better sources

2024-09-25 14:50:53 +02:00 · 2024-09-25 14:50:53 +02:00 · 4870c89787
parent fe9035fd18
commit 4870c89787
61 changed files with 22319 additions and 1494 deletions
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+%%
--- a/.trash/Untitled
+++ b/.trash/Untitled
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+++ b/.trash/Untitled.canvas
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+{}
--- a/.trash/accelerance.pdf
+++ b/.trash/accelerance.pdf
--- a/organigrames/knowledge.md
+++ b/organigrames/knowledge.md
--- a/.trash/passive
+++ b/.trash/passive
--- a/archive.md
+++ b/archive.md
@ -0,0 +1,10 @@
+#archive
+
+Here lies the work that I do not think will be useful, but could be nice to keep *just in case*
+
+[[First theme links draft]]
+First draft of the themes links of the concepts (when I knew nothing about the subject).
+
+[[Newmark Time Integration]]
+I came across it in a paper, it is a method used for differential equations.
+
--- a/descriptions.md
+++ b/descriptions.md
@ -1,6 +1,9 @@
-# optimization of carbon-epoxy plates with a viscoelastic layer
+#description

-[[Article_Taylor_and_Francis_vfinal.pdf|ref]]
+# optimization of carbon-epoxy plates with a viscoelastic layer
+*2020*
+[online ref](https://www.tandfonline.com/doi/abs/10.1080/15376494.2021.1882626)
+[[Article_Taylor_and_Francis_vfinal.pdf|local ref]]

 **basis of the work**

@ -10,7 +13,7 @@ This papers explore the use of [[PCLD]], its goal is to optimise the damping (of

 The bridges are made by puncturing the viscoelastic layer with holes so that some of the epoxy matrix fills them.

-The simulations where made using the finite element model, with 2D elements for the carbon-epoxy layers and 3D elements with a [[Neo Hookean Behavior Law|neo-hookean visco-hyper-elastic behavior law]] for the inserted layer. The simulations are accurate with the experiments.
+The simulations where made using the [[Finite element method]], with 2D elements for the carbon-epoxy layers and 3D elements with a [[Neo Hookean Behavior Law|neo-hookean visco-hyper-elastic behavior law]] for the inserted layer. The simulations are accurate with the experiments.

 The paper also points out an issue with the manufacturing of the bridges : the epoxy does not fill the holes fully, so there are bubbles or gaps, diminishing the properties of the material.

