This document discusses models for simulating viscoelastic materials. It derives the Maxwell and Kelvin equations for viscoelasticity by modeling materials as combinations of springs and dampers. The Maxwell model treats materials as a spring and damper in series, while the Kelvin model uses a spring and damper in parallel. The document shows that while both models can describe viscoelastic behavior, the Kelvin model is more accurate because it does not require assumptions about small deformations over short time periods like the Maxwell model. Creep and relaxation behaviors are also examined using the derived Maxwell and Kelvin equations. The document concludes the Kelvin model better matches real viscoelastic material behavior in fast deformations.
NUMERICAL SIMULATION OF WAVES AND FRONTSberezovski
A. Berezovski, M. Berezovski, J. Engelbrecht, G.A. Maugin
Numerical simulation of waves and fronts in inhomogeneous solids,
in: Multi-Phase and Multi-Component Materials Under Dynamic Loading,
W.K. Nowacki and Han Zhao (Eds.) Inst. Fund. Technol. Res.
Warsaw, (EMMC-10 Conference proceedings), 2007, pp. 71-80.
Viscoelasticity is the property of materials that exhibit both viscous and elastic characteristics when undergoing deformation. Viscous materials, like water, resist shear flow and strain linearly with time when a stress is applied. Elastic materials strain when stretched and immediately return to their original state once the stress is removed.
What is viscoelastic damping?
What are the classical models?
What is creep?
What is Relaxation?
What is complex modulus?
#WikiCourses
http://wikicourses.wikispaces.com/Topic01+Viscoelastic+Materials
NUMERICAL SIMULATION OF WAVES AND FRONTSberezovski
A. Berezovski, M. Berezovski, J. Engelbrecht, G.A. Maugin
Numerical simulation of waves and fronts in inhomogeneous solids,
in: Multi-Phase and Multi-Component Materials Under Dynamic Loading,
W.K. Nowacki and Han Zhao (Eds.) Inst. Fund. Technol. Res.
Warsaw, (EMMC-10 Conference proceedings), 2007, pp. 71-80.
Viscoelasticity is the property of materials that exhibit both viscous and elastic characteristics when undergoing deformation. Viscous materials, like water, resist shear flow and strain linearly with time when a stress is applied. Elastic materials strain when stretched and immediately return to their original state once the stress is removed.
What is viscoelastic damping?
What are the classical models?
What is creep?
What is Relaxation?
What is complex modulus?
#WikiCourses
http://wikicourses.wikispaces.com/Topic01+Viscoelastic+Materials
Application of Schrodinger Equation to particle in one Dimensional Box: Energ...limbraj Ravangave
It is very interesting application of Schrodinger equation.. we find the solution to Schrodinger equation for particle moving under some type of interaction. the motion of particle in one dimensional box is to and fro motion in uniform potential. the problem is explore in easy way and better for understanding to the students.
visit our blog
https://elearnerphysics.blogspot.com/
Derivation of Maxwell's Equation for Diffusion Current and Klein-Gordon Equat...iosrjce
IOSR Journal of Applied Physics (IOSR-JAP) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of physics and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in applied physics. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Strong Nuclear Force and Quantum Vacuum as Gravity (FUNDAMENTAL TENSOR)SergioPrezFelipe
Publication at ccsenet. Gravity explained by a new theory, ‘Superconducting String Theory (SST)’, completely opposite from current field emission based and inspired on originals string theories. Strengths are decomposed to make strings behave as one-dimensional structure with universe acting as a superconductor where resistance is near 0 and the matter moves inside. Strong nuclear force, with an attraction of 10.000 Newtons is which makes space to curve, generating acceleration, more matter more acceleration. Electromagnetic moves in 8 decimals, gravity is moved to more than 30 decimals to work as a superconductor.
The electromagnetism and gravity are unified where, while the first originates from the electric charges in a
linear exposition, the second emerges in a quadratic manifestation of it, making the gravity always
attractive. This helps identify the inner structures of all the primary particles—quarks, leptons, and the
{Z,W} bosons as well as the 125 GeV state without the Higgs mechanism—to predict their masses by one
integer parameter formulas in close agreement with the observed values. This in turn enables
determination of the mechanism for building their ground and excited compound states. The consequences
are far-reaching and embracing, for examples, from identifying dark matter and energy that makes the
explanation of masses in the Universe 100 % inclusive, to solving the hackneyed yet equally elusive puzzle
of why the inertial mass is equal to the gravitational mass.
