The shift towards more sustainable energy sources allows for lattice structures to play an emergent role in the design of future generations of energy storage and conversion devices, such as Li-ion batteries and thermoelectric generators. Particularly, three-dimensional electrode architectures have the potential to provide shorter ion-diffusion paths due to the greater surface-to-volume ratios of the active electrode material. Thus, the power density of batteries can be improved, which leads to shorter charging times. Nevertheless, the modeling and simulation of lattices structures (let alone their optimization) with commonly used methods, such as continuum finite elements, is computationally expensive. A way to mitigate this adversity is the use of beam theories. However, an efficient numerical scheme for the modeling and simulation of 3D beams that allows for large volumetric strain, induced primarily by Li-ion diffusion, has not been found in the literature. This contribution aims to provide essential steps in this direction. For the Cosserat beam, a mixed isogeometric collocation method (IGA-C) that alleviates locking phenomena has already been developed and validated. In this contribution, this model is further enhanced to incorporate axial and radial strains, both small and large, that result from the beam’s interaction with a temperature or a concentration field. Additionally, the elastic beam quantities, i.e., the stress and strain resultants, are thoroughly derived from principles consistent with 3D continuum mechanics. The latter is achieved following a multiplicative split of the deformation gradient. Moreover, the coupling of the mechanical with the thermal/chemical system is realized through a staggered scheme, where the diffusion equation is also solved following an IGA-C approach. Assuming rotational symmetry of the temperature or the concentration field, the diffusion equation is reduced to a 2D problem, thus improving the overall computational effort while retaining reliable results. The novelty of the presented method is twofold. First, it relates beam theory, and consequently small elastic strains, with large swelling deformation stemming from diffusion phenomena. Second, it also provides insight into the implementation of IGA-C for solving diffusion equations subject to large deformations. Ultimately, the current model represents the starting point for the coupling between thermo- and chemo-mechanics, beam theory, and IGA-C.