--- a/articles/Secondary
+++ b/articles/Secondary
@ -0,0 +1,187 @@
+#description
+
+# Collisions
+## Hard and Soft Collisions
+*webpage*
+[ref](https://www.compadre.org/Physlets/mechanics/illustration8_3.cfm)
+
+A soft [[Impact-Shock-Collision|collision]] is an inelastic collision, which means that kinetic energy 
+is not conserved (because internal friction). However, the momentum is still
+conserved.
+
+A perfectly inelastic collision occurs when the two bodies stays together, 
+and the energy is lost by bonding the two bodies.
+
+## Inelastic impacts for composite materials
+*1990*
+[online ref](https://doi.org/10.1016/0263-8223(90)90025-A)
+[[Inelastic_impacts_for_composite_materials.pdf|local ref]]
+
+Use the [[Finite element method|finite element model]] to get the dynamic response.
+
+The structure is considered elastic but the loading is considered
+inelastic.
+
+The isoparametric linear shell element is modified
+to take into account the shear deformation and rotatory inertia.
+
+[[Inelastic Collisions]] : masses added together and
+momentum conserved, used for slamming or other wave-like loading
+
+This model is reasonable when the impactor is relatively soft and the mass 
+of impactor is larger than the mass of the node being impacted.
+
+## FEM of low-velocity impact on composite materials
+*2011*
+[online ref](https://doi.org/10.1016/j.compstruct.2010.10.003)
+[[FEM_of_low-velocity_impact_on_composite_materials.pdf|local ref]]
+
+use of ABAQUS
+
+examination of the validity of different models
+
+propose a  benchmark method in low-velocity [[Impact Models|impact modeling]] of composite structures
+
+---
+# Background
+
+## Machine Vibration
+*2021 (info from the metadata of the PDF)* 
+[online ref](https://www.machinedyn.com/docs/articles/Real_Physics.pdf)
+[[Real_Physics_of_Machine_Vibration.pdf|local ref]]
+
+Very practical paper, an introduction to vibrations in engineering. It has useful definitions and explanations of the terms.
+Critique of Newtonian physics ($F=ma$) and Hooke's law ($F=kx$).
+Because it assumes constant masse and stiffness.
+
+In a dynamic world, $F = mr\omega^2$. 
+
+To preserve the linearity of Newton's $2^{nd}$ law a dynamic mass is defined : 
+$m(\omega)$.
+The reciprocal of dynamic mass is accelerance, and is also a function of frequency : Accelerance $= \frac{1}{m(\omega)} = \frac{a(\omega)}{F(\omega)}$
+
+This paper advocate for less design and more tests because the theory is too far from the real world.
+
+**Symmetry is bad practice because it support resonant modes**
+
+Force is a wave that travels at the speed of sound.
+
+(see [[Accelerance]])
+
+---
+
+# VEM
+
+## Passive Constrained Layer Damping, SotA
+*2019*
+[online ref](https://iopscience.iop.org/article/10.1088/1757-899X/653/1/012036)
+[[PCLD_SotA.pdf|local ref]]
+
+This paper discuss the advancement of the PCLD technique used for structural vibration control. In addition to that, there are a lot of sources on the models developed.
+
+[[Viscoelasticity|Viscoelastic materials (VEM)]] dissipate energy under a transient deformation. Used in a form of a layer that is either freely attached (UCLD ie *unconstrained layer damping*) or in a sandwich (CLD/PCLD ie *constrained layer damping/passive constrained layer damping*).
+
+ In most of the analyses, extensional/compressional strains of the viscoelastic layer are not taken into account since the damping comes mostly from the shear strain.
+
+The mathematical models are either [[Finite element method|FE]] or analytical.
+
+(see [[PCLD]])
+
+## Layerwise Analyses VEM
+*2016*
+[online ref](https://doi.org/10.1115/1.4034023)
+[[Layerwise_Analysis_VEM.pdf|local ref]]
+
+This paper evaluates the vibrations characteristics of structures with [[Viscoelasticity|viscoelastic materials]]. The equations of motions are derived with the principle of virtual displacement (PVD) and solved with the [[Finite element method]].
+This paper uses the layerwise approach to tackle the analysis.
+
+This paper focus its study on beams.
+
+Layerwise approach : Lagrange-like polynomial expansions have been adopted to develop the kinematic assumptions (?)
+
+Issues of [[Viscoelasticity|viscoelastic]] layers dynamic study :
+- the modeling of material properties
+	-> tests to characterize the material
+- the solution of nonlinear complex eigenvalue problems
+	-> methods have been developed like the modal strain energy technique, the direct frequency response method, the iterative complex eigensolution and the asymptotic solution method
+- the kinematic modeling of the structure
+	-> main topic of the paper
+	-> damping through maximizing shear => need accurate stress distribution
+
+This paper wish to provide an alternative to the 3D modeling, preserving the numerical efficiency of 1D theories.
+
+## Analysis of the compressible neo-Hookean model
+*2023*
+[online ref](https://link.springer.com/article/10.1007/s11012-022-01633-2)
+[[Analysis_of_the_compressible_neo-Hookean_model.pdf|local ref]]
+
+Analysis of the model implemented in the commercial [[Finite element method|finite element]] software ABAQUS, ANSYS and COMSOL.
+
+Its physical limitations are explored, to underline the model's advantages and limitations.
+
+**To further read, but not necessary at first glance for my study**
+
+## Optimization method of composite laminates with a viscoelastic layer
+*2009* #perforated_vel
+[[Optimization_of_composite_laminate_with_viscoelastic_layer.pdf|local ref]]
+
+This paper develops a method to transform a multi objective (damping and stiffness)
+into a single one, to facilitate optimization.
+
+The [[Viscoelasticity|viscoelastic]] layer is **perforated**, and the sandwich is [[Co-curing|co-cured]].
+
+Co-curing means the viscoelastic material within the composite laminate undergo the temperature and pressure cycle needed to cure the composite material.
+
+---
+
+# Composite laminates
+
+## First order Zig-Zag plate Theory
+*2000*
+[online ref](https://doi.org/10.1016/S0263-8223(99)00063-X)
+[[First_order_Zig-Zag_plate_Theory.pdf|local ref]]
+
+This paper develops and assess a laminated plate theory x 3D finite element, based on [[Zig-Zag Theories|first order zig zag sublaminate approximations]].
+
+Zig Zag functions are evaluated by enforcing the continuity of the transverse shear stresses at layer interfaces.
+=> accounts for discrete layers without increasing the number of degrees of freedom as the number of layers is increased.
+
+5 degrees of freedom per node (8 nodes brick), 3 translation and 2 rotations.
+
+full name : zig-zag in-plane displacement theories
+
+[[Equivalent Single Layer Theories|ESL]] : the laminate is modeled as an equivalent single anisotropic layer
+-> most popular : [[Equivalent Single Layer Theories#First-order Shear Deformation Theory (FSDT)|FSDT]] , but does not account for warpage of the cross section.
+High-order Shear Deformation theory (HSDT)
+[[Equivalent Single Layer Theories#High-order Shear Deformation theory (HSDT)|HSDT]] : it is assumed that the displacements are of higher order polynomial form and are $C^1$ continuous through the thickness. This allows for non-linear variation of displacements, strain and stresses through the thickness.
+
+[[Equivalent Single Layer Theories|ESL]] issue : unable to account for discontinuities in transverse shear strains at interfaces between layers with different stiffness.
+
+[[Layerwise Theories|Layerwise]] : unique displacement field per layer + interlaminar continuity of displacements (and sometimes of transverse stresses).
+-> very computationally expensive, since the number of degrees of freedom increase proportionally with the number of layers.
+
+FZZT (First Order Zig-Zag Theory) :
+In-plane displacements are assumed to be layerwise linear and continuous through the thickness.
+5 degrees of freedom (does not depend on the number of layers) achieved with the transverse shear stress continuity at each interface.
+-> very good with symmetrical laminates
+
+HZZT (Higher Order Zig-Zag Theories) :
+FZZT + piecewise linear variation of in-plane displacement on a continuous cubic function of the transverse coordinate.
+-> better displacement field for unsymmetrical laminates. 
+\+ homogeneous shear traction boundary conditions at the top and bottom surfaces to keep 5 degrees of freedom.
+issue : the transverse deflection degree of freedom $w_0$ is required to be $C^1$ continuous. Therefor additional rotational degrees of freedom (gradients of $w_0$) are present -> more than 6 degrees of freedom -> tough to implement in commercial finite element software.
+
+Goal : keep it accurate, $C^0$ continuous and 5 degrees of freedom
+
+(see [[Zig-Zag Theories]])
+
+## Historical review of Zig-Zag theories
+*2003*
+[online ref](https://asmedigitalcollection.asme.org/appliedmechanicsreviews/article-abstract/56/3/287/446373/Historical-review-of-Zig-Zag-theories-for)
+[[Historical_review_of_Zig-Zag_Theories.pdf|local ref]]
+
+This papers explore the history of the development of zig-zag theories, their hypothesis and use-cases. It intends as well to properly address who contributed to what. 
+
+[[Zig-Zag Theories]] are theories which describe the piecewise form of transverse stress (Zig-Zag, ZZ) and displacement fields (Interlaminar Continuity, IC).
+
+This papers explain thoroughly the different theories developed and how they function (maybe a bit too much for what I need).
--- a/descriptions.md
+++ b/descriptions.md
@ -1,50 +1,77 @@
+#description

-# finite element method
-
+# Finite element method
 full notes : [[Finite element method]]

-[weak formulation](https://www.youtube.com/watch?v=xZpESocdvn4) *(30min)*
+### Weak Formulation
+[video](https://www.youtube.com/watch?v=xZpESocdvn4) *(30min)*

 The weak formulation is the formulation of the differential equation so that it becomes solvable using the finite elements method.

 This video shows how the weak formulation is derived from the initial problem, and its use.

-[finite element method](https://www.youtube.com/watch?v=1wSE6iQiScg) *(40min)*
+### Mathematical Finite element method base
+[video](https://www.youtube.com/watch?v=1wSE6iQiScg) *(40min)*

 The finite element method is a mathematical method to be able to computationally solve a differential equation.