Derivation of Schrodinger and Einstein Energy Equations from Maxwell's Electr...iosrjce
IOSR Journal of Applied Physics (IOSR-JAP) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of physics and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in applied physics. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Superconductivity and Spin Density Wave (SDW) in NaFe1-xCoxAsEditor IJCATR
A model is presented utilizing a Hamiltonian with equal spin singlet and triplet pairings based on quantum field theory and
green function formalism, to show the correlation between the superconducting and spin density wave (SDW) order parameters. The
model exhibits a distinct possibility of the coexistence of superconductivity and long-range magnetic phase, which are two usually
incompatible cooperative phenomena. The work is motivated by the recent experimental evidences on high-TC superconductivity in
the FeAs-based superconductors. The theoretical results are then applied to show the coexistence of superconductivity and spin density
wave (SDW) in NaFe1-xCoxAs.
درس استاتیک یکی از دروس پایه ای رشته مکانیک و سایر رشته های مرتبط هست. پایه و اساس این درس قوانین نیوتن است که به ما کمک می کند مسائل را با استفاده از ابزارهایی که در این درس آشنا خواهیم شد، تحلیل کنیم. اجسام مورد بررسی در استاتیک صلب و بدون حرکت در نظر گرفته می شود. از مهمترین مباحث این درس، بحث تعادل می باشد که ما در صل اول مورد بررسی قرار خواهیم داد که قوی ترین ابزار ما برای تحلیل سازه ها می باشد.
سرفصل هایی که در این آموزش به آن پرداخته شده است:
فصل اول: روابط تعادل
فصل دوم: خرپاها
فصل سوم: تیرها
فصل چهارم: کابل ها
...
برای توضیحات بیشتر و تهیه این آموزش لطفا به لینک زیر مراجعه بفرمائید:
http://faradars.org/courses/fvmec94053
Application of Schrodinger Equation to particle in one Dimensional Box: Energ...limbraj Ravangave
It is very interesting application of Schrodinger equation.. we find the solution to Schrodinger equation for particle moving under some type of interaction. the motion of particle in one dimensional box is to and fro motion in uniform potential. the problem is explore in easy way and better for understanding to the students.
visit our blog
https://elearnerphysics.blogspot.com/
Derivation of Maxwell's Equation for Diffusion Current and Klein-Gordon Equat...iosrjce
IOSR Journal of Applied Physics (IOSR-JAP) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of physics and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in applied physics. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Strong Nuclear Force and Quantum Vacuum as Gravity (FUNDAMENTAL TENSOR)SergioPrezFelipe
Publication at ccsenet. Gravity explained by a new theory, ‘Superconducting String Theory (SST)’, completely opposite from current field emission based and inspired on originals string theories. Strengths are decomposed to make strings behave as one-dimensional structure with universe acting as a superconductor where resistance is near 0 and the matter moves inside. Strong nuclear force, with an attraction of 10.000 Newtons is which makes space to curve, generating acceleration, more matter more acceleration. Electromagnetic moves in 8 decimals, gravity is moved to more than 30 decimals to work as a superconductor.
The electromagnetism and gravity are unified where, while the first originates from the electric charges in a
linear exposition, the second emerges in a quadratic manifestation of it, making the gravity always
attractive. This helps identify the inner structures of all the primary particles—quarks, leptons, and the
{Z,W} bosons as well as the 125 GeV state without the Higgs mechanism—to predict their masses by one
integer parameter formulas in close agreement with the observed values. This in turn enables
determination of the mechanism for building their ground and excited compound states. The consequences
are far-reaching and embracing, for examples, from identifying dark matter and energy that makes the
explanation of masses in the Universe 100 % inclusive, to solving the hackneyed yet equally elusive puzzle
of why the inertial mass is equal to the gravitational mass.
