The sector of electromobility and the intermediate storage sector for renewable energies use, among other energy options, lithium-ion batteries, which have become increasingly important in recent times. To improve the cell performance which is determined by the individual components on micro level, further investigations are needed. This includes gaining better understanding about the interaction of individual particles of the granular cathode, which make up its overall material behaviour. The cathode consists of a mixture of active material, which has elastic properties and defines the main part of the granular structure and binder, which is localised in the pore space of the active particles.  Nanoscale conductivity-enhancing additives are mixed into the binder.
The Discrete Element Method (DEM) [1] represents a method which makes it possible to calculate motion sequences of such discontinuous structures like the cathode. In this method, Newton’s equations of motion are solved under the action of contact forces and moments. The assumption of a discrete element applies to each granular particle without locally resolving fields inside, e.g. stress, strain and/ or temperature. Each element is uniquely defined by its position, velocity, shape, orientation and size. DEM uses suitable rheological contact models to capture the interparticle forces as realistically as possible. The interaction between elastic active material particles is described in DEM simulations by using a Hertzian [2] spring dashpot model (HSD), which represents the behaviour of a nonlinear spring and a non-physical dashpot connected in parallel (Fig. 1a)) for dissipating kinetic energy towards static equilibrium. To implement viscoelastic mechanical behaviour due to the presence of the binder with a special focus on the rate-dependent aspect, the Maxwell-Zener model (MZ) is used in this work [2].
To begin with, the contact behaviour of fully viscoelastic particles is investigated first (Fig.1 b)). Finally, the analysis will be extended to a modeling of core-shell particles (CS), i.e. overall spherical particles, which have a core consisting of an inner elastic sphere as the active material and a viscoelastic shell (Fig.1 c)) representing the binder in the pore space. Due to the time-dependent material behaviour of the binder, a dynamic implementation of the DEM is used here calculating in physical time steps, whereas the exclusive investigation of the active material can also be calculated using a quasi-static routine based on the assumption of an infinitely slow motion procedure which is constituted of a sequence of static equilibrium states. All these diversities make DEM a computationally efficient tool which enables the study of systems consisting of many particles. Finally, the packing and overall stress states of the granular cathode structure can be calculated.
In this work we present the main differences of the two implementation routines of the DEM and we demonstrate that the time-dependent MZ model can be applied in DEM simulations using the dynamic routine. This provides the basis to computationally reproduce the behaviour of the active material and binder in the presence of viscous effects. Besides studying purely elastic and viscoelastic particles, the combination of both models, expressed by the core-shell model, which is intended to reflect the behaviour of assemblies of elastic particles with viscoelastic material in the pore space, will be investigated here.