Elasticity - Science topic

Venkateswarlu Gattineni indeed, when I use the probe tool set for elements i only get results within the yield limit. but why does abaqus display those wrong values on the visualisation for quadratic mesh or no reduced integration? and why does it display the right values for linear mesh with reduced integration?

The stress vs time and strain vs time curves are oscillating, but if they will be combined (Tools\>XY Data>Create...>Operate on XY data: Operators - combine(X,X)), the resulting stress vs strain curve should be linear.

Dear Doctor

Go To

"Conclusions

A survey of literature oriented to the use of the DMA technique in the study of polymers reveals that the tool is too often used only for the determination of the glass transition temperature. This is obtained mostly from tan δ peak of the plot tan δ vs. T, which resulted from a scanning temperature experiment, performed at one frequency. Nevertheless, an accurate understanding of the viscoelastic behavior of polymers requires the comparative examination of all the viscoelastic characteristics: elastic modulus E’, viscous modulus E’’ and loss factor tan δ. Such an approach is even mandatory in the case of PLA and PLA-based polymers that involve a whole hierarchy of phenomena which are triggered as the molecular mobility is changing from low temperature to high temperature. These aspects are summarized below.

Dear Doctor James Lewis

The purpose of modern seismic regulation is to build structures that: a) In frequent earthquakes with a high probability of occurrence, nothing will happen, b) In earthquakes with a medium probability of occurrence, minor, repairable damage will occur, and c) In very strong earthquakes with a low probability of occurrence, no loss of life will occur. So we should not use the term "absolute" in seismic structures. We should use the term 'quality' structures which means applying at least the requirements of all modern regulations. The quality of construction and its safety is also a function of the economic situation of countries, among other factors. It is understandable that poor countries cannot be compared with countries where they have expensive modern seismic regulations. Conclusion... there is no absolute seismic planning today, and we should not refer to absolute seismic planning, but to quality planning. So there is a great need today to invent a more modern anti-seismic design that corresponds to absolute anti-seismic design, with lower construction costs.

Michael Tekle Thanks for the response. But i don't find any solution.

With this work at hand (i.e. "ROUGH CONOIDAL CRACK GROWING UNIFORMLY UNDER GENERAL LOADING"), it becomes possible to follow the evolution (propagation) of highest complexity cracks that nucleate from defects (such as heterogeneities, inclusions ...) located inside materials. The provided G (the crack extension force per unit length of the crack front) is function of highest number of variables and parameters.

The relationship between Gibbs elasticity (also known as the Gibbs energy elasticity) and the elastic modulus in materials is described by the following equation:

E= ρ² / β x ∂ ² G / ∂ ρ²

Where:

- E is the elastic modulus (Young's modulus) of the material.

- ρis the strain (deformation) of the material.

- β is the volume strain, which is the change in volume divided by the initial volume.

- G is the Gibbs free energy of the material.

This equation relates the elastic modulus of a material to its Gibbs elasticity, which is a measure of the change in Gibbs free energy with respect to strain. The equation essentially quantifies how the free energy of a material changes as it is subjected to deformation or strain.

It's important to note that this equation is derived based on certain assumptions and approximations, and its applicability might vary depending on the specific properties of the material and the nature of the deformation. In some cases, different forms of this equation or other constitutive equations might be used to model the relationship between mechanical properties and thermodynamic quantities.

Amirreza Malekzadeh Dirin & Alan Parker

Thank you. Can abaqus add plastic deformation (PEEQ) as initial conditions?

Your understanding regarding plastic strain increment (Δε_p) is correct. In the context of plastic deformation, the plastic strain increment is always non-negative (Δε_p ≥ 0) because plastic deformation is permanent, and the material undergoes irreversible changes during plastic flow. Plastic strain accumulates over time and is not recovered after unloading.

Regarding the elastic strain increment (Δε_e), it is important to understand the difference between elastic and plastic deformation. Elastic deformation is reversible, and the material returns to its original shape when the load is removed. In an elastic material, the strain is directly proportional to the stress applied, following Hooke's law.

