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.

The functional properties of multi-component materials are often determined by a rearrangement of their different phases and by chemical reactions of their components. In this contribution, a material model is presented which enables computational simulations and structural optimization of solid multi-component systems. Typical Systems of this kind are anodes in batteries, reactive polymer blends and propellants. The physical processes which are assumed to contribute to the microstructural evolution are: (i) particle exchange and mechanical deformation; (ii) spinodal decomposition and phase coarsening; (iii) chemical reactions between the components; and (iv) energetic forces associated with the elastic field of the solid. To illustrate the capability of the deduced coupled field model, three-dimensional Non-Uniform Rational Basis Spline (NURBS) based finite element simulations of such multi-component structures are presented.

Numerical techniques to simulate crack propagation can roughly be divided into sharp and diffuse interface methods. Two prominent approaches to quantitative dynamic fracture analysis are compared here. Specifically, an adaptive cohesive element technique and a phase-field fracture approach are applied to simulate Hopkinson bar experiments on the fracture toughness of high-performance concrete. The experimental results are validated numerically in the sense of an inverse analysis. Both methods allow predictive numerical simulations of crack growth with an a priori unknown path and determine the related material parameter in a quantitative manner. Reliability, precision, and numerical costs differ however.