 The core of the method is to discretise the problem, because computer cannot solve the problem analytically.

-# continuum mechanics
-
+# Continuum mechanics
 full notes : [[Continuum Mechanics]]

-[continuum mechanics](https://www.youtube.com/watch?v=rhDkluTuWlQ) *(10min)*
+### Continuum mechanics
+[video](https://www.youtube.com/watch?v=rhDkluTuWlQ) *(10min)*

 This video goes over what is continuum mechanics, and the uses of fields to describe matter. It presents as well the boundary value problem.

-[strain tensor formula](https://www.youtube.com/watch?v=X-H3Fwdm-kI) *(10min)*
+### Strain tensor formula
+[video](https://www.youtube.com/watch?v=X-H3Fwdm-kI) *(10min)*

 The strain tensor is the symmetric part of the gradient of the displacement field vector.
 This video manages to make this confusing statement a lot clearer.

-
-[visualizing the strain tensor](https://www.youtube.com/watch?v=UQ4GnWACesY) *(10min)*
+### Visualizing the strain tensor
+[video](https://www.youtube.com/watch?v=UQ4GnWACesY) *(10min)*

 This video makes the physical effect of each element of the tensor more apparent.

-[stress and traction](https://www.youtube.com/watch?v=NtTVEzZS3Bg) *(10min)*
+### Stress and traction
+[video](https://www.youtube.com/watch?v=NtTVEzZS3Bg) *(10min)*

 In continuum mechanics, the force over an area is not the stress, it is traction. This video helps getting a clearer understanding of the stress tensor.

-# laminate analysis
+# Laminate analysis

-[composite materials](https://www.youtube.com/watch?v=j3rvtgqrGsQ) *(1h30)*
+### Composite materials course
+[video](https://www.youtube.com/watch?v=j3rvtgqrGsQ) *(1h30)*

 This video is a course on the analysis of composite laminate. Mainly the maths to compute the stress/strain relationship with discrete layers.
 (see [[Layerwise Theories]])

-[modeling layered composite](https://www.comsol.fr/video/modeling-layered-composite-structures-with-comsol-multiphysics-nov-29-2018) *(1h)*
+## Modeling layered composite
+[video](https://www.comsol.fr/video/modeling-layered-composite-structures-with-comsol-multiphysics-nov-29-2018) *(1h)*