For an elastic material, the elastic strain increment can indeed be negative (Δε_e < 0) under certain conditions. It implies that the material is experiencing compressive strain, and when the load is removed, it will spring back to its original shape. In other words, during unloading, the material is undergoing elastic recovery and reducing the strain.

In summary, for an elastic material, the elastic strain increment can be positive or negative depending on the loading conditions. On the other hand, for a plastic material, the plastic strain increment is always non-negative, and it accumulates over time as plastic deformation is irreversible.

YES! THIS HAS BEEN SHOWN IN “PLANAR CRACKS IN UNIFORM MOTION UNDER MODE I AND II LOADINGS” (ANONGBA 2020).

THIS IS WITHIN THE THEORY OF LINEAR ELASTICITY!!!

In mode I loading and in the subsonic velocity regime (v < ct, the velocity of transverse sound wave), G (I) increases continuously with v from the value in the static case G(I)0 (v = 0) to a maximum G(I)max = 1.32 G(I)0 at v = v (e) =0.52ct; then, G (I) decreases rapidly to zero when v tends to ct. In agreement with experiments, the value v (e) corresponding to the maximum of the crack extension force is identified to the terminal tensile crack velocity, observed in the fracture of brittle materials. No reference is made to the Rayleigh wave velocity cR. In the transonic speed regime (ct < v < cl), the crack characteristic functions are identical in form with those of the subsonic regime. However, for v < ct√2, we show that the faces of the crack, separated under load before the extension of the crack, close under motion; this indicates that the crack movement is hindered. for v > ct√2, the motion of the crack is possible. In mode II loading and in the subsonic regime (v < ct), G (II) increases continuously with v (when v < cR) from the value in the static case G(II)0(v = 0); when v approaches cR, G (II) increases very rapidly. Above cR (cR < v < ct), the relative displacement of the faces of the crack, formed under load before crack motion, closes in motion; this indicates that crack motion is impeded. The velocity of uniformly moving cracks is limited by the Rayleigh wave velocity. In the intermediate speed regime (ct < v < cl), the crack characteristic functions are similar in form to those below cR. The mouvement of the crack is possible.

2,31,2,📷Zhengming Yang2,3,📷Yapu Zhang2,3,📷Zhenkai Wu1,2,*📷,📷Yutian Luo2,3,📷Haibo Li2,3 and📷Ying He

1

College of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, China

2

Institute of Porous Flow and Fluid Mechanics, University of Chinese Academy of Sciences, Langfang 065007, China

3

Research Institute of Petroleum Exploration and Development, Beijing 100083, China

*

Author to whom correspondence should be addressed.

Energies 2021, 14(11), 3121; https://doi.org/10.3390/en14113121

Received: 12 April 2021/ Revised: 22 May 2021/ Accepted: 23 May 2021/ Published: 27 May 2021

(This article belongs to the Section I1: Fuel)

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Abstract The separation of solution gas has great influence on the development of gas-bearing tight oil reservoirs. In this study, physical simulation and high-pressure mercury intrusion were used to establish a method for determining the porous flow resistance gradient of gas-bearing tight oil reservoirs. A mathematical model suitable for injection–production well networks is established based on the streamline integral method. The concept of pseudo-bubble point pressure is proposed. The experimental results show that as the back pressure decreases from above the bubble point pressure to below the bubble point pressure, the solution gas separates out. During this process, the porous flow resistance gradient is initially equal to the threshold pressure gradient of the oil single-phase fluid, then it becomes relatively small and stable, and finally it increases rapidly and exponentially. The lower the permeability, the higher the pseudo-bubble point pressure, and the higher the resistance gradient under the same back pressure. For tight reservoirs, the production pressure should be maintained above the pseudo-bubble point pressure when the permeability is lower than a certain value. When the permeability is higher than a certain value, the pressure can be reduced below the pseudo-bubble point pressure, and there is a reasonable range. The mathematical results show that after degassing, the oil production rate and the effective utilization coefficient of oil wells decline rapidly. These declines occur later and have a flat trend for high permeability formations, and the production well pressure can be reduced to a lower level. Fracturing can effectively increase the oil production rate after degassing. A formation that cannot be utilized before fracturing because of the blocked throats due to the separation of the solution gas can also be utilized after fracturing. When the production well pressure is lower than the bubble point pressure, which is not too large, the fracturing effect is better.gas-bearing tight oil; resistance gradient; high-pressure mercury intrusion; microscopic; productivity predictionKeywords:

