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Modified LSM for size-dependent wave propagation: comparison with modified couple stress theory. (English) Zbl 1440.74170
Summary: A modified LSM is proposed by introducing an independent micro-rotational inertia, which may help characterize the scale-dependent effect and avoid the Poisson’s ratio limitation of regular triangle lattices in two dimensions. For this method, some factors may affect data pickup and modeling accuracy, but the ‘optimal’ inputs, like stiffness ratio, numerical damping, and micro-rotational inertia, could be obtained from parameter identification by the Dakota toolkit [B. M. Adams et al., “A multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis: version 5.0 user’s manual”, Tech. Rep. SAND2010-2183. Sandia National Laboratories (2009)], when a suitable excitation source function and lattice spacing are set up. By comparing with the modified couple stress theory, we analyze the dispersion relationship of elastic waves for the estimation of the characteristic material length. It shows that this modified LSM may provide an alternative and promising way to investigate the size-dependent wave propagation in elastic media numerically.
MSC:
74J10 Bulk waves in solid mechanics
74A60 Micromechanical theories
74M25 Micromechanics of solids
Software:
DAKOTA
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