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

Scientific reports·2020

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Analysis of planes within reduced micromorphic model.

A R El Dhaba¹, S Mahmoud Mousavi²

¹Department of Mathematics, Faculty of Science, Damanhour University, Damanhour, Egypt.

Scientific Reports

|July 31, 2021

Summary

This study analyzes a plane under static load using a reduced micromorphic model, a generalized continuum theory. The finite element method reveals microstructure-loading interactions and demonstrates classical/nonclassical deformation measures.

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Area of Science:

Continuum Mechanics
Materials Science
Computational Mechanics

Background:

Generalized continuum theories capture microstructure interactions.
Reduced micromorphic models homogenize complex microstructures.
Analyzing microstructural behavior under external loads is crucial.

Purpose of the Study:

To investigate a plane under static load using a reduced micromorphic model.
To analyze the interaction between microstructure and external loading.
To demonstrate classical and nonclassical deformation measures for this model.

Main Methods:

Dimensional reduction of a 3D reduced micromorphic formulation to a 2D plane.
Discretization and solution of governing partial differential equations using the finite element method.
Application of consistent boundary conditions.

Main Results:

The finite element method successfully analyzed the reduced micromorphic model under in-plane load.
The interaction between microstructure and external loading was revealed.
Classical and nonclassical deformation measures were demonstrated for the first time in this context.

Conclusions:

The reduced micromorphic model provides a viable approach to study microstructure-loading interactions.
The finite element method is effective for solving these complex models.
This work introduces novel insights into deformation measures within reduced micromorphic materials.