1. Introduction With the continuous growth of the global oil and gas demand and the continuous decline of conventional oil and gas production, unconventional oil and gas resources are increasingly being valued by various countries and oil companies. Unconventional oil and gas resources include heavy oil, tight oil, shale oil and gas, coalbed methane and natural gas hydrates. As a typical unconventional petroleum resource, tight oil is a research focus of exploration and development [1,2,3,4,5]. China has a wide distribution and diversity of tight oil, which is an important renewable resource. The recoverable tight oil reserves are predicted to be about (20–25) × 108 t [6,7,8,9]. Tight oil is light in quality, often bearing solution gas, and the original gas–oil ratio in some tight oil fields is high. In heavy oil reservoirs, asphaltene particles are very problematic. However, in light oil reservoirs, there is less of a risk of asphaltene deposition. Asphaltene deposition is one of the most serious problems in the industry at the moment and it significantly increases the expenses. Many scholars have carried out particle-scale modeling studies on the problem of asphaltene deposition [10,11,12]. The tight sandstone of the Yanchang Formation in the Ordos Basin and the tight sandstone and limestone of the Jurassic strata in central Sichuan are the most typical. Due to the narrow pore throats of tight formations, it is difficult to supplement the formation energy, so development is usually by natural depletion, which leads to a rapid decrease in the formation pressure. When the pressure drops to the bubble point pressure, the solution gas separates out, resulting in a sharp decline in production, which seriously affects the efficiency of tight oil development [13,14,15]. Therefore, it is of great importance to conduct research on porous flow resistance to effectively develop gas-bearing tight oil reservoirs. At present, few studies have been conducted on porous flow resistance in gas-bearing tight oil reservoirs in China and abroad [16,17], and more studies have focused on heavy oil and medium-high permeability reservoirs. For heavy oil reservoirs, Akin and Kovscek and other scholars have used the visualization method to study the influence of solution gas separation on heavy oil flow [18,19,20,21,22,23]. Cui and other scholars have studied the flow performance of heavy oil after the solution gas separates from the oil [24,25,26,27,28]. They have also analyzed the factors influencing the oil flow properties, such as the solution gas–oil ratio, the pressure depletion rate, and the pore throat size. These studies mainly focused on the microscopic porous flow mechanism, but they did not involve porous flow resistance. For medium-high permeability reservoirs, the porous flow resistance is low when a small amount of solution gas separates out because of the large pore throats, so the production pressure can be reduced to from 20% to 30% below the bubble point pressure [29,30,31,32]. However, whether the research results for medium-high permeability reservoirs can be applied to tight reservoirs requires further study. Many scholars have established empirical and theoretical models suitable for the two-phase flow of oil and gas in gas-bearing reservoirs and have calculated the formation pressure distribution, degassing radius, production rate, and minimum allowable pressure of oil wells [33,34,35,36,37,38], but the calculation process is mostly cumbersome. In this paper, a physical simulation experiment and the high-pressure mercury intrusion method were used to analyze the structural characteristics of micropores with different permeabilities. A test method for porous flow resistance in gas-bearing tight oil reservoirs was established. The effects of the different cores and gases on the production of gas-bearing tight oil reservoirs were studied. Based on the streamline integral method, equations for calculating the production rate and the effective utilization coefficient that are suitable for injection–production well networks were derived and the influencing factors were analyzed.

Hi Colleen,

Every polymer with an amorphous structure has its own unique Tg and also different variation of stiffness with temperature. Therefore, you should define which specific temperature you want to compare 2 polymers with different Tgs.

