Lithium ion batteries have gained widespread popularity due to their applications in electric vehicles, solar cells, laptops, cell phones, digital cameras and many other electronic devices. During their functioning nonuniform concentrations of Li develop within the electrodes resulting in mechanical deformation and stresses. Many anode materials such as Si and Sn are currently being considered as anodes to increase the capacity of the Li-ion battery. Some of these materials can show a time-dependent stress-strain constitutive relationship. It is not clear how stress evolution, particle sizes and material parameters interact during charging/discharging of the anodes. In the current work the interactions of stress and diffusion is studied on a viscoelastic material and compared to that in an elastic material. The main aim is to develop a fundamental understanding of the relationships between particle size, diffusion and stress-relaxation. To this end a mathematical framework and its numerical scheme is developed for an isotropic viscoelastic material. The ensuing governing differential equations are solved using the finite element method using an open source software, deal ii (a C++ based library). Comparison studies have been conducted between elastic and viscoelastic material to explain how geometry and material related parameters determine the stress distributions within the particle.