Adaptive selection of reference stiffness in virtual clustering analysis

Abstract Virtual clustering analysis (VCA) has been developed for numerical homogenization of heterogeneous material. The integral form of the material system is the Lippmann–Schwinger equation, which imposes boundary condition at infinity for fictitious surrounding homogeneous reference material. The artificially chosen reference stiffness induces a distribution for traction on the material boundary. The deviation from a uniform loading traction boundary condition degrades the accuracy in predicting the average stiffness of the material under consideration. In this work, we suggest that the induced traction should be within one standard deviation from the loading traction, and propose an adaptive strategy to update the reference stiffness. Numerical tests for inclusion problems with elasto-plasticity compositions verify the effectiveness of the proposed strategy.

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