Experimental measurement of 2D strain hardening reveals local yield stress distribution of a Carbopol gel

Yield stress fluids (YSFs) are ubiquitous in everyday life, such as gels, fresh cement, food emulsions, and clays. They flow only above their yield threshold. The complexity of these materials lies in their combination of elastic and plastic properties of solids with the viscous properties of fluids. While steady-state features are reasonably well understood, the response to complex flow histories, common in applications like pumping, mixing, or under vibration, is less known. In these complex deformation protocols, it is crucial to consider the full tensorial character of the mechanical response.

We present the elasto-plastic tensorial behavior of a Carbopol gel (a model YSFs) in an original two-dimensional shear experiment with varying shear directions [1]. This elasto-plastic response is studied by imposing a slow shear flow at an angle θ to the preshear flow direction. When the material is first presheared in a given direction and then left at rest, our experiment shows two very different responses depending on the subsequent direction of start-up flow. When sheared again in the same direction (θ=0), it exhibits an almost perfect linear and reversible (elastic) stress increase up to the steady-state stress. When sheared in the opposite direction to the preshear (θ=π), it shows a slow, nonlinear stress increase due to both elastic and plastic deformations. This progressive strengthening of the material up to steady-state is known as strain hardening [2]. Our 2D experiment reveals strain hardening of the Carbopol gel across any change in shear direction θ.

We also found that the shear force shows a non-trivial component orthogonal to the shear direction. Interestingly, the transient regime of this perpendicular force persists longer than that of the force aligned with the shear direction.



This memory effect on orthogonal stress and, more generally, on the transient behavior of the stress tensor can be quantitatively captured by a tensorial generalization of mesoscopic elasto-plastic model [3,4] that reveals the distribution of local yield stresses in the material.



[1] Blanc F, et al. PRL 130.11 (2023): 118202.



[2] Deboeuf S, et al. Soft Matter 18.46 (2022): 8756-8770.



[3] Hébraud P, and Lequeux F. PRL 81.14 (1998): 2934.



[4] Olivier J., Renardy M. Arch Rational Mech Anal 208, 569–601 (2013)