This is the peer reviewed version of the following article: Kavallaris, N. I. (2015). Explosive solutions of a stochastic non-local reaction–diffusion equation arising in shear band formation. Mathematical Methods in the Applied Sciences 38(16): 3564-3574, which has been published in final form at DOI: 10.1002/mma.3514. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.In this paper, we consider a non-local stochastic parabolic equation which actually serves as a mathematical model describing the adiabatic shear-banding formation phenomena in strained metals. We first present the derivation of the mathematical model. Then we investigate under which circumstances a finite-time explosion for this non-local SPDE, corresponding to shear-banding formation, occurs. For that purpose some results related to the maximum principle for this non-local SPDE are derived and afterwards the Kaplan's eigenfunction method is employed