 This video exposes multiple models for composite laminates, for example equivalent single layer (eql) and layerwise (lw)
 (see [[Composite laminate models]])
+
+
+# Failure theories
+full notes : [[Failure Theories]]
+
+### Failure theories
+[video](https://www.youtube.com/watch?v=xkbQnBAOFEg) (15min)
+
+This video presents a few failure theories, and their physical meaning :
+
+Ductile materials :
+- Tresca
+- von Mises
+
+Brittle materials :
+- Coulomb-Mohr
+
+
+
+
+
--- a/articles/primary/Article_Taylor_and_Francis_vfinal.pdf
+++ b/articles/primary/Article_Taylor_and_Francis_vfinal.pdf
--- a/articles/primary/manuscrit_de_these_de_Remy_Mateu_Pastor.pdf
+++ b/articles/primary/manuscrit_de_these_de_Remy_Mateu_Pastor.pdf
--- a/articles/secondary/FEM_of_low-velocity_impact_on_composite_materials.pdf
+++ b/articles/secondary/FEM_of_low-velocity_impact_on_composite_materials.pdf
--- a/articles/secondary/First_order_Zig-Zag_plate_Theory.pdf
+++ b/articles/secondary/First_order_Zig-Zag_plate_Theory.pdf
--- a/articles/secondary/Historical_review_of_Zig-Zag_Theories.pdf
+++ b/articles/secondary/Historical_review_of_Zig-Zag_Theories.pdf
--- a/articles/secondary/Impact_and_vibration_of_hybrid_fiber_metal_laminates.pdf
+++ b/articles/secondary/Impact_and_vibration_of_hybrid_fiber_metal_laminates.pdf
--- a/articles/secondary/Inelastic_impacts_for_composite_materials.pdf
+++ b/articles/secondary/Inelastic_impacts_for_composite_materials.pdf
--- a/articles/secondary/Layerwise_Analysis_VEM.pdf
+++ b/articles/secondary/Layerwise_Analysis_VEM.pdf
--- a/articles/secondary/PCLD_SotA.pdf
+++ b/articles/secondary/PCLD_SotA.pdf
--- a/articles/secondary/Real_Physics_of_Machine_Vibration.pdf
+++ b/articles/secondary/Real_Physics_of_Machine_Vibration.pdf
--- a/read/Analysis_of_Laminated_Composites_Subjected_to_Impact.pdf
+++ b/read/Analysis_of_Laminated_Composites_Subjected_to_Impact.pdf
--- a/read/Analysis_of_the_compressible_neo-Hookean_model.pdf
+++ b/read/Analysis_of_the_compressible_neo-Hookean_model.pdf
--- a/read/Experimental_investigation_of_the_dissipation_of_a_viscoelastic_inserted_layer_with_perforations.pdf
+++ b/read/Experimental_investigation_of_the_dissipation_of_a_viscoelastic_inserted_layer_with_perforations.pdf
--- a/read/Optimization_of_composite_laminate_with_viscoelastic_layer.pdf
+++ b/read/Optimization_of_composite_laminate_with_viscoelastic_layer.pdf
--- a/read/Viscoelastic_damping_design.pdf
+++ b/read/Viscoelastic_damping_design.pdf
--- a/organigrames/First
+++ b/organigrames/First
@ -0,0 +1,173 @@
+---
+excalidraw-plugin: parsed
+tags:
+  - excalidraw
+  - archive
+---
+==⚠  Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
+
+# Excalidraw Data
+## Text Elements
+study of shocks 
+to a carbon-epoxy plate with 
+an inserted viscoelastic layer ^27UZMz0J
+
+inelastic collisions ^I9y5xW57
+
+inelastic impacts to
+composite materials
+(naval context) ^a6Zsyp5G
+
+impact models for
+composite structures ^JtNEDx2B
+
+passive constrained layer damping ^V8vHzeG4
+
+viscoelasticity ^RfgLXN72
+
+model for impact on 
+fiber metal laminate 
+with a viscoelastic layer ^6hgiwXJq
+
+impact analysis of
+laminated composite plates ^n1hf1yIu
+
+finite element modeling of impact 
+on laminated composite plates
+(ABAQUS) ^KHykGchi
+
+hard impact on 
+laminated composite
+(recent) ^pQjM5Y0t
+
+study of shocks ^tcohMC3g
+
+## Element Links
+27UZMz0J: https://sci-hub.se/10.1080/15376494.2021.1882626
+
+a6Zsyp5G: https://sci-hub.se/https://doi.org/10.1016/0263-8223(90)90025-A
+
+JtNEDx2B: https://sci-hub.se/https://doi.org/10.1016/S0263-8223(00)00138-0
+
+V8vHzeG4: https://iopscience.iop.org/article/10.1088/1757-899X/653/1/012036/pdf
+
+6hgiwXJq: https://sci-hub.se/https://doi.org/10.1016/j.ijmecsci.2021.106298
+
+n1hf1yIu: https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=6fc8e48508ef0e5929372f19a8b12ec23a04f607
+
+KHykGchi: https://sci-hub.se/https://doi.org/10.1016/j.compstruct.2010.10.003
+
+pQjM5Y0t: https://sci-hub.se/https://link.springer.com/chapter/10.1007/978-3-030-66717-7_19
+
+%%
+## Drawing
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+
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+```
+%%
--- a/organigrames/Kirchoff's
+++ b/organigrames/Kirchoff's
@ -0,0 +1,145 @@
+---
+
+excalidraw-plugin: parsed
+tags: [excalidraw]
+
+---
+==⚠  Switch to EXCALIDRAW VIEW in the MORE OPTIONS menu of this document. ⚠== You can decompress Drawing data with the command palette: 'Decompress current Excalidraw file'. For more info check in plugin settings under 'Saving'
+
+
+# Excalidraw Data
+## Text Elements
+x ^nC08p2Ha
+
+z ^b0bUYAoW
+
+A ^cNzsewAD
+
+A' ^FAPf2i6B
+
+A ^1UqNmzTk
+
+A' ^IkWnryBa
+
+geometric midplane ^4ETCitlj
+
+(a) Undeformed ^YxHRA4dE
+
+(b) Deformed ^UMONNFg8
+
+%%
+## Drawing
+```compressed-json
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+
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+
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+
+tAQ8vdPOFk//mLHsX2KvyJy/ArGzNKNwIiWtVPzpGGcMwEwPPjaAC3IWLd+KYvggPm7PLh2VlsYC/AXkomFQ+AuvtVw+qSwmjkPFqEZFSI2hTsH1NyWIjUuxX+sel23T5vojpgq8qm2ygyI0hd8ODSEibLaMIQ5hRzO3ASwRjwkahbLMjc1GNjVD8YBeOYT3GxetGpFfujV+ft2m55l9ecHnQzMqgmzJAdwpViYDmF0ypITc+iDQZl1D4lkvES4V
+
+a+kXWs4VaVSsTjHEE4p4V+sB1+1P/n4vxxrNvC49fPsS7ubj1gN48NJHACsR1gcAOAPCEESjNoAUYTIIh2XT1AGAhAe5p9JFMcNjgWN7G6iGuYiA7kdwA4FGiKU1sIplh/G+zCJvo3Nzop5sWGYpvZBCbGQBAleRz3I3sADNqAEzeJvo6KTeN6oJTYyDwhi0bNwoPzYJtE2YsOO4BeLcFv6AU0eQgvfTYFuM2ibCBYQz1LWPk2VbXNtWxLMtPs3O
+
+b3N2Vv6fGli2ObOt7m9Dfkquakcst1WxkHdH3rt9hu3GxbYlsZAXYLwKxgwlxvMBsANQWEEXTfokJauKVlqN1FmtZREoAdk0PgCDmqgv4PMXUM0rcuNDtM4JNgAYBHkMACAchFQi8srya4dU9t3WxkClulSp2ywXG26BIAWm9myN2u/nQOBqwxWYtpuz8DYArB3RuATQMEC+HKxjWW5g7RAAfAmhiIpAZQM6A2OHy+88wOe9QHZ7xBtjjoSQsoDr
+
+BVA/qU93ADPc6CL2FYXQXgHvaXsr31Cpd4W5vAVu0FOA3MngkVMyCSFTIxrUDGnCyC93+74J1M3NKICt3UAQFyAKawRt2sbZNacQhEmAcIAz7dgWNQDWYBPBTWvwLuwgB7t93Jl6wAGoQEYAvAs7+AHO1ZjCDBAMHpqX4mLGYL6BvbmJCZQPckrohkIGDrBzg/1japwA4MTWDCHCCAw38PYIAA==
+```
+%%
--- a/organigrames/old.excalidraw
+++ b/organigrames/old.excalidraw
--- a/plan.md
+++ b/plan.md
@ -0,0 +1,17 @@
+#organisation
+
+Part 1: Dynamic response of bridged carbon-epoxy laminates with viscoelastic film (since 2017)
+
+1. Literature review on carbon-epoxy laminates
+2. Study of viscoelastic properties and dynamic mechanical analysis (DMA)
+3. Research on bridging techniques in composite laminates
+4. Analysis of recent developments in viscoelastic film integration
+5. Review of dynamic response studies on similar composite structures
+
+Part 2: Impact studies on bridged carbon-epoxy laminates with viscoelastic film
+
+1. Literature review on impact testing methods for composites
+2. Analysis of low-velocity impact studies on carbon-epoxy laminates
+3. Research on high strain rate behavior of advanced composites
+4. Study of impact effects on viscoelastic properties
+5. Investigation of potential impact testing methodologies for your specific material
--- a/ressources/Accelerance.md
+++ b/ressources/Accelerance.md
@ -1,2 +1,32 @@
 Accelerance is a measure used in mechanical systems that relates acceleration to applied force.