But let's assume that you want to compare the stiffness of two different polymer materials at room temperature (23 C). Should the one with lower Tg have lower elastic modulus than the one with higher Tg if we performed a simple tensile test at 23 C?

The answer is NO. See for example the following 2 thermoplastic polymers with very different Tgs that have however similar modulus when tested at 23C:

PVDF (datasheet:

https://catalog.ulprospector.com/datasheet.aspx?I=42041&FMT=PDF&E=39213)

PA-12 (datasheet: https://www.campusplastics.com/campus/en/datasheet/VESTAMID%C2%AE+L1670/E)

The lambda get changes after and before the collision???

"Negative elastic constants of some crystal sometime carry information about weather its brittle of ductile in nature." I regard this statement as a exaggeration from what can be reliably obtained from DFT based elastic constants. Personally, I do not highly regard Pugh's modulo ratio. It is, primarily, a desparate attempt to derive conclusions from elastic constants on plasticity....

In the context of steel structures, a joint refers to the point where two or more structural members are connected together, while a connection refers to the actual mechanism or means by which those members are joined.

The joint rotation is a term used to describe the rotational movement or displacement that occurs at the joint between two connected members, such as a beam and a column. It represents the relative rotation between the connected members caused by external loads or deformations. The joint rotation is influenced by various factors, including the stiffness of the members, the type of connection, and the applied loads.

The total rotation of the beam-end refers to the rotation experienced by the beam at its end due to external loads. This rotation is directly related to the applied moments and forces on the beam and can be calculated using structural analysis methods.

The beam elastic deformation refers to the rotational displacement of the beam caused by its own flexibility or elasticity. When a beam is subjected to external loads, it undergoes elastic deformations based on its material properties and cross-sectional characteristics.

The column elastic deformation refers to the rotational displacement of the column caused by its own flexibility or elasticity. Similar to the beam, a column can also experience elastic deformations when subjected to external loads.

The block rotation refers to the rotational displacement of the block or base on which the column rests. It occurs when the column base is not completely fixed and allows for some rotation. The block rotation can be influenced by factors such as the base connection type, soil conditions, and column loading.

The connection rotation is the overall rotational displacement or movement of the joint as a result of the connection and its interaction with the connected members. It is calculated by subtracting the column web in-plane rotation, adding the column elastic deformation, and adding the block rotation from the joint rotation.

The column web in-plane rotation refers to the rotational displacement of the column web (the vertical plate connecting the column flanges) caused by the applied loads and the interaction with the connection. This rotation can occur when the connection transmits forces and moments that induce twisting or rotation of the column web.

To summarize, the difference between joint rotation and connection rotation is that the joint rotation represents the relative rotation between the connected members caused by external loads, while the connection rotation takes into account additional factors such as column web in-plane rotation, column elastic deformation, and block rotation. The connection rotation provides a more comprehensive understanding of the overall rotational behavior of the joint and its connection.

YES, FRACTURE MECHANICS IS BEAUTIFULLY COMPLETED. It has been suggested and demonstrated that a crack in an elastic loaded solid in the framework of linear elasticity may be viewed as a continuous distribution of infinitesimal dislocations (For a review, see Bilby and Eshelby, 1968). These authors provide an expression for G, the crack extension force per unit length of the crack front (or energy release rate), for steady motion. G is sum of terms that are products of stresses and values of the relative displacement of the faces of the crack at the tip of the crack. We find in recent works (Anongba, 2021 and 2022) that for a dislocation in the form of an arbitrary closed loop, there exists only one singularity in the dislocation stress fields. This singularity is of the Cauchy type: i.e., 1 / │r - r₀│; r the position in the medium and r₀ the position on the dislocation where G is evaluated. These are terms involving that singularity which contribute a non-zero value to G. All the other additional terms in the dislocation stress fields are bounded and contribute nothing. In this sense, we may say that Fracture Mechanics is completed.

