Elasticity - Science topic

To study the kinetics of ordering based on changes in mechanical properties, is it more accurate to use yield stress data (point B, determined by the conventional 0.2% offset method) or flow stress at point A (transition of the curve from linear elastic to nonlinear plastic behavior)? It should be noted that in the range where ordering occurs, other transformations, such as recrystallization, are also taking place, and recrystallization affects the yield stress. Could you please recommend references on this topic?

Would a polyamide composed of cis/trans‐1,4‐cyclohexanedicarboxylic acid and cis/trans‐1,4‐cyclohexanediamine be inherently elastic?

I am new to LAMMPS and want to calculate the elastic constants of Ar at 60K and 1bar by explicit deformation of 0.01 strain to mimic work done in a research paper, I have written the code the results aren't look good can someone please help me. Link to the article:

My LAMMPS code is attached as file here. Please help me

How can I find the Elastic properties of matrix material reinforced with nanofillers, is there any relation or formula to find it?

Which technique is best used to determine the modulus of elasticity of pure and filled fluoroplastic (PTFE)? The literature does not always indicate the method, and the variation of modulus values for pure material is from 400 to 1000 MPa. The problem is that the material has a low modulus of elasticity in combination with a maximum deformation of up to 400%. Measurement of the acoustic modulus of the filled material gave a value of 5 GPa

So I have a structure with a pile foundation and a gravity load acting on the structure. The demand curve is drawn by running an elastic analysis. Pile-Soil is modelled as p-y, t-z, and q-z curves. When i run a pushover analysis that starts after the gravity nonlinear case ends, i find a high loss of initial stiffness. However, if pushover starts with zero initial conditions, the curve almost follows the elastic demand curve. Can anyone provide any reasoning behind this phenomenon? Note that all layers of soil mobilize in skin friction under gravity non-linear case.

what is relationship between 𝐷 / 𝑑 and a ?

the parameter being k. It follows that𝐷/𝑑 is independent of the elastic properties of the rod.

it's about this article: A property of a buckled elastic rod

Leaf, British Journal of Applied Physics, Vol. 9. 1958

i would be very grateful if you help me.

best regards.

Hello every one

I have modeled a steel frame FRP shear wall in abaqus and I'm performing riks step to obtain the load capacity of shear wall to use that in designing a cyclic loading history based on ATC-24 protocol (for obtaining the yield deformation parameter Dy in the protocol). I have specified elastic and plastic properties for steel materials and also elastic and Hashin criteria for FRP material and I insert the imperfection from first buckling mode. But when the wall undergoes some deformation it encounters with the error "A ZERO DISPLACEMENT SOLUTION WAS FOUND IN THE FIRST ITERATION OF A RIKS STEP" some times I get this error when one of hashin damage initiation parameters reach to 1 and sometimes in smaller numbers, I have used both force control and displacement control analysis and also but the error persists. but in a similar model with less beam span the damage countinues and some damage evolution parameters reach to 1. what is the reason for this error and how should I solve it?

sorry for the long question.

In fracture, the various expressions of G the crack extension force per unit length of the crack-front (or energy release rate) show invariably a linear dependence of G with the crack half-length c. This is true whatever the shape (planar or non-planar) of the crack and the form f of the crack-front (f can be developed in Fourier forms). Hence some expressions of G (see relation (2.25), page 37 in Lawn (1993) Second Edition, for example) provided for the DCB specimens are under question. Are these concerned with crack propagation?

I have modeled a prestressed concrete beam in ABAQUS using following element type:

Concrete- C3D8R, Steel Strand- T3D2.

I have considered elastic and plastic behavior of both steel and concrete(CDP). While comparing load-deflection curve from both experiment and FEA, it has given me pretty much accurate value for ultimate load. However, the elastic response of the structure is much more stiffer from experiment data. I have already updated the FE model based on constructed specimen such as diameter of steel bar and prestress strand, concrete strength. What could be the problem?

