# Interesting but old


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# Context

## Virtual displacement dynamics
[online ref](https://people.duke.edu/~hpgavin/StructuralDynamics/VirtualDisplacementsDynamics.pdf)
[[Virtual_Displacements_Dynamics.pdf|local ref]]

## Classical, Refined, Zig-Zag, Layer-Wise Models and Best Theory Diagrams for Laminated Structures
*2023*
[online ref](https://worldscientific.com/doi/abs/10.1142/9781800611887_0004)
[[Mathematical_Methods_and_Models_in_Composites.pdf|local ref (pp. 153-208)]]

## Rheology
*2022*
[[Rheology.pdf|local ref]]

#### Continuum mechanics is a foundation of rheology

The characteristic size of the molecule is 1 nm, so one may neglect the molecular structure only when dealing with sizes of the order of at least $10 nm$. Thus the physical "point" is a volume of $10^3 nm^3$.

Stress tensor can be divided between the hydrostatic part (known as spherical), responsible for volume changes, and the part (know as deviatoric) responsible for shape changes.

Heterogeneous displacement field -> relative displacements -> deformations

Same as the Stress tensor, the deformation tensor can be divided between the spherical part (volume changes), and the deviatoric part (shape changes)
#### viscoelasticity

Two basic models
Newton law of liquids :
$$\dot{\gamma}=\frac{\sigma}{\eta}$$
Hooke's law of solids :
$$\varepsilon=\frac{\sigma_E}{E}$$
where $\varepsilon$ - deformation, $\dot{\gamma}$ - rate of shear deformation, $\sigma$ - shear stress, $\sigma_E$ - tensile stress, $E$ - elastic (or Young's) modulus, $\eta$ - viscosity

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# Full paper not found
## Topology optimization of viscoelastic damping layer in sandwich panels
*2024*
[online ref](https://www.tandfonline.com/doi/abs/10.1080/15397734.2024.2315168)
**not found**

## Dynamic properties of composite plates with embedded viscoelastic membranes
*2022*
[online ref](https://www.tandfonline.com/doi/abs/10.1080/15376494.2022.2097355)
**not found**

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# Bonus

Analysis of Intact/Delaminated Composite and Sandwich Beams Using a Higher-Order Modeling Technique   

Classical, Refined, Zig-Zag, Layer-Wise Models and Best Theory Diagrams for Laminated Structures

https://www.semanticscholar.org/paper/Topology-optimization-of-embedded-and-co-cured-Wang-Li/4b99213e5e66a48dd52fb77058aebf34d6023108

https://www.semanticscholar.org/paper/Dynamic-characteristics-of-carbon-fiber-reinforced-Yang-Zheng/51dcb618cfeae4527b52e97a578428b88fc8c475

https://www.semanticscholar.org/paper/Structural-dynamic-properties-of-stiffened-plates-Wang-Guo/cbd4d646dc97ec8e4fba405046ee8584ea8d316b