+# Introduction
+([[Secondary articles descriptions#Machine Vibration|source]])
+
+In a dynamic world, $F = mr\omega^2$. The mass and stiffness are not constant anymore and we cannot continue to use Newtonian physics ($F=ma$) and Hooke's law ($F=kx$).
+
+To preserve the linearity of Newton's $2^{nd}$ law a dynamic mass is defined : 
+$m(\omega)$.
+The reciprocal of dynamic mass is accelerance, and is also a function of frequency : Accelerance $= \frac{1}{m(\omega)} = \frac{a(\omega)}{F(\omega)}$
+
+**Symmetry is bad practice because it support resonant modes**
+
+Force is a wave that travels at the speed of sound.
+
+# Formalisation
+([web source](https://eng.libretexts.org/Bookshelves/Electrical_Engineering/Signal_Processing_and_Modeling/Introduction_to_Linear_Time-Invariant_Dynamic_Systems_for_Students_of_Engineering_(Hallauer)/10%3A_Second_Order_Systems/10.05%3A_Common_Frequency-Response_Functions))
+
+We define the dimensionless excitation frequency ratio, the excitation frequency relative to the system undamped natural frequency :
+$$\beta \equiv \frac{\omega}{\omega_{n}}\tag{1}$$
+And we define :
+$$\omega_{n}=\sqrt{\frac{k}{m}}, \quad \zeta \equiv \frac{c}{2 m \omega_{n}}=\frac{c}{2 \sqrt{m k}} \equiv \frac{c}{c_{c}}, \quad u(t) \equiv \frac{1}{k} f_{x}(t)$$
+
+For an $m-c-k$ system, from Laplace transformation of the ODE (*ordinary differential equation*) $m\ddot{x}+c\dot{x}+kx = f_x(t)$, and with use of notation defined in Equations $(1)$ and $(2)$, the equation for complex mechanical admittance is :
+
+$$\left\{\frac{L[x(t)]}{L\left[f_{x}(t)\right]}\right\}_{s=j \omega}=\frac{1}{\left(k-\omega^{2} m\right)+j \omega c}=\frac{1}{k}\left[\frac{1}{\left(1-\beta^{2}\right)+j 2 \zeta \beta}\right]\tag{3}$$
+
+(The inverse being *dynamic stiffness*)
+
+For _accelerance_ (also known as _inertance_), the subject variable is an acceleration, and the reference variable is an action. Since $L[\ddot{x}(t)]=s^{2} \times L[x(t)]$, the accelerance of an $m-c-k$ system, from Equation $(3)$, is
+$$\left\{\frac{L[\ddot{x}(t)]}{L\left[f_{x}(t)\right]}\right\}_{s=j\omega}=\frac{(j\omega)^{2}}{\left(k-\omega^{2}m\right)+j\omega c}=\frac{1}{m}\left[\frac{-\beta^{2}}{\left(1-\beta^{2}\right)+j2\zeta\beta}\right]\tag{4}$$
+(The inverse of accelerance is called _apparent mass_)
--- a/ressources/Co-curing.md
+++ b/ressources/Co-curing.md
@ -0,0 +1,3 @@
+([[Secondary articles descriptions#Optimization method of composite laminates with a viscoelastic layer|source]])
+
+Co-curing means the viscoelastic material within the composite laminate undergo the temperature and pressure cycle needed to cure the composite material.
--- a/ressources/Composite
+++ b/ressources/Composite
@ -16,4 +16,8 @@ Those theories describe kinetically each layer. They can be used for very thick
 ---
 ## Zig-Zag

+[[Layerwise Theories]] with shear continuities between layers to keep the same number of degrees of freedom as the number of layers is increased. (so less computationally expensive)
+
+It captures the "zig-zag" pattern of displacements through the thickness that occurs due to different layer stiffness.
+
 (see [[Zig-Zag Theories]])
--- a/ressources/Continuum
+++ b/ressources/Continuum
@ -1,4 +1,4 @@
-see [[videos]] for references
+([[Videos descriptions#continuum mechanics|video source]])

 The strain tensor is the symmetric part of the gradient of the displacement field vector.
 $$\varepsilon = \frac{\nabla{U} +\nabla{U}^T}{2}$$
--- a/ressources/Equivalent
+++ b/ressources/Equivalent
@ -1,16 +1,27 @@
 To [[Composite laminate models|model a composite laminate]] there are a few options, the most important are the equivalent single layer and the [[Layerwise Theories|layerwise]].

-Those theories works by computing the homogenized material properties, and solving only at the mid plane. They are useful for global response for thin laminates and are computationnally inexpensive.
+Those theories works by computing the homogenized material properties, and solving only at the mid plane. 
+The laminate is therefore modeled as an equivalent single anisotropic layer. They are useful for global response for thin laminates and are computationnally inexpensive.
+-> most popular : FSDT

 *They have issue with layers of different properties.*

-#### Classical Laminate Theory (CLT), hypothesis :
-The normal line to the median plane of the plate before deformation stays normal to the plane after deformation.
+#### Classical Laminate Theory (CLT) :
+Hypothesis : The normal line to the median plane of the plate before deformation stays normal to the plane after deformation.
 -> lack of transverse shear
+(see [[Kirchhoff's hypothesis]])

-#### First-order Shear Deformation Theory (FSDT), hypothesis :
-The normal line to the median plane of the plate stays straight after deformation but it is not normal to the middle plane, the shear constraint stays constant along the thickness of the plate.
+(extension of the **Kirchhoff-Love** plate theory)
+
+#### First-order Shear Deformation Theory (FSDT) :
+Hypothesis : The normal line to the median plane of the plate stays straight after deformation but it is not normal to the middle plane, the shear constraint stays constant along the thickness of the plate.
+
+Only two assumptions remains :
+- *straight lines normal to the mid-surface remain straight after deformation*
+- *the thickness of the plate does not change during a deformation.*

 #### High-order Shear Deformation theory (HSDT) :
 More complex variation of the shear constraint along the thickness of the plate, but more computationally expensive.