It is a widely used approach to calculate the equilibrium volume of a solid via minimization of its Gibbs free energy G=F+pV with respect to volume V. For an insulator F(V,T)=E(V)+Fph(V,T), where Fph(V,T) is the phonon contribution and E(V) is “static” elastic energy of a solid. E(V) is usually calculated via DFT by taking several values of the unit cell volume, which is obtained by changing the lattice constants. This approach is realized in codes such as Gibbs and QHA. It is straightforward for an isotropic solid (with cubic symmetry) since all three lattice constants change with temperature by the same relative amount i.e. Δa/a=Δb/a=Δc/c. However, for anisotropic solids the lattice constants may change by different amounts, thermal expansion becomes anisotropic and one has to use more general Gruneisen formalism as implemented e.g. here https://doi.org/10.1016/j.commatsci.2018.04.036 . I was not able to find codes implementing general Gruneisen formalism except this one https://github.com/gangliu-github/gruneisen-formula . However, this code just calculates anisotropic thermal expansion from given files of Phonopy calculations for strained supercells, and does not provide the strains that should be applied for a particular crystal structure. Therefore, my questions are:

1) Does somebody know codes implementing Gruneisen formalism for calculation of anisotropic coefficient of thermal expansion “from scratch” ?

2) Is the conventional approach described above (where the relative change of all lattice constants is the same) correct for anisotropic solids at least for calculating the average thermal expansion (and bulk modulus)?

I have data obtained from compression test. how to calculate young modulus from a compression test (stress-strain curve) with nonlinear elastic region?

Please see the attached document for a summary of my proof of rigidity.

I have written a numerical model for calculating the elastic deformation of two elastic bodies in 3D static contact. The code takes the applied laod, Young's Modulus, Poisson ratio, and surface profile of each body. Calculates influence coefficients based on the equation provided by Love [1]. The problem is solved by conjugate gradient descent and elastic deformation is calculated by Discrete Fourier Transform- Discrete Convolution method.

I tested the model on ball-on-flat and ball-on-ball geometries with the same material properties of each body. I am facing the problem that the elastic deformation contour is diagonal instead of concentric in these cases. The pressure distribution normalized at Hertz Contact pressure and contact width is correct, but the deformation is not. I have double-checked by Kernal/influence coefficient matrix but can not seem to understand this behavior. I have attached the 3D plots of the example (ball-on-ball), the 3D plot of the influence coefficient at 1 point, and the contour of calculated deformation.

Any help, guidance to solve, or help in understanding the problem would be greatly appreciated.

Thanks.

A.E.H. Love. Stress produced in a semi-innite solid by pressure on part of the boundary. Philosophical Transactions of the Royal Society of London, 377:54{59, 1929.

I need to model an anisotropic material in which the Poisson's ratio ν_12 ≠ ν_21 and so on. Therefore, the elastic compliance matrix wouldn't be a symmetric one. In ANSYS APDL, for TB,ANEL command, the stiffness matrix must be a symmetric one with 21 elements.

How to model this anisotropic material in ANSYS APDL?

Using COMSOL Multiphysics, I am aiming to model and simulate the compression and tensile test scenarios of 3D printed samples (ABS, PLA, PETG). However, it would appear that the default equations used for the Nonlinear Elastic Material section of the the Solid Mechanics Physics model is Isotropic. I would like to use an Anisotropic approach given how the printing parameters in the lab would change the samples' outcome from an Isotropic to an Anisotropic material.

Any advice would be greatly appreciated. I've attached a snap shot of the compression model along with the equations involved for the Nonlinear Elastic Material

The aim of the research here is to prevent the propagation of the crack in the fabricated elastic medium with useful applications.

..

Aim is to simulate the shape of Mobius strip (an elastic ribbon) in simple way ( using Abaqus Learning edition). In literature, Mobius strip is modeled as Kirchhoff Rod / Cosserat plate. But, such specialized continuum models can't be incorporated without user subroutines - Abaqus Learning edition provides us with no user subroutine provision.

Creating geometric model is fine but what should be discretization & element to be used? Material model is isotropic, linear elastic.

I understand the basic definition for both. I found a literature to describe both of them.

