Characterisation of damage by means of electrical measurements: Numerical predictions

Understanding damage mechanisms and quantifying damage is important in order to optimise structures and to increase their reliability. To achieve this goal, experimental‐ and simulation‐based techniques are to be combined. Different methods exist for the analysis of damage phenomena such as fracture mechanics, phase field models, cohesive zone formulations and continuum damage modelling. Assuming a typical ‐type damage formulation, the governing equations of continua that account for gradient‐enhanced ductile damage under mechanical and electrical loads are derived. The mechanical and electrical sub‐problems give rise to the local form of the balance equation of linear momentum, the micromorphic balance relation and the continuity equation for the electric charge, respectively. Experimental investigations indicate that changes in electrical conductivity arise due to the evolution of the underlying microstructure, for example, of cracks and dislocations. Therefore, motivated by deformation‐induced property changes, the effective electrical conductivity is assumed to be a function of the damage variable. This eventually allows the prediction of experimentally recorded changes in the electrical resistance due to mechanically‐induced damage processes. Interpreting the resistivity as a fingerprint of the material microstructure, the simulation approach proposed in the present work contributes to the development of non‐destructive electrical‐resistance‐based characterisation methods. To demonstrate the applicability of the proposed framework, different representative simulations are studied.