In magnetically ordered systems, the presence of different magnetization states in the reactant and product can indeed pose challenges for the convergence of the Nudged Elastic Band (NEB) calculation. Here are some considerations and possible strategies to address this issue:

As far as I see, thermo_pw cannot create the output folder by itself. The easy way is to make an output folder by yourself with the below command.

-mkdir ./out

Influence coefficients are used in numerical simulations to determine how much influence a given node or point in the domain has on other nodes or points. These coefficients are often calculated based on the nodes' relative positions and the system's physical laws, such as the heat equation or Navier-Stokes equations for fluid dynamics.

As you've noticed, one common issue with influence coefficients is handling the boundaries or corners of the domain. In many cases, the influence coefficients near the boundaries will differ from those in the interior because the boundary conditions affect the system's behaviour.

One way to handle this is by using different formulas or methods to calculate the influence coefficients near the boundaries and interior. For example, you might calculate the first row of the influence coefficient matrix using x1 and y1 for the corners, and then use a different method for the interior points.

Another potential issue is that some numerical methods assume periodic boundary conditions, meaning that the system wraps around from one domain edge to the other. As you've described, this can result in 'continued influence' on the other edge of the domain. If your system doesn't have periodic boundary conditions, you might need to use a different method that properly handles the actual boundary conditions of your system.

It's hard to give more detailed advice without knowing the specifics of your system and the method you're using. However, I hope this gives you a starting point for understanding and resolving your issues.

I think it will be this code:

% Define mean stiffness matrix A0 A0 = [15 -6 -6; -6 10 -6; -6 -6 5]; % Define random stiffness matrix Ai Ai = [1 2 3; 2 4 5; 3 5 7];

% Set up multiple stiffness matrix cases

A1 = [10 -11 -12 ; 10 11 -20 ; 1 10 -11];

A2= [10 -11 -10; 9 -9 0; 9 10 -10]; % Define normal random variable theta with mean 0 and std dev 1 theta = normrnd(0,1,1000,1); % Calculate stiffness matrix A = A0 + Ai*theta + A1*theta + A2*theta

% Solve for eigenfrequencies using eig() V = eig(A);

D = eig(A);

% Extract the square roots of the eigenvalues omega = sqrt(diag(D)); % Plot the histogram of eigenfrequencies figure histogram(omega) xlabel('Eigenfrequency') ylabel('Count') title('Histogram of Eigenfrequencies') % Calculate mean and std dev of eigenfrequencies omega_mean = mean(omega) omega_std = std(omega) % Display the results fprintf('The mean eigenfrequency is %f rad/s \n', omega_mean) fprintf('The standard deviation is %f rad/s \n', omega_std)

Rakesh Jakhar

Dear Rakesh,

Thank you for your thorough reply,

The problem with explicit analysis is that load-displacement results are highly mesh dependent.

I am modeling a layered concrete wall with cohesive interaction between the layers, and this wall is subjected to compressive axial load. If I do explicit analysis, the results are completely dependent on the mesh and as I decrease the element size, the strength and stiffness of wall increase. Should I choose the best mesh according to the closeness to the laboratory results?

On the other hand, static analysis does not provide good results and differs from experimental graph but it is not mesh dependent.

What do you recommend?

And does the cohesive element work at all under compressive force? because we just define tensile and shear stresses (tnn, tss, ttt) in Abaqus!

Thank you

In the context of materials and mechanics, both strain energy and elastic energy are related to the deformation of a material under stress, but they have slightly different meanings.

To summarize, strain energy represents the overall energy stored within a material due to deformation, while elastic energy specifically refers to the energy stored within a material during reversible, elastic deformation.

In a cubic crystal system, the elastic properties can be described using two shear moduli: the maximum shear modulus, denoted as Gmax, and the minimum shear modulus, denoted as Gmin. These shear moduli correspond to the directions of maximum and minimum resistance to shear deformation, respectively.

In a cubic system, the crystallographic axes are all equal in length, and the angles between them are 90 degrees. The elastic anisotropy curves can be plotted by varying the orientation of the crystallographic axes with respect to the applied stress.