In the paper, they states:

If a stress is applied to a concrete body, the body experiences an elastic deformation which is, to a first approximation, independent of time. If, however, this stress is maintained for a considerable period of time, the body suffers a further, time-dependent deformation. This additional deformation is com- monly known as creep. In a creep experiment the stress is usually kept constant. If instead of the stress, the length of a stressed specimen is kept constant, the creep leads to a gradual reduction of the stress originally present. This process is called stress relaxation.

Based on the paper’s description, creep and stress relaxation depends on which factor is maintained (I.e. stress or strain).

If strain change, it is a creep deformation

if stress change, it is a stress relaxation.

How do you know which one is change or maintained in the material or in a strcuture? Stress or strain?

See the attached file for an illustration of this problem.

Consider an elastic sheet S (orange) that’s laying atop a solid base B (blue). The sheet is under tension (arrows) and is held to the base by surface tension due to a fluid between S and B (arrowhead). I’m looking for an expression of how closely the top of the sheet S reflects the shape of the base B.

If the base has a gentle wave to it (middle panel), then the top surface of the sheet will reflect what’s below it, though the curvature will change due to the added thickness, t. It’s straightforward to estimate how closely the top surface of the sheet will reflect what’s below it. But what if the change in shape is abrupt, or very narrow, like shown in the bottom panel? How do I best estimate the limits of how closely the sheet follows that shape?

I understand the basic definition for both. I found a literature to describe both of them.

In the paper, they states:

If a stress is applied to a concrete body, the body experiences an elastic deformation which is, to a first approximation, independent of time. If, however, this stress is maintained for a considerable period of time, the body suffers a further, time-dependent deformation. This additional deformation is com- monly known as creep. In a creep experiment the stress is usually kept constant. If instead of the stress, the length of a stressed specimen is kept constant, the creep leads to a gradual reduction of the stress originally present. This process is called stress relaxation.

Based on the paper’s description, creep and stress relaxation depends on which factor is maintained (I.e. stress or strain).

If strain change, it is a creep deformation

if stress change, it is a stress relaxation.

How do you know which one is change or maintained in the material or in a strcuture? Stress or strain?

Can an elliptic crack (small enough to remain a single entity, with no internal pressure or shear force) inside an isotropic material (no boundary effect) be expanded in its own plane under externally applied shearing stresses only?

If yes, how did you show that? Do we have experimental evidence for the process?

A simple crack system (Figure 1) can be readily studied to estimate the Hertzian conoidal crack angle and length, and also the stress intensity factor.

This is a 3-D brittle elastic half-space on the flat boundary Ox1x3 of which a rectilinear contact pressure along Ox3 is exerted by a cylinder whose axis is parallel to x3; the cylinder lies along Ox3 on the flat boundary. A planar straight-front crack inclined by an angle θ with respect to x1x3 is present under the action of the load along x2 due to the cylinder. The relevance of this modelling may be understood as follows. A slab of cylinder with thickness dx3 at spatial position O’ (0, 0, x3) exerts elastic fields (displacement and stress) proportional to those of a point load at O’ (proportionality coefficient dx3). Physically, this corresponds to the action of a spherical indenter to which is associated a conoidal fracture surface for sufficiently large load (Roesler (1956) as quoted by Frank and Lawn (1967)). The coalescence of conoidal cracks from different slabs of cylinder along Ox3 would produce planar fracture surface envelops parallel to x3 at large crack lengths. Therefore, we expect the modelling in Figure 1 to provide the experimentally observed fracture surface inclination angle θ and crack length l as a function of critical load P by both a spherical indenter and cylinder. This is the essence of the modelling depicted schematically in Figure 1.

I‘m going to run a crystal plasticity model with XFEM crack. the material properties are defined as USER MATERIAL. when the job was submitted, an error message was appeared :"39600 Elements are missing elastic property reference. The elements have been identified in element set ErrElemMissingElastic PropRef". I was confused by this message, because the elastic and plastic deformation were descripted in UMAT. but the job can't be submitted sucessfully.

Any response are appreciated, thanks you!

Cross-slip, twinning and fracture are major deformation modes adopted by loaded materials. It appears sound that these apparently different deformation mechanisms can be analysed on the equal manner!

I want to do modal analysis on a body which has two components which are in dynamic elastic and frictional contact with each other.

