Cation-based (or electrochemical) resistive memory devices are gaining increasing interest in neuromorphic applications due to their capability to emulate the dynamic behaviour of biological neurons and synapses. The utilization of such devices in neuromorphic systems necessitates a reliable physical model for the resistance switching mechanism, which is based on the formation and dissolution of a conductive filament in a thin dielectric layer, sandwiched between two metal electrodes. We propose a comprehensive model to simulate the evolution of the filament geometry under the effect of both surface diffusion caused by curvature gradient and electromechanical stress, and mass injection due to electrodeposition of cations. The model has been implemented in a C++ platform using a level-set approach based on a mixed finite element formulation, enriched by a mesh adaptation strategy to accurately and …