Sharp Stability Estimates for the Accurate Prediction of Instabilities by the Quasicontinuum Method
نویسندگان
چکیده
We propose that sharp stability estimates are essential for evaluating the predictive capability of atomistic-to-continuum coupling methods up to the limit load for atomistic instabilities such as fracture, dislocation movement, or crack tip propagation. Using rigorous analysis, asymptotic methods, and numerical experiments, we obtain such sharp stability estimates for the basic conservative quasicontinuum methods in a one-dimensional model problem. Our results show that consistent QC methods such as the quasi-nonlocal coupling method reproduce the stability of the atomistic system, whereas the inconsistent energy-based quasicontinuum method predicts instability at a significantly reduced applied load.
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