I was running elastic constant calculation using IRelast package in Wien2k 19.2.When i ran set_elast_pressure and after giving value of pressure i was getting error as given in the attachment.Can anybody kindly help me to resolve this error

I've been trying to find an explanation for why bandgaps can form in periodic elastic laminates but so far I haven't found a good explanation. Can anyone point me to any resources which might provide an explanation or give a good analogy between this and other areas of physics where bandgaps may occur?

In the cubic structure, there are mainly 3 elastic constants including C11, C11, and C44. Now, in my simulation, the value of C11 is becoming very high due to applying pressure. So far, in the simulations I've done, it's reached around 570 GPa. If more pressure is induced, it could increase further. My question is, is this increase normal?

Hi all,

I have a scenario where the yield limit on my stress-strain curve is sitting beyond the proportional limit. How can I define the yield point in ABAQUS when I am only allowed to define the elastic phase up to the proportional limit? See the example below, suppose my yield limit is at Point C and the proportional limit is at Point A. Do I use a secant modulus in this case? If so, I lose some stiffness up to the proportional limit which is wrong.

Any help would be greatly appreciated, cheers!

Regards,

Heng

I want to study the effects of train induced vibrations on nearby structures. For this purpose I used this paper :

I modeled the ballasted railway with infinite element boundary with elastic geo-material. The properties that I used are similar to the information provided in Table 1 of this paper. I simulated the wheels of the train with rigid cubes and then applied the load of each wheel on the reference point of the cube as mentioned in the paper. The steel rail is constrained at the bottom to the top surface of sleepers with the so called "Tie" constraint in the Interaction module. In addition the contact between the sleepers and the ballast is modeled using the general contact option in Abaqus (tangential behavior is assumed rough and normal behavior is the so-called Hard contact.) and finally the contact between rigid cubes (wheels) and top of the rail is modeled with the frictionless tangential behavior and Hard contact normal behavior using the individual property assignment in the general contact tab.

The problem I have is that my results don't match the results of the paper. The vertical stress in control points M1 & M3 are the same with the results of the paper however the vertical displacements in these points have a large error.

I attached my results below. What's wrong with my simulation and how can I correct my results (vertical displacement)?

Hello everyone, I am currently a beginner in the field of using the Thermo PW code for elastic constant determination. I am working on  perovskite of type A2BB'X5, which is stable in the tetragonal phase. I have encountered an issue in my calculations. While employing the Thermo PW code, I find that it generates seven elastic constants(Cij) instead of the six(Cij) (expected for tetragonal structure). below, I mention the obtained elastic constants for the same. I am reaching out to seek guidance or assistance from anyone who may have experience with this code or a similar situation. It would be immensely grateful.

Elastic constants C_ij (kbar)     i j=        1           2           3           4           5           6     1   234.09216    54.10432   122.15608     0.00000     0.00000     0.00000     2    54.10432   234.09216   122.15608     0.00000     0.00000     0.00000     3   127.14759   127.14759   346.94234     0.00000     0.00000     0.00000     4     0.00000     0.00000     0.00000    62.34926     0.00000     0.00000     5     0.00000     0.00000     0.00000     0.00000    62.34926     0.00000     6     0.00000     0.00000     0.00000     0.00000     0.00000    85.50041      1 bar = 10^5 Pa; 10 kbar = 1 GPa; 1 atm = 1.01325 bar; 1 Pa = 1 N/m^2      1 Pa = 10 dyn/cm^2; 1 Mbar = 10^11 Pa      1 torr = 1 mm Hg = 1/760 bar = 7.5006 x 10^-3 Pa                     ----------------------------------------      Elastic compliances  S_ij (1/Mbar)     i j=        1           2           3           4           5           6     1     5.29482    -0.26111    -1.77233     0.00000     0.00000     0.00000     2    -0.26111     5.29482    -1.77233     0.00000     0.00000     0.00000     3    -1.84475    -1.84475     4.18137     0.00000     0.00000     0.00000     4     0.00000     0.00000     0.00000    16.03868     0.00000     0.00000     5     0.00000     0.00000     0.00000     0.00000    16.03868     0.00000     6     0.00000     0.00000     0.00000     0.00000     0.00000    11.69585

Thank you for your time and consideration.--

Heena

Research scholar

JMI

I am trying to do elastic property calculation in QE, with ibrav=8 using thermo_pw. But getting an error shown below.