+ It is assumed that the displacements are of higher order polynomial form and are $C^1$ continuous through the thickness. This allows for non-linear variation of displacements, strain and stresses through the thickness.
+([[Secondary articles descriptions#First order Zig-Zag plate Theory|source]])
--- a/ressources/Failure
+++ b/ressources/Failure
@ -0,0 +1,20 @@
+[[Videos descriptions#Failure theories|video source]]
+
+The hydrostatic stress is the average stress on all axis, it relates to the stress that want to change the volume like under water pressure (hence hydrostatic), by contrast to the deviatoric stress that act on the shape of the element.
+### For ductile materials :
+
+The hydrostatic stress has no effect on failure.
+
+Tresca : easier to apply, more conservative
+*hexagonal prism in stress space*
+
+von Mises : better agreement with experimental data
+*cylinder in stress space*
+
+### For brittle materials :
+
+Compressive strength >>> Tensile strength
+
+The hydrostatic stress affects failure.
+
+Coulomb-Mohr : general case of Tresca
--- a/ressources/Finite
+++ b/ressources/Finite
@ -2,13 +2,15 @@ The finite element method is a mathematical method to be able to computationally

 The core of the method is to discretise the problem, because computer cannot solve the problem analytically.

-[weak formulation](https://www.youtube.com/watch?v=xZpESocdvn4) *(30min)*
+## Weak formulation
+([[Videos descriptions#Weak Formulation|video source]])

 The weak formulation is the formulation of the differential equation so that it becomes solvable using the finite elements method.

 This video shows how the weak formulation is derived from the initial problem, and its use.

-[finite element method](https://www.youtube.com/watch?v=1wSE6iQiScg) *(40min)*
+## Mathematical Finite element method base
+([[Videos descriptions#Mathematical Finite element method base|video source]])

 The finite element method is a mathematical method to be able to computationally solve a differential equation.

--- a/ressources/Hertz
+++ b/ressources/Hertz
@ -1,4 +1,4 @@
-[ref](https://www.sciencedirect.com/topics/engineering/hertz-theory)
+([web source](https://www.sciencedirect.com/topics/engineering/hertz-theory))

 describes the contact between two elastic solids

--- a/ressources/Hysteresis.md
+++ b/ressources/Hysteresis.md
@ -1,3 +1,3 @@
-[ref](https://en.wikipedia.org/wiki/Hysteresis)
+[web source](https://en.wikipedia.org/wiki/Hysteresis)

 the dependence of the state of a system on its history.
--- a/ressources/Impact-Shock-Collision.md
+++ b/ressources/Impact-Shock-Collision.md
@ -1,11 +1,16 @@
-# collision
+# Collision

 A collision is a broad term that describes any event where two or more bodies exert forces on each other for a relatively short time.

-# impact 
+The [[Hertz Law]] describe the contact between two elastic solids.
+
+There is also [[Inelastic Collisions]].
+# Impact 

 An impact is a type of collision with a high force over a short duration.

-# shock
+(see [[Impact Models]])
+
+# Shock

 A shock is a transient high force event with clearly defined parameters for testing purposes. Can be an impact, an other type of collision, an explosion, etc...
--- a/ressources/Inelastic
+++ b/ressources/Inelastic
@ -0,0 +1,5 @@
+During **inelastic collisions**, masses are added together and
+momentum are conserved. This can be used for slamming or other wave-like loading.
+
+This model is reasonable when the impactor is relatively soft and the mass 
+of impactor is larger than the mass of the node being impacted.
--- a/ressources/Kirchhoff's
+++ b/ressources/Kirchhoff's
@ -0,0 +1,7 @@
+([web source](https://www.sciencedirect.com/topics/engineering/kirchhoff-hypothesis))
+
+- *straight lines normal to the mid-surface remain straight after deformation*
+- *straight lines normal to the mid-surface remain normal to the mid-surface after deformation*
+- *the thickness of the plate does not change during a deformation.*
+
+![[Kirchoff's Hypothesis Diagram]]
--- a/ressources/Layerwise
+++ b/ressources/Layerwise
@ -2,9 +2,12 @@ To [[Composite laminate models|model a composite laminate]] there are a few opti

 Those theories describe kinetically each layer. They can be used for very thick laminate, and useful to compute delamination. They predicts correct inter-laminar stresses and there is no need of shear correction factor.

-## Stiffness
+There is a unique displacement field per layer + interlaminar continuity of displacements (and sometimes of transverse stresses).
+-> very computationally expensive, since the number of degrees of freedom increase proportionally with the number of layers.
+([[Secondary articles descriptions#First order Zig-Zag plate Theory|source]])

-[course](https://www.youtube.com/watch?v=j3rvtgqrGsQ) *(1h30)*
+## Stiffness
+([[Videos descriptions#Composite materials course|video source]])

 When pulling on the material, strain is the same for every ply, but stress is not.

--- a/ressources/Neo
+++ b/ressources/Neo
@ -1,10 +1,12 @@
-hook law for large deformations
-[ref](https://en.wikiversity.org/wiki/Advanced_elasticity/Neo-Hookean_material)
+([web source](https://en.wikiversity.org/wiki/Advanced_elasticity/Neo-Hookean_material))

-neo-Hookean material ~ hyperelastic material
+Hook law for large deformations

-no linear relationship between stress and strain
+Neo-Hookean material ~ hyperelastic material

+No linear relationship between stress and strain

-even better : [mooney-rivin solid](https://en.wikipedia.org/wiki/Mooney%E2%80%93Rivlin_solid)
+---
+
+Even better : [mooney-rivin solid](https://en.wikipedia.org/wiki/Mooney%E2%80%93Rivlin_solid)

--- a/ressources/Newmark
+++ b/ressources/Newmark
@ -1,3 +1,3 @@
-[ref](https://www.sciencedirect.com/topics/engineering/newmark-method)
+([web source](https://www.sciencedirect.com/topics/engineering/newmark-method))   #archive

 A method of numerical integration used to solve certain differential equations.
--- a/ressources/PCLD.md
+++ b/ressources/PCLD.md
@ -1,10 +1,9 @@
+([[Secondary articles descriptions#Passive Constrained Layer Damping, SotA|source]])
+
 *Passive Constrained Layer Damping*

-[[passive constrained layer damping.pdf|ref]]
+[[Viscoelasticity|Viscoelastic materials (VEM)]] dissipate energy under a transient deformation. Used in a form of a layer that is either freely attached (UCLD ie *unconstrained layer damping*) or in a sandwich (CLD/PCLD ie *constrained layer damping/passive constrained layer damping*).

-UCLD : unconstrained, the dampening occurs through compression/traction.
+In most of the analyses, extensional/compressional strains of the viscoelastic layer are not taken into account since the damping comes mostly from the shear strain. However, with a thick layer, compressional damping cannot be neglected.

