A reduced micromorphic model for multiscale materials and its applications in wave propagation

@article{Shaat2018ARM,
  title={A reduced micromorphic model for multiscale materials and its applications in wave propagation},
  author={Mohamed Shaat},
  journal={Composite Structures},
  year={2018}
}
  • M. Shaat
  • Published 2 December 2017
  • Engineering
  • Composite Structures

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References

SHOWING 1-10 OF 47 REFERENCES

Wave propagation in relaxed micromorphic continua: modeling metamaterials with frequency band-gaps

In this paper, the relaxed micromorphic model proposed in Ghiba et al. (Math Mech Solids, 2013), Neff et al. (Contin Mech Thermodyn, 2013) has been used to study wave propagation in unbounded

Modeling Phononic Crystals via the Weighted Relaxed Micromorphic Model with Free and Gradient Micro-Inertia

In this paper the relaxed micromorphic continuum model with weighted free and gradient micro-inertia is used to describe the dynamical behavior of a real two-dimensional phononic crystal for a wide

Wave beaming effects in two-dimensional cellular structures

Cellular structures like honeycombs or reticulated micro-frames are widely used in sandwich construction because of their superior structural static and dynamic properties. The aim of this study is

A unifying perspective: the relaxed linear micromorphic continuum

We formulate a relaxed linear elastic micromorphic continuum model with symmetric Cauchy force stresses and curvature contribution depending only on the micro-dislocation tensor. Our relaxed model is