Structural battery composites belong to the category of multifunctional materials with the ability to store electrochemical energy and carry mechanical load simultaneously. A conventional lithium-ion battery comprises a positive electrode, separator, and a negative electrode. The constituents are soaked in a liquid electrolyte, allowing lithium-ion exchange between the electrodes while electrons travel through an external circuit. In structural batteries, the negative electrode is replaced by multifunctional carbon fibres, enabling the additional function as mechanical reinforcement. The liquid electrolyte is replaced by a porous two-phase matrix material, in which the solid polymer phase transfers mechanical loads between carbon fibres, and the lithium ions travel in the liquid phase of the matrix. The lithium ions react on the carbon-fibre / electrolyte interface, forming neutral lithium that diffuses inside the carbon fibres. The process is accompanied by extensive carbon fibre expansion and change in elastic moduli, causing internal stresses. Conversely, applying a mechanical load to lithiated carbon induces a response in electric potential. To evaluate the behaviour and performance of the carbon fibre electrode against a known reference potential, the positive electrode can be replaced with lithium metal, known as a half-cell representation. The modelling of half-cell structural batteries has been addressed by Carlstedt et al., where a fully coupled electro-chemo-mechanical framework is introduced. The presented model considers linear elastic materials and uses linearized reaction kinetics on the carbon-fibre electrode / electrolyte interface. In this work, we model a full cell structural battery by by considering a design where the positive electrode consists of coated, load carrying, fibres. To understand the details of chemical reactions in the battery, we adopt non-linear reaction kinetics on the electrode / electrolyte interfaces using the Butler-Volmer relation. In partucilar, we discuss the electro-chemo-mechanical modelling the positive electrode, and the pertinent calibration towards experimental findings.