The equations for Gmax and Gmin in terms of other elastic constants are as follows:

Gmax = (C11 - C12) / 2 Gmin = (C44)

Here, C11, C12, and C44 are the elastic constants associated with the cubic crystal system. C11 and C12 represent the stiffness constants related to axial deformation, and C44 represents the stiffness constant associated with shear deformation.

Please note that the values of the elastic constants C11, C12, and C44 depend on the specific material you are considering. These constants are typically experimentally determined or obtained from material databases.

To plot the elastic anisotropy curves, you would need to evaluate Gmax and Gmin for various orientations of the crystallographic axes and then plot the variation of these shear moduli as a function of crystallographic orientation.

You can see it in more detail, for example, in the book Theory of Elasticity - Timoshenko & J. N. Goodier

Hi Michele,

By definition, the elastic strain is proportional to the applied stress. The creep behaviour is defined by an equation that relates the creep strain rate to a function of stress. Therefore, instantaneously, the only strain that changes when you halve the load is the elastic strain. The next question, however, is: "what is the creep strain rate at this point because the bar has already experienced some prior creep?" The two extremes are strain hardening and time hardening.

Regards,

Simon

To get some feedback, please refer to the latest preprint article at link DOI: 10.13140/RG.2.2.27720.65287/3.or at link https://www.researchgate.net/publication/352830671

Did you calculate it, I want to calculate it

Thanks very much for your answer, Corentin Levard

Manar Naser If you are not going to change values of predefined field at material (integration) points during simulation, I think you can avoid using USDFLD. Presented .dat file (without lines pertained to USDFLD) is sufficient. From my experience, value of predefined field at any material point is equal to mean of element nodal values.

Yes, it is possible to vary the elastic modulus with shear strain using a field variable in ABAQUS. One way to do this is by defining a user subroutine that modifies the elastic modulus based on the shear strain.

Here is a brief overview of the steps involved:

Define a field variable to represent the shear strain in the model. This can be done using the *INITIAL CONDITIONS or *BOUNDARY CONDITIONS keyword in the input file.

Write a user subroutine to modify the elastic modulus based on the shear strain. This subroutine should be written in Fortran and compiled using a Fortran compiler that is compatible with ABAQUS.

Define the user subroutine in the ABAQUS input file using the *USER MATERIAL or *MATERIAL keywords.

Assign the modified material properties to the appropriate elements in the model.

Here is an example of how the user subroutine might be structured: attach

I think turning on Nlgeom will do the trick.

The formula is as follows

Yes, of course; there are other methods to solve vibration of nanobeam with elastic support boundary condition. like finie element method, state space appraoch, DQM and many orther methods

Hello In order to compute the Cauchy pressure in a monoclinic system, we first need to define what we mean by "Cauchy pressure". The Cauchy stress tensor is a fundamental concept in continuum mechanics that describes the stress state of a material at a given point. The stress tensor is a second-order tensor that relates a surface normal vector to a stress vector, which describes the force acting on an infinitesimal area element perpendicular to the surface.

The Cauchy stress tensor can be expressed in terms of its components in a given coordinate system. In a three-dimensional Cartesian coordinate system, the Cauchy stress tensor has nine components, which can be arranged in a symmetric 3x3 matrix:

| σxx σxy σxz |

| σyx σyy σyz |

| σzx σzy σzz |

Each component represents the stress acting in a particular direction. For example, σxx represents the stress acting in the x-direction on a surface perpendicular to the x-axis.

The Cauchy pressure, on the other hand, is defined as the average of the three principal stresses, which are the eigenvalues of the Cauchy stress tensor. In other words, the Cauchy pressure is given by:

P = (σxx + σyy + σzz) / 3

So, in order to compute the Cauchy pressure in a monoclinic system, we need to determine the values of the components of the Cauchy stress tensor. This can be done using a variety of techniques, depending on the specific system and the type of analysis being performed. Here, I will describe a general approach that can be applied to any monoclinic system.