Can anyone suggest how to resolve it?

Every common source avoids the derivation, saying it to be too difficult. Where can i fiend volterra's original derivation? Knowing which mathematics would be necessary?

Problem to model a simple (at first glance) stationary problem of thermomechanics in an elastic formulation in ANSYS Mechanical APDL.

There is a simple block (brick), with spatial non-uniform volumetric heat generation (HGEN).

The back and front faces are convectively cooled with given (but different) HTC's and fluids temperatures.

The properties of block (thermophysics + mechanics) are assumed to depend on temperature.

HOW TO simulate the temperature field in a brick, taking into account thermal expansion?

Hello, everyone

I need some help regarding elastic constant calculation of LiMgF3 compound. I am facing following issue:

task # 0

from initialize_elastic_cons : error # 1

Laue class not available

task # 1

from initialize_elastic_cons : error # 1

Laue class not available

My pw.x input file is as follows:

&CONTROL

calculation = "relax"

forc_conv_thr = 1.00000e-03

max_seconds = 1.72800e+05

nstep = 100

pseudo_dir = "./"

/

&SYSTEM

a = 3.958

degauss = 1.00000e-02

ecutrho = 5.23088e+02

ecutwfc = 5.81209e+01

input_DFT = "PBE"

ibrav = 1

nat = 5

ntyp = 3

occupations = "smearing"

smearing = "gaussian"

/

&ELECTRONS

conv_thr = 1.00000e-06

electron_maxstep = 200

mixing_beta = 7.00000e-01

startingpot = "atomic"

startingwfc = "atomic+random"

/

&IONS

ion_dynamics = "bfgs"

/

&CELL

/

K_POINTS {automatic}

3 3 3 0 0 0

ATOMIC_SPECIES

Li 6.9400 Li.pbe-mt_fhi.UPF

Mg 24.305 Mg.pbe-mt_fhi.UPF

F 18.998 F.pbe-mt_fhi.UPF

ATOMIC_POSITIONS {angstrom}

Li 0.000000 0.000000 0.000000

Mg 1.904000 1.904000 1.904000

F 1.904000 0.000000 1.904000

F 1.904000 1.904000 0.000000

F 0.000000 1.904000 1.904000

And thermo_control file is as follows:

&INPUT_THERMO

what='elastic_constants_t',

frozen_ions=.FALSE.

elastic_algorithm='energy'

use_free_energy=.TRUE.

lmurn=.FALSE.

tmin=1.,

tmax=3000.,

deltat=3.,

/

Please help me in this regards. Thanks

In the field of Elasto-Dynamic, the answers or solution procedures for problems in the book entitled "Wave Motion in Elastic Solids" by "Karl F. Graff" is needed.

The first three chapters include "Wave and Vibration in Strings", "Logintiudnal Waves in Thin Rods" and "Flexural Waves in Thin Rods".

Dear All

I am new to Thermo_pw software. I am currently working on Heusler alloys and trying to find out the elastic properties of one of the alloys using Thermo_Pw. But everytime I am getting a negative value for the shear modulus and other elastic constants are also not matching with the previous results. I have tried it number of times by changing the parameters appering in the input file but every time I am getting the negative results.

Please help.

Dear fellow contact mechanicists,

it is well known that the elastic edge singularity for the contact pressure in the vicinity of a singular contact boundary with a smooth boundary line is analogous to the elastic stress singularity for a crack with a smooth crack frontline, and of the form p(s) ~ s^(-1/2).

Now, what happens at a singular sharp corner of the contact boundary, e.g., under the indentation by a rigid square flat punch? I would assume, the exponent of the pressure singularity depends on the inner angle \theta of the corner, and will be p ~ 1/s (?) for \theta = 0, p ~ s^(-1/2) for \theta = \pi (the known edge singularity), and there is no singularity for \theta = 2\pi.