-CLD : constrained, the dampening occurs through shear, but compressional 
-damping cannot be neglected (especially if thick layer)
-
-Usually done using a [[Viscoelasticity|viscoelastic material]]
+The mathematical models are either [[Finite element method|FE]] or analytical.
--- a/ressources/Viscoelasticity.md
+++ b/ressources/Viscoelasticity.md
@ -11,5 +11,7 @@ its stiffness depends on the strain rate

 A viscoelastic substance dissipates energy when a load is applied, then removed.

-### nota bene
-The properties of a viscoelastic layer change with the frequency of excitation 
+In most of the analyses, extensional/compressional strains of the viscoelastic layer are not taken into account since the damping comes mostly from the shear strain.
+
+### Nota Bene
+The properties of a viscoelastic layer change with the frequency of excitation .
--- a/ressources/Zig-Zag
+++ b/ressources/Zig-Zag
@ -1,12 +1,38 @@
-first-order zig-zag theory (FZZT),
-[ref](https://www.sciencedirect.com/science/article/abs/pii/S026382239900063X)
+*zig-zag in-plane displacement theories*

-allowing for discontinuities in displacement between layers.
- captures the "zig-zag" pattern of displacements through the thickness that occurs due to different layer stiffness.
- 
-The first-order zig-zag theory introduces additional terms to the displacement field assumptions used in classical laminate theory:
+To [[Composite laminate models|model a composite laminate]] there are a few options, the most important are the [[Equivalent Single Layer Theories|equivalent single layer]] and the [[Layerwise Theories|layerwise]]. However there was a need to get theories that were less computationally expensive than the layerwise, and more accurate than the equivalent single layer.

-1. It adds a zig-zag function that allows for slope discontinuities at layer interfaces.
-2. It maintains continuity of transverse stresses between layers.
-3. It satisfies the traction-free boundary conditions on the top and bottom surfaces.
+They are theories which describe the piecewise form of transverse stress (Zig-Zag, ZZ) and displacement fields (Interlaminar Continuity, IC).

+# General Zig-Zag Theories
+([[Secondary articles descriptions#First order Zig-Zag plate Theory|source]])
+
+[[Layerwise Theories]] with shear continuities between layers to keep the same number of degrees of freedom as the number of layers is increased.
+
+It captures the "zig-zag" pattern of displacements through the thickness that occurs due to different layer stiffness.
+
+Improvements of the model consist in keeping it accurate, only needing $C^0$ continuous and 5 degrees of freedom.
+
+# First Order Zig-Zag Theory (FZZT)
+
+In-plane displacements are assumed to be layerwise linear and continuous through the thickness. This allows for slope discontinuities at layer interfaces.
+
+5 degrees of freedom (does not depend on the number of layers) are achieved by using the transverse shear stress continuity at each interface.
+
+This theory is the most accurate for symmetrical laminates.
+
+# Higher Order Zig-Zag Theories (HZZT)
+
+To improve the [[#First Order Zig-Zag Theory (FZZT)|FZZT]], a piecewise linear variation of in-plane displacement is superimposed on a continuous cubic function of the transverse coordinate.
+This allows for better displacement field of unsymmetrical laminates. 
+
+The homogeneous shear traction boundary conditions at the top and bottom surfaces allows us to keep 5 degrees of freedom.
+
+However the main issue is that the transverse deflection degree of freedom $w_0$ is required to be $C^1$ continuous. 
+
+Therefore additional rotational degrees of freedom (gradients of $w_0$) are present -> more than 6 degrees of freedom -> tough to implement in commercial finite element software.
+
+
+# Refined Zig-Zag Theory (RZT) ?
+
+https://rzt.larc.nasa.gov/
--- a/reunions/17-09.md
+++ b/reunions/17-09.md
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+#reunion
 # Objectif principal du mémoire 