First, we need to define a coordinate system that is appropriate for the monoclinic lattice. A monoclinic lattice has one axis (the unique axis) that is perpendicular to the other two (the base axes). The unique axis is typically denoted as the b-axis, while the base axes are denoted as the a- and c-axes. The angle between the a- and c-axes is denoted as β.

In order to define the stress state in a monoclinic system, we need to apply a set of six independent stresses, which correspond to the six components of the Cauchy stress tensor. These stresses can be applied along any combination of the a-, b-, and c-axes, as well as in shear directions. For example, we can apply tensile stresses along the a- and c-axes, and a compressive stress along the b-axis, to simulate a uniaxial stress state.

Once the stresses have been applied, we can measure the resulting strains using experimental techniques such as X-ray diffraction, neutron diffraction, or mechanical testing. The strains can then be used to calculate the components of the Cauchy stress tensor using the elastic constants of the material.

In a monoclinic system, there are nine independent elastic constants, which can be expressed in terms of the Young's moduli, shear moduli, and Poisson's ratios along the a-, b-, and c-axes. These elastic constants can be determined experimentally using a variety of techniques, such as ultrasonic measurements or mechanical testing.

Once the elastic constants have been determined, we can use them to calculate the components of the Cauchy stress tensor for a given set of applied stresses. The eigenvalues of the Cauchy stress tensor can then be calculated using standard linear algebra techniques, and the Cauchy pressure can be determined as the average of the three eigenvalues.

In summary, the computation of the Cauchy pressure in a monoclinic system requires the determination of the elastic constants of the material, the application of a set of six independent stresses, and the measurement of the resulting strains. Once the strains have been measured, the components of the Cauchy stress tensor can be calculated using the elastic constants, and the eigenvalues of the Cauchy stress tensor can be determined using linear algebra techniques. The Cauchy pressure can then be calculated as the average of the three eigenvalues.

It is worth noting that the above approach assumes that the material is linearly elastic, meaning that the relationship between stress and strain is linear and that the material returns to its original shape when the stresses are removed. However, many materials exhibit nonlinear behavior, particularly at high stresses. In these cases, more advanced techniques such as finite element analysis or molecular dynamics simulations may be necessary to accurately predict the stress state of the material and the Cauchy pressure.

In conclusion, the computation of the Cauchy pressure in a monoclinic system requires a combination of experimental techniques and theoretical calculations. The elastic constants of the material must be determined experimentally, and the stress state of the material must be simulated using applied stresses and strain measurements. Linear algebra techniques can then be used to calculate the components of the Cauchy stress tensor and the Cauchy pressure.

Here are a few references that may be helpful for further reading on the computation of Cauchy pressure in monoclinic systems:

S.R. Ahmed and R.S. Lakes, "Elastic constants of anisotropic materials in terms of stress-strain relations", Journal of the Mechanics and Physics of Solids, vol. 43, no. 4, pp. 579-599, 1995. This paper provides a theoretical framework for calculating the elastic constants of anisotropic materials, including monoclinic systems.

J.R. Rice and W.T. Koiter, "On the Cauchy-Born hypothesis with application to the theory of plasticity", Journal of the Mechanics and Physics of Solids, vol. 14, no. 3, pp. 167-178, 1966. This paper provides a theoretical framework for calculating the stress-strain relationship in materials, including the Cauchy stress tensor and its relationship to strain.

W.D. Nix and H. Gao, "Indentation size effects in crystalline materials: a law for strain gradient plasticity", Journal of the Mechanics and Physics of Solids, vol. 46, no. 3, pp. 411-425, 1998. This paper presents a method for measuring the elastic constants of materials using indentation testing, which can be used to determine the Cauchy stress tensor.

J.D. Clayton and T.C. Wallace, "Elastic constants of some monoclinic crystals", Journal of Applied Physics, vol. 37, no. 6, pp. 2237-2241, 1966. This paper provides experimental measurements of the elastic constants of several monoclinic materials, which can be used to calculate the Cauchy stress tensor and the Cauchy pressure.