Are there asymptotic analytic solutions for this kind of singular indentation problems?

For the "crack analogue", the corresponding task has been solved in the work

Xu, L.; Kundu, T.: Stress Singularities at Crack Comers. Journal of Elasticity, 39, 1–16 (1995).

However, I think, the "analogue" only works for the edge singularity; for example, for a right-angled crack corner the singularity should be \sigma(s) ~ s^(-0.9) (approximately), but in a boundary element simulation for the indentation by a square flat punch, I obtain the asymptotic behavior p ~ s^(-0.7) (approximately).

Best regards,

Emanuel

This is the very definition of elastic collision.

By definition, elastic collision means the collision in which there are no dissipations due to heat, plastic deformation, sound waves, etc.

So, by conservation of energy, we mean that the initial kinetic energy before the collision is equal to the kinetic energy after the collision, because it is not converted to any other type of energy.

If two particles with kinetic energies E1 and E2 and momentum P1 and P2 collide, then their energies and momentum after the collision would follow the

report :-

E1*+E2*=E1+E2 . . . (1)

P1*+P2*=P1+P2 . . . (2)

Equation 1 does not hold if the collision is an inelastic collision while Relation 2 holds whether the collision is an elastic collision or not, but the question is why?

Is there a way to vary the elastic modulus with respect to the strain rate using field variable in ABAQUS/Explicit?

ICMEAAE 2024 provides an enabling platform for Materials Engineering and Applied Mechanics experts to exchange new ideas and present research results. This conference also promotes the establishment of business or research relations among global partners for future collaboration. We hope that this conference could make a significant contribution to the update of knowledge about this latest scientific field.

ICMEAAE 2024 warmly invite you to participate in and look forward to seeing you in Changsha, China.

The topics of interest include, but are not limited to:

1. Materials

- Materials Science and Engineering

- Nanomaterials

- New Energy Materials

......

2. Applied Mechanics

- Vibration Science

- Elasticity

- Particle mechanics

......

All accepted full papers will be published in the conference proceedings and will be submitted to EI Compendex / Scopus for indexing.

Full Paper Submission Date: February 23, 2024

Registration Deadline: March 1, 2024

Final Paper Submission Date: March 8, 2024

Conference Dates: March 15-17, 2024

When calculating elastic modulus of CNM reinforced FRP under cyclic loading, should one calculate it based on the slight increasing slope before the flatbed region or based on the clear and sharp increasing slope?

I am interested in methods/equations for calculating the interaction volume during elastic nanoindentation. Specifically, I'm interested in determining how much of the material (other than the displaced volume) is responsible for the observed properties and measurements. Insights into methodologies or approaches to assess the proportion of material contributing to these responses would be highly valuable.

explain your idea

Hello dear colleagues,

I am looking for a elastic actuator for a robotic arm. It should be able to contribute 1/3rd in lifting the arm with the motor as the motor contributes 2/3rd. It should also ensure safe landing of the arm instead of free fall and also during emergency situations like, if the motor's program is bugged and it actuates in the wrong direction then also the actuator should ensure safe landing. My intial ideas were a spring and damper syste, torsional spring alone but there are some restrictions with them so, please suggest something.

Generally in the stress vs strain curve of polycrystalline metals and their alloys, we tend to observe an initial elastic deformation followed by plastic deformation marked with strain hardening. This strain hardening follows a parabolic behavior. A linear strain hardening is also observed in the second zone of single crystal stress vs strain behavior. How come a linear strain hardening behavior in polycrystals??

Sincere regards

Subha Sanket

IIT Kanpur

What is the relevant theory of calculating elastic constant by finite difference method？and what is the difference between it and energy strain method？

The motivation comes from the following common observation. Blocks of stone with large dimensions (say of the order of three meters or larger) can be easily fractured into two pieces. First, cylindrical holes are introduced at top surface using drills. Second, fracture is initiated from the holes with the help of sledgehammers and wedges. Without any additional action, the crack will move with time downward other very large distance and separate the block of stone into two parts. The fracture surface is perfectly flat. What is the reason?

