# Analytical solution of the uniaxial extension problem for the relaxed micromorphic continuum and other generalized continua (including full derivations)

@article{Rizzi2021AnalyticalSO, title={Analytical solution of the uniaxial extension problem for the relaxed micromorphic continuum and other generalized continua (including full derivations)}, author={Gianluca Rizzi and Hassam Khan and Ionel‐Dumitrel Ghiba and Angela Madeo and Patrizio Neff}, journal={Archive of Applied Mechanics}, year={2021}, volume={93}, pages={5 - 21} }

We derive analytical solutions for the uniaxial extension problem for the relaxed micromorphic continuum and other generalized continua. These solutions may help in the identification of material parameters of generalized continua which are able to disclose size effects.

## 11 Citations

### Primal and mixed finite element formulations for the relaxed micromorphic model

- BiologyComputer Methods in Applied Mechanics and Engineering
- 2022

### Experimental evaluation of micromorphic elastic constants in foams and lattices

- EngineeringZeitschrift für angewandte Mathematik und Physik
- 2022

Micromorphic (microstructure) elastic constants are considered within the context of experimental results for foams and rib lattices and of subsets such as Cosserat elasticity, void elasticity and…

### Size-effects of metamaterial beams subjected to pure bending: on boundary conditions and parameter identification in the relaxed micromorphic model

- EngineeringArXiv
- 2022

We devote this paper to model the size-eﬀects of metamaterial beams under bending with the aid of the relaxed micromorphic continuum. We analyze ﬁrst the size-dependent bending stiﬀness of…

### Lagrange and $H(\operatorname{curl},{\cal B})$ based Finite Element formulations for the relaxed micromorphic model

- Computer Science
- 2021

The characteristic length effect on the different components of the model is analyzed and it is revealed how the size-effect property is captured via this characteristic length.

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

- Engineering
- 2021

### A benchmark strain gradient elasticity solution in two-dimensions for verifying computational approaches by means of the finite element method

- EngineeringMathematics and Mechanics of Solids
- 2022

In elasticity, microstructure-related deviations may be modeled by strain gradient elasticity. For so-called metamaterials, different implementations are possible for solving strain gradient…

### Higher order Bernstein-Bézier and Nédélec finite elements for the relaxed micromorphic model

- Computer ScienceArXiv
- 2023

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### Mechanics of size-dependent materials

- EngineeringArchive of Applied Mechanics
- 2022

The main driving force in modern technology is to make systems of smaller dimensions and novel materials. This poses enormous technological challenges to manufacturing procedures, both at structural…

### Lagrange and $$H({\text {curl}},{{\mathcal {B}}})$$ based finite element formulations for the relaxed micromorphic model

- Computer ScienceComputational Mechanics
- 2022

The characteristic length effect on the different components of the model is analyzed and how the size-effect property is captured via this characteristic length parameter is revealed.

### The consistent coupling boundary condition for the classical micromorphic model: existence, uniqueness and interpretation of parameters

- Materials ScienceContinuum Mechanics and Thermodynamics
- 2022

We consider the classical Mindlin–Eringen linear micromorphic model with a new strictly weaker set of displacement boundary conditions. The new consistent coupling condition aims at minimizing…

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