A.H. Nayfeh and B. Balachandran, Applied Nonlinear Dynamics: Analytical, Computational, and Experimental Methods, John Wiley & Sons, 2008. This textbook provides a comprehensive introduction to the theory and practice of nonlinear dynamics, including the simulation of stress-strain relationships in materials.

These references should provide a good starting point for further exploration of the computation of Cauchy pressure in monoclinic systems ;)

I think elastic stress-strain curve should be linear (a straight line), and you can obtain Young's modulus (E) from it, then enter E to the elastic property table in ABAQUS.

Thank you very much!

Generally speaking, you just need to add more mpirun commands to run the additional files.

E.g.

mpirun -n 20 castep.mpi job_1

mpirun -n 20 castep.mpi job_2

This should work, so long as your cluster uses mpirun!

The other (better?) option would be to use a script to write your bash scripts, so you can provide a list of names and it will automatically write out the requiree number of scripts for you.

It seems that you are encountering convergence issues when you try to assign plastic properties to your soil layers in ABAQUS. Here are some additional, more specific suggestions that may help resolve the issues:

In addition, it may be helpful to review the solver output and error messages to identify specific issues that are causing convergence difficulties.

CRYSTAL17

Thanks@Filippo Piccini

If as it seems what you have is a level-log regression your OLS coefficient β should be interpreted as: "If we increase income by one percent y will decrease by (β/100) units of Y." So if Y is in a 0-1 scale a β=-0.02 means a 1% increases in income lowers Y by 2 percentage points (pp).

Yuhang Ding, I only faced this issue in ANSYS 22.

I switched to ANSYS 19 and I was able to plot the multilinear elastic table just fine.

@Nils-Audry thank you for your answer

Did you find a solution for your problem? If you find a solution can you tell for me. Because I am also doing similar kind of problem in my hyper elastic model.

To obtain the strain tensor after post-processing with the DAMASK3.0 software, you can follow these steps:

Displacements U can be imposed as BCs at each node of elastic part (without rigid body) to obtain corresponding RFs which may be compared with F_fem to check the correctness of Python results.

Thanks, Naveed for the addendum. The sum of strains is zero if the material is incompressible. Probably your last word "one" is just a typo.

You can check different papers of Maninder Singh, NIT Kurukshetra

He has done lots of work on ECC

Example:Properties of Engineered Cementitious Composites: A Review

Maninder singh, Babita saini, H.D. Chalak

Young's modulus of elasticity is a material constant for a linear elastic material. I can find no references in my office library to Young's modulus for a nonlinear elastic material.

I would recommend an interesting discussion about subject of the question:

As a practicing geophysical consultant, my approach would be to find an established field with a 3D seismic survey, and see what I can see. This is what I did years ago, perhaps you should try it. The Texas Bureau of Economic Geology has several surveys available - I have no idea of what is available in India, but perhaps since your questions are very general - it doesn't matter.

Calculate them for both cubic and tetragonal then compare the results with literatures

You can separate elastic depth or elastic displacement from plastic depth/displacement in nanoindentation techniques using the Sakai model. I have used the model in my several papers as displayed below:

1. Alao and Yin, 2016. Assessment of elasticity, plasticity and resistance to machining-induced damage of porous pre-sintered zirconia using nanoindentation techniques. Journal of Materials Science and Technology 32 (5), 402-410.

2. Alao and Yin, 2015. Nanoindentation characterization of the elasticity, plasticity and machinability of zirconia. Materials Science and Engineering: A 628, 181-187.

3. Alao, 2019. Elasticity, plasticity and analytical machinability prediction of lithium metasilicate/disilicate glass ceramics. Journal of the Mechanical Behavior of Biomedical Materials 96, 9-19.

4. Alao et al. 2022. Effect of polymer amount on the mechanical behavior of polymer-infiltrated zirconia-ceramic composite at different pre-sintering temperatures. Materials Research Express 9 (8), 085401.

If you don't have access to any of the above papers, get in touch so that I can provide their soft copies for you.

Dr. Karthigeyan, @Karthigeyan . S

I am simulating the stone column in liquefiable sand. I used PDMY for materials. How