Abstract
An electrochemical–thermomechanical model for the description of charging and discharging processes in lithium electrodes is presented. Multi-physics coupling is achieved through the constitutive relations, obtained within a consistent thermodynamic framework based on the definition of the free energy density, sum of distinct contributions from different physics. The system is characterized by finite kinematics, under the assumption of locality of deformation, and the deformation gradient is decomposed into the product of elastic and inelastic parts. Specifically, a Taylor series expansion is used to approximate the inelastic deformation due to ion intercalation. The elastic part can be described alternatively by two finite kinematics models of neo-Hookean elasticity, and a Maxwell-type viscoelastic model accounts for time-dependent mechanical aspects. The model is implemented into a finite element code that uses B-spline basis functions. We illustrate the features of the model by means of selects examples, showing that chemo-mechanical interaction affects the equilibrium concentrations of the phases. The model captures the fundamental aspects of the anode charging and discharging processes.
Highlights
The increasing use of portable electronics, handy devices, and electric automotive conveys an impending growth in the demand for secondary batteries [1], among which the most successful at the present are lithium based
The features of the proposed electrochemical–thermomechanical model are summarized in Sect. 7, while Appendix provides some fundamental relations
Electricity, temperature, and displacement fields arises from the constitutive relations and is accounted for in the kinematics through the multiplicative decomposition of the deformation gradient, which splits into elastic and inelastic parts
Summary
The increasing use of portable electronics, handy devices, and electric automotive conveys an impending growth in the demand for secondary batteries [1], among which the most successful at the present are lithium based. In the automotive industry alone, the world market for lithium-based batteries could grow from the registered $24 billion in 2017 to $65 billion by 2025 [53] This extraordinary potential explains the strong interest in the development of high energy-density batteries with optimized electrodes for which design intuition, experimental results, and numerical simulations are needed. A continuum-level theory, coupling diffusion and finite deformations, was proposed in [2] and later solved in a simplified manner by standard finite elements (FEM), [26,38] Typical cathode materials, such as lithium manganate, have been investigated for stress-related phase separation [22,66] using a nonlocal diffusion model [62]. The features of the proposed electrochemical–thermomechanical model are summarized in Sect. 7, while Appendix provides some fundamental relations
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