Derivation of Schrodinger and Einstein Energy Equations from Maxwell's Electr...iosrjce
IOSR Journal of Applied Physics (IOSR-JAP) is a double blind peer reviewed International Journal that provides rapid publication (within a month) of articles in all areas of physics and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in applied physics. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Superconductivity and Spin Density Wave (SDW) in NaFe1-xCoxAsEditor IJCATR
A model is presented utilizing a Hamiltonian with equal spin singlet and triplet pairings based on quantum field theory and
green function formalism, to show the correlation between the superconducting and spin density wave (SDW) order parameters. The
model exhibits a distinct possibility of the coexistence of superconductivity and long-range magnetic phase, which are two usually
incompatible cooperative phenomena. The work is motivated by the recent experimental evidences on high-TC superconductivity in
the FeAs-based superconductors. The theoretical results are then applied to show the coexistence of superconductivity and spin density
wave (SDW) in NaFe1-xCoxAs.
درس استاتیک یکی از دروس پایه ای رشته مکانیک و سایر رشته های مرتبط هست. پایه و اساس این درس قوانین نیوتن است که به ما کمک می کند مسائل را با استفاده از ابزارهایی که در این درس آشنا خواهیم شد، تحلیل کنیم. اجسام مورد بررسی در استاتیک صلب و بدون حرکت در نظر گرفته می شود. از مهمترین مباحث این درس، بحث تعادل می باشد که ما در صل اول مورد بررسی قرار خواهیم داد که قوی ترین ابزار ما برای تحلیل سازه ها می باشد.
سرفصل هایی که در این آموزش به آن پرداخته شده است:
فصل اول: روابط تعادل
فصل دوم: خرپاها
فصل سوم: تیرها
فصل چهارم: کابل ها
...
برای توضیحات بیشتر و تهیه این آموزش لطفا به لینک زیر مراجعه بفرمائید:
http://faradars.org/courses/fvmec94053
Business with Impact – BEAM Summary Report of Future Watch Session, Team Finl...Team Finland Future Watch
Achieving Business Impact in Sub-Saharan Africa workshop brought together specialists from business, public, non-governmental and research organizations to discuss about the future business and collaboration opportunities in Sub-Saharan Africa. Discussion was organized around nine themes: urbanization, water management, education, financial services, collaboration in Africa, mobile Africa, energy, health and adding higher local value.
The way in which material is transferred from the tip of the consumable electrode into the weld pool has a significant influence on the overall performance of GMAW.
it affects process stability, spatter generation, weld quality and the positional capabilities of the process.
Phenomenological studies of the mode of metal transfer have been carried out using high-speed cine or stroboscopic cine and video techniques.
The ICES Symposium “Effects of fishing on benthic fauna, habitat and ecosystem function” took place in Tromsø, Norway from 16-19th June 2014.
Abstract:
Beam trawling causes physical disruption to the seafloor through physical contact of the gear components on the sediment and the resuspension of sediment into the water column in the turbulent wake of the gear. Recently Dutch beam trawlers have replaced tickler chains by electrodes as alternative stimulation for catching flatfish. It is claimed that benthic impacts are reduced. Here we report on trials in a medium sand fishing ground to compare the physical impact of a conventional 4m commercial tickler chain beam trawl with that of the new commercial “Delmeco” pulse trawl. We use a Kongsberg EM2040 multibeam echo sounder (MBES) to measure the extent to which the beam trawls modify the topography of the substrate and a particle size analyser (LISST 100X) to measure the concentration and particle size distribution of the sediment mobilized into the water column. MBES measurements reveal that the disturbed sediment in the trawl track was on average located at a centimetre deeper after trawling of the conventional beam trawl than after pulse trawling. Particle size distributions of the sediment plumes were measured at 25m, 45m and 65m behind the gear and did not reveal any differences in concentrations between the two trawls. Whereas the empirical data serve comparative purposes, their lack of predictive capacity limits extrapolation to fleet level. Finite element (FE) models have shown to overcome this for otter trawls by predicting the penetration depth and sediment displacement associated with each gear component in different sediment types. In this study, FE models were developed for the conventional tickler chain beam trawl and the pulse trawl. Predictions were validated by results obtained during sea trials. As such, this study attempts to provide the basis for future predictions of physical impacts of beam trawling and its technical advances on a larger spatial scale.