 état de l'art post 2020 sur les composite avec couche visco-élastique pontés
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-# optimization method of composite laminates with a viscoelastic layer
-
-[ref](https://d1wqtxts1xzle7.cloudfront.net/33874260/2011-2-libre.pdf?1401929433=&response-content-disposition=inline%3B+filename%3DMulti_objective_Optimization_of_Co_cured.pdf&Expires=1726671246&Signature=X30Tmzd9RIn7nsIGU2Q4ZgeCchtgP~md5owXYAwnVnZj9pZCx1Ck~6owvGcTyWQwCJcm~i3zbXCXioNqPemkodqkkJ3m3mQZJ5yY7FYpc2i86ZUsACau8A-Gr3YNQ0XNFIGO4drqLGq21zz67T-CnsYfUV3LRpvY4wiZ2TWs4Q~ImvfTtlxcDTCCr4JW5abxR75Fi0yiSe6og7qjwdLh8E50qFdcXTvijO6qm9dnpW854ozStXkGkhsq16PzBfIbFLE7yrXc6zzAtUUHF5YpUfZRYl7V2xfu8s51Cvp9-YIJ8gt2v-qm2uQM92DPbZ9J62unLsIog2pr-HUWUxjqDw__&Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA)
-
-This paper develops a method to transform a multi objective (damping and stiffness)
-into a single one, to facilitate optimization.
-
-# experimental investigation of the dissipation of a viscoelastic inserted layer
-
-[ref](https://sci-hub.se/https://journals.sagepub.com/doi/abs/10.1177/1077546319844545)
-
-This paper try to assess the damping qualities of a visco elastic insert. It found that it is very efficient in medium and high frequency ranges.
-
---
---
-
-# model for impact on fiber metal laminate with a viscoelastic layer
-
-[ref](https://doi.org/10.1016/j.ijmecsci.2021.106298)
-
-_can teach about impact on viscoelastic sandwich impact_
-
-Use a specific criterion to quantitatively estimate whether the composite 
-structure is damaged subjected to impact excitation.
-
-Reddy’s high-order shear deformation theory for the viscoelastic layer
-
-
-
---
-
-# Hard and Soft Collisions
-
-[ref](https://www.compadre.org/Physlets/mechanics/illustration8_3.cfm)
-
-A soft collision is an inelastic collision, which means that kinetic energy 
-is not conserved (because internal friction). However, the momentum is still
-conserved.
-
-A perfectly inelastic collision occurs when the two bodies stays together, 
-and the energy is lost by bonding the two bodies.
-
-# inelastic collison for composite materials
-
-[ref](https://doi.org/10.1016/0263-8223(90)90025-A)
-
-Use the finite element model to get the dynamic response.
-
-The structure is considered elastic but the loading is considered
-inelastic.
-
-The isoparametric linear shell element is modified
-to take into account the shear deformation and rotatory inertia.
-
-
-
-inelastic collision : masses added together and
-momentum conserved, used for slamming or other wave-like loading
-
-This model is reasonable when the impactor is relatively soft and the mass 
-of impactor is larger than the mass of the node being impacted.
-
-# finite element modeling of low-velocity impact on laminated composite plates and cylindrical shells
-
-[ref](https://doi.org/10.1016/j.compstruct.2010.10.003)
-
-use of abaqus
-
-examination of the validity of different models
-
-propose a  benchmark method in low-velocity impact modeling of composite structures
-
-# Analysis of Laminated Composites Subjected to Impact (p 243)
-
-[ref](https://link.springer.com/chapter/10.1007/978-3-030-66717-7_19)
-
-very recent paper, propose both theoretical and experimental approaches to
-the analysis of laminated composite response to impact loading
--- a/do.md
+++ b/do.md
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+#organisation
+
 - [x] get used to the college library (download pdf ?)
 - [x] read thesis
 - [x] read articles 58->61
 - [x] find article who reference article 57->61
 - [x] format latex
- [ ] mail Herve for project launching
+- [x] mail Herve for project launching
+- [x] analyse de risques
 - [ ] [get article](https://www.tandfonline.com/doi/abs/10.1080/15376494.2022.2097355)
- [ ] plan
+- [ ] work on [[plan]]
+- [ ] check [[unknown]]
+- [ ] doc revue lancement de projet
+- [ ] gantt
+- [ ] stage (5 candidatures)
 # to read (take notes)
- [ ] [[accelerance.pdf]]
- [ ] [[neo-hookean model analysis.pdf]]
- [ ] [[passive constrained layer damping.pdf]]
- [ ] [[viscoelastic damping design.pdf]]
- [ ] [[zig-zag.pdf]]
- [ ] [[Impact_and_vibration_of_hybrid_fiber_metal_laminates.pdf]]
- [ ] [laminate theory of composite materials](https://link.springer.com/book/10.1007/978-3-031-32975-3)
-
+[[to read]]
+- [x] Machine Vibration
+- [x] Analysis of the compressible neo-Hookean model
+- [x] Historical review of Zig-Zag Theories
+- [x] Layerwise Analysis VEM
+- [x] First order Zig-Zag plate Theory
+- [ ] Viscoelastic damping design
+- [ ] Experiments on dissipation of VEM layer
+- [ ] Optimization method of composite + VEM
+- [ ] Analysis of composites subjected to impact
+- [ ] Model for impact metal fiber laminate + VEM
 # to watch
 - [x] [composite material modeling](https://www.comsol.fr/video/modeling-layered-composite-structures-with-comsol-multiphysics-nov-29-2018)
 - [x] obsidian tutorial

-# to fill (check things to read)
- [ ] [[Accelerance]]
- [ ] [[Zig-Zag Theories]]
+# to fill 
+- [x] Accelerance
+- [x] Zig-Zag Theories
+- [x] PCLD
+- [x] Viscoelasticity
 - [ ] [[Neo Hookean Behavior Law]]
- [ ] [[PCLD]]
- [ ] [[Viscoelasticity]]
-
-## bonus
-
-[naval impact study (without viscoelastic layer)](https://sci-hub.se/https://doi.org/10.1016/0263-8223(90)90025-A)
--- a/read.md
+++ b/read.md
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+#organisation
+
+## Viscoelastic damping design
+*2023*
+[online ref](https://www.sciencedirect.com/science/article/abs/pii/S0022460X23001529)
+[[Viscoelastic_damping_design.pdf|local ref]]
+
+## Experimental investigation of the dissipation of a viscoelastic inserted layer with perforations
+*2019*
+[online ref](https://journals.sagepub.com/doi/abs/10.1177/1077546319844545)
+[[Experimental_investigation_of_the_dissipation_of_a_viscoelastic_inserted_layer_with_perforations.pdf|local ref]]
+
+This paper try to assess the damping qualities of a visco elastic insert. It found that it is very efficient in medium and high frequency ranges.
+
+**perforations ~ bridges ??**
+
+## Analysis of Laminated Composites Subjected to Impact (p 243)
+*2021*
+[online ref](https://link.springer.com/chapter/10.1007/978-3-030-66717-7_19)
+[[Analysis_of_Laminated_Composites_Subjected_to_Impact.pdf|local ref]]
+
+Propose both theoretical and experimental approaches to the analysis of laminated composite response to impact loading.
+
+## Model for impact on fiber metal laminate with a viscoelastic layer
+*2021*
+[online ref](https://doi.org/10.1016/j.ijmecsci.2021.106298)
+[[Impact_and_vibration_of_hybrid_fiber_metal_laminates.pdf|local ref]]
+
+_Can teach about impact on [[Viscoelasticity|viscoelastic]] sandwich impact._
+
+Use a specific criterion to quantitatively estimate whether the composite 
+structure is damaged subjected to impact excitation.
+
+Reddy’s [[Equivalent Single Layer Theories|high-order shear deformation theory]] for the [[Viscoelasticity|viscoelastic]] layer
+# bonus
+
+[naval impact study (without viscoelastic layer)](https://sci-hub.se/https://doi.org/10.1016/0263-8223(90)90025-A)
--- a/unknown.md
+++ b/unknown.md
@ -1,9 +1,16 @@
+#organisation
+
 ### to learn

-classical plate theory/classical shell theory (Kirchhoff hypothesis)
-finite elements and alternative : the immersion method, the method of R-functions
-accélérance
-Zig-Zag model theory
+finite elements and alternative : 
+- the immersion method, 
+- [the method of R-functions](https://asmedigitalcollection.asme.org/appliedmechanicsreviews/article-abstract/48/4/151/401230/R-Functions-in-Boundary-Value-Problems-in)
+Zig-Zag Theories 
+
+[[Secondary articles descriptions#Layerwise Analyses VEM]]
+the principle of virtual displacement (PVD)
+complex eigenvalue problems
+modal strain energy technique

 ### questions