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

@article{Shaat2017ARM,
  title={A reduced micromorphic model for multiscale materials and its applications in wave propagation},
  author={Mohamed Shaat},
  journal={Composite Structures},
  year={2017}
}
  • M. Shaat
  • Published 2 December 2017
  • Engineering
  • Composite Structures
View PDF on arXiv
34 Citations
Highly Influential Citations
1
Background Citations
5
Methods Citations
4

Figures and Tables from this paper

34 Citations

Analysis of planes within reduced micromorphic model

Three-dimensional formulation of the reduced micromorphic model is dimensionally reduced to address a plane under in-plane external load and the governing system of partial differential equations with corresponding consistent boundary conditions are discretized and solved using the finite element method.

Reduced micromorphic model in orthogonal curvilinear coordinates and its application to a metamaterial hemisphere

The reduced micromorphic model is used to study the effect of the applied force on a hemisphere made of phononic crystals that belongs to the metamaterials group and showed that the displacement has a greater effect rather than the micro-strain, when it is measured relative to the classical physical quantities.

Dynamic Response of Composite Materials with 2D Reduced Micromorphic Model

In this article, we introduce a complete set of constitutive relations and field equations for the linear reduced micromorphic model. We further investigate the internal variables and their…

On the equivalent shear modulus of composite metamaterials

A Micromorphic Beam Theory for Beams with Elongated Microstructures

A novel micromorphic beam theory that considers the exact shape and size of the beam’s microstructure is developed and would find many important applications including the mechanics of advanced beams such as meta-, phononic, and photonic beams.

Large elastic deformation of micromorphic shells. Part I: Variational formulation

We aimed to study the static deformation of geometrically nonlinear shell-type structures on the basis of micromorphic theory. Employing the most comprehensive model in the micro-continuum field,…

Analysis of the size-dependent wave propagation of a single lamellae based on the nonlocal strain gradient theory

In the present article, the general wave propagation behavior of a single lamellae biological system was analyzed. The Lamellae is the main component of cortical bone. Its shape can be approximated…

Integral and differential nonlocal micromorphic theory

Purpose This paper aims to combine Eringen’s micromorphic and nonlocal theories and thus develop a comprehensive size-dependent beam model capable of capturing the effects of…

A non-classical Bernoulli-Euler beam model based on a simplified micromorphic elasticity theory

Analytical solutions of the cylindrical bending problem for the relaxed micromorphic continuum and other generalized continua

We consider the cylindrical bending problem for an infinite plate as modeled with a family of generalized continuum models, including the micromorphic approach. The models allow to describe length…

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…

Transparent anisotropy for the relaxed micromorphic model: macroscopic consistency conditions and long wave length asymptotics

Multi-scale micromorphic theory for hierarchical materials

Multiscale finite element analysis of wave propagation in periodic solids

A general nonlocal theory and its approximations for slowly varying acoustic waves

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…

Anti-plane problems of piezoelectric material with a micro-void or micro-inclusion based on micromorphic electroelastic theory

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…

Multiscale modeling of polycrystalline nickel-based superalloys accounting for subgrain microstructures

Effects of grain size and microstructure rigid rotations on the bending behavior of nanocrystalline material beams

  • M. Shaat
  • Engineering, Materials Science
  • 2015