My name is Paulin O. I am associated with solidworksassignmenthelp.com for the past 10 years and have been helping the engineering students with their assignments I have a Masters in mechanical Engineering from Cornell University, USA.
Maxwell equations without a polarization field august 15 1 2020Bob Eisenberg
Electrodynamics is almost always written using a polarization vector field to describe the response of matter to an electric field, or more specifically, to describe the change in distribution of charges as an electric field is applied or changed. This approach does not allow unique specification of a polarization field from measurements of the electric and magnetic fields and electrical current.
Many polarization fields will produce the same electric and magnetic fields, and current, because only the divergence of the polarization enters Maxwell’s first equation, relating charge and electric field. The curl of any function can be added to a polarization field without changing the electric field at all. The divergence of the curl is always zero. Models of structures that produce polarization cannot be uniquely determined from electrical measurements for the same reason. Models must describe charge distribution not just distribution of polarization to be unique.
I propose a different approach, using a different paradigm to describe field dependent charge, i.e., to describe the phenomena of polarization. I propose an operational definition of polarization that has worked well in biophysics where a field dependent, time dependent polarization provides the gating current that makes neuronal sodium and potassium channels respond to voltage. The operational definition has been applied successfully to experiments for nearly fifty years. Estimates of polarization have been computed from simulations, models, and theories using this definition and they fit experimental data quite well.
I propose that the same operational definition be used to define polarization charge in experiments, models, computations, theories, and simulations of other systems. Charge movement needs to be computed from a combination of electrodynamics and mechanics because ‘everything interacts with everything else’.
The classical polarization field need not enter into that treatment at all.
Quantum-Gravity Thermodynamics, Incorporating the Theory of Exactly Soluble Active Stochastic Processes, with Applications
by Daley, K.
Published in IJTP in 2009. http://adsabs.harvard.edu/abs/2009IJTP..tmp...67D
VIBRATION ANALYSIS OF AIRFOIL MODEL WITH NONLINEAR HEREDITARY DEFORMABLE SUSP...ijmech
In the present work, the vibratory behavior of an airfoil is discussed. The airfoil is considered as twodegree-of-freedom structure with hereditary deformable suspensions. The weak singular integrodifferential equation is numerically solved using numerical integration method. Finally, numerical results for the creep response and resonance behavior of the viscoelastic materials were analyzed. These results are obtained for the perfect elastic and viscoelastic suspensions with the nonlinearity feature. As demonstrated in the airfoil model, the equation of motion with hereditary and nonlinear terms successfully illustrate realistic vibratory characteristics of two-dimensional viscoelastic problems.
1. Date: 22/08/2011
Report Number: 2
Title: self‐healing structures
Keywords: Viscoelastic mechanical models, Maxwell bar, Kelvin bar
Elements in Continuum Mechanics
For simulation the part of elasticity in a material we use a linear spring with constant of Yang's
modulus.
Damper is an element in modeling of viscosity of a material that works with rate of strain.
The last element is friction element that implies in modeling of plasticity of a material, and if stress
amount increases more than yield stress it will affect.
Viscolelasticity
In [1] Maxwell and Kelvin models are described for viscoelastic material (Figure 1), but when I
derived the equations myself I found a hidden assume that it can limited Maxwell model only for
small interval of times and small changes, in continue I begin with assumptions which are used for
equations.
Figure 1. Maxwell model (a) and Kelvin model (b) for modeling viscoelastic materials.