It was easy to find the equation of indentation from Hertz contact theory when a sphere and a flat surface are indenting or 2 spheres are indenting, from Hertz contact theory. However, currently, I am indenting a cylindrical-shaped fibre with a flat plate indenter (so it's a flat-cylindrical contact). I saw the equation of contact area but I did not see the equation for contact depth. Can you please give me with some references?

A number of works on modifying epoxy properties with polysulfone thermoplastic additives provide data that additives in amounts up to 20% by volume do not change the yield strength, elastic modulus and ultimate deformation. Which is natural, since the mechanical properties of the polymers are similar, but the same works say that in this case the fracture toughness K1c and fracture energy G1c increase. Could this be possible?

I am performing tensile test using ansys explicit dynamics for orthotropic material the force reaction fluctuates in the elastic region

by Using the material property such as Elastic, Hyperelastic, viscoelastic and Hyper-Viscoelastic, I got the same result.

I use the ABAQUS version 2023

explain your idea

II am working with composite materials manufactured by vacuum bag and I want to simulate the mechanical behavior of these materials. However, I believe that the elastic properties of the laminae from the Ansys library are always much higher than the elastic properties of the material I manufacture.

Three balls with masses m1, m2, m3 can slide without friction along a straight horizontal line, with ball 2 located between balls 1 and 3 (Fig.). It is known that m1 >> m2, m3 >> m2. Determine the maximum velocities of the two outer balls if they were initially at rest and the middle ball was moving with speed v0. The impacts are considered absolutely elastic.

I am not getting accurate elastic constants while trying to use thermo_pw on Li3PS4 (space group: Pnma). I am not sure where I am going wrong as I have tried to implement the thermo_pw tool. Can you please have a look at my input files and let me know where exactly I am going wrong?

I am not sure why exactly I am facing this issue. For some materials I am geeting quite accurate values, however for some materials like in this case Li3PS4, my attempts are unsuccessful.

Verification with literature link: https://next-gen.materialsproject.org/materials/mp-985583?formula=Li3PS4#elastic_constants

Calculating the specific heat of a simple liquid by the number of elastic oscillators.

Calculate the specific heat of a simple liquid using the number of elastic oscillators

Each liquid molecule has an average of 8 elastic oscillators around it, and the specific heat contributed by the elastic energy is 4R。Therefore, near the three phase points, the specific heat at constant pressure of a single atomic liquid is 5.5R, and the specific heat at constant pressure of a diatomic liquid is 6.5R. Low temperature liquids such as Ar, Kr, Xe, O2, N2, F2, etc. conform to this conclusion.

Please read the following link for details

I have a four-story steel structure

When conducting a pushover analysis and examining the results, the structure's ductility ratio at the performance point did not exceed 1, and the equivalent damping remained at 5% according to the FEMA400 EL method.

How to reduce elastic modulus and improve plasticity by doping pedot

I use plastic behaviour for a material in abaqus:

YS plastic strain

8MPa 0

8MPa 1

8MPa 100

And Abaqus seems to ignore the elastic limit, the von Mises stress happily rises above 8MPa. But it does not happen when the mesh is linear with ticked reduced integration. Why is this and how do I fix this bug?

Under dominant mode I loading, planar cracks have been observed to move from zero velocity v= 0; for a certain value v= v₁, these turn into non-planar crack configurations. An explanation is offered below.

I want to know the theory of elasticity in differential geometry, and if there are any basic courses in this field. THANKS

Dear ResearchGate Community,

I am currently working on nanoindentation experiments using a Berkovich indenter on MG-WE43 alloy samples. My primary objective is to determine the hardness and elastic modulus of the material using the Oliver-Pharr method. However, I have encountered some issues in my analysis code, and I am seeking technical guidance to overcome these challenges.

Here is a brief overview of my experimental setup and the problems I am facing:

If any of you have experience with nanoindentation on similar materials or with the Oliver-Pharr method, I would greatly appreciate your insights and recommendations. Additionally, if you could share any MATLAB or Python code snippets tailored to this specific analysis, it would be immensely helpful.

Thank you in advance for your assistance.

In my model, each element has a different material prop and EX. (plotting output data is pretty straightforward, however input data is the trouble I so much need help with).