Hencky model to incorporate locking

Abstract

By just replacing the infinitesimal strains by logarithmic strains, the Hencky strain energy has proven to extend successfully the infinitesimal framework to moderately large strains, as those found in brain. However, as polymers and soft tissues, brain presents an important strain-stiffening towards locking. Based on both observations, in this paper we propose a simple two-parameter isotropic strain energy function for representing the inviscid (conservative) behavior of brain matter. The two parameters of the model are the Young modulus (or alternatively the shear modulus) and the locking stretch during a test. Through a comparison with experimental data, we show that with this simple model, employing the two material parameters directly measured from a tensile test, we capture the qualitative aspects and quantitative behavior of brain mater in tension, compression and simple shear tests with good accuracy.

Statement of Significance

This paper shows a simple mathematical model capable of reproducing qualitative aspects and quantitative behavior of brain matter in tension, compression and simple shear tests with good accuracy. The model is governed by only two parameters, namely Young's modulus (or alternatively the shear modulus) and the locking stretch.