In physical equations for linear springs we can write Hook Law (eq.1) as below:
ܨ ൌ ܭΔܮ (1)
2. And we can extend constant of spring for parallel and cascades configuration respectively (Figure2)
by below forms (eq.2, 3):
Figure 2. Parallel (a) and Cascade (b) springs
ܭ்௧ ൌ ܭଵ ܭଶ (2)
ଵ
ೌ
ൌ ଵ
భ
ଵ
మ
(3)
The above equations are extracted from length of model and their effective forces on cascade and
parallel system like below (eq.4, 5):
ܨ்௧ ൌ ܨଵ ൌ ܨଶ
ܮ்௧ ൌ ܮଵ ܮଶ
൜
(4)
ܮ்௧ ൌ ܮଵ ൌ ܮଶ
ܨ்௧ ൌ ܨଵ ܨଶ
൜
(5)
Now, I'm going to start with these assumptions and derive Maxwell and Kelvin formulations for
viscoelasticity models. At first for Maxwell (Figure 1) we have:
ቄ
ߪ ൌ ߪଵ ൌ ߪଶ
ܮ ൌ ܮଵ ܮଶ , Δܮ ൌ Δܮଵ Δܮଶ
(6)
ߝ ൌ Δ
(7)
3. So, we can divide part 2 of (eq.6) to Δܮ:
(8)
Δ ൌ భ
Δ మ
Δ
ΔୀΔభାΔమ ሳልልልልልልልሰ
Δ ൌ భ
ΔభାΔభ
మ
ΔమାΔభ
௩௦
ሳልልልልሰ Δ
ൌ ΔభାΔభ
భ
ΔమାΔభ
మ
֜ Δ
ൌ Δభ
భ
Δమ
మ
Δమ
భ
Δభ
మ
.
ሳልሰ ߝ ൌ ߝଵ ߝଶ ΔభΔమ
బమΔమାబభΔభ
Now, if we consider (eq.9) then
ΔభΔమ
బమΔమାబభΔభ
ൎ 0 (9)
ߝ ൌ ߝଵ ߝଶ (10)
From (eq. 6, 10) for a cascade model and linear relation between stress, strain and Yang's modulus
(eq. 11, 12) and using (eq.13), we can reach (eq. 14) for (Figure 1) which is Maxwell equation for
viscoelastic materials.
ߪ ൌ ߟߝ (11)
ߪ ൌ ߪଵ ൌ ߟߝଵ , ߪ ൌ ߪଶ ൌ ߟߝሶଵ
(12)
ߪ ൌ ߟߝ
ሺ ሻ
ሳሰ ߪሶൌ ߟሶߝ ߟߝሶ
ఎሶୀ ᇲ௦ ௗ௨௨௦
ሳልልልልልልልልልልልልልልልልልልልልልልልሰ ߪሶൌ ߟߝሶ (13)
ߝሶൌ ߝሶଵ
ߝሶଶ
.ଵଶ,ଵଷ
ሳልልልልሰ ߝሶൌ ఙሶ
ఎ ఙ
ఎ
(14)
In continue for parallel model of viscoelastic material we have below equations:
Δܮ ൌ Δܮଵ ൌ Δܮଶ
ܮ ൌ ܮଵ ൌ ܮଶ ൠ ֜ ߝ ൌ ߝଵ ൌ ߝଶ (15)
൜
By fill (eq.12) in part one of (eq.15) we will have:
ߪ ൌ ߝߟ ߝሶߟ (16)
This is known as Kelvin equation for viscoelastic materials. From method of derivation of Kelvin
equation and from (eq.9), we can say that the Kelvin bar model doesn't have any vanishing
assumption so in compare to Maxwell model, Kelvin model has better accuracy in matching with real
behaviors of viscoelastic material.
Creep and Relaxation
Creep is a kind of phenomena that we have strain of specimen under constant stress during time, so
mathematically it happens when ߪሶൌ 0, and in Relaxation we face with constant strain respect to
4. time (ߝሶൌ 0), so we can extract equation of stress during time for Relaxation phenomena of a
viscoelastic material from Maxwell equation (eq.17).
ߪሶൌ െ ఎ
ఎ ߪ (17)
Now we can separate variables and solve ODE1 like below:
ௗఙ
ఙ ൌ െ ఎ
ఎ ݀ݐ (18)
ߪ ൌ ߪ݁ିആ
ആ௧
(19)
The above equation is the relation for Relaxation test on a Maxwell bar.
Figure 3. Relaxation test of a Maxwell bar
Conclusion
Briefly, from deriving Maxwell and Kelvin equations for viscoelastic materials, we could find that the
Kelvin model will have more similar results with real model in fast deformations which we couldn't
vanish some parts.
Next duty
I'm going to find different definitions of crack in materials and compare them.
1 . Ordinary Differential Equation