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Adaptive quasicontinuum (QC) methods are important methodologies in molecularmechanics for the simulations of materials with defects, intending to achievethe optimal balance of accuracy and efficiency on the fly. In this study, wepropose a residual-force based a posteriori error estimate that is simple andis unified for consistent quasicontinuum methods, as opposed to the widelyadopted residual-stress based a posteriori error estimates which arecomplicated and need to be derived for the particular QC method underconsideration. The simple and unified formulation of the estimator, togetherwith certain sampling techniques, leads to a highly efficient and adaptableimplementation. We also prove in theory that the unified error estimatorprovides an upper bound of the true error. We develop adaptive algorithms basedon this unified estimator and validate the algorithms by several representativequasicontinuum methods for various types of crystalline defects, in terms ofconvergence and efficiency. In particular, the adaptive simulations of theanti-plane crack, of which we possess little a priori knowledge, demonstratethe necessity and significance of the proposed a posteriori estimates and theadaptive strategies.

Adaptive Quasicontinuum Methods and Simulations for Crystal Defects with a Theory based Unified a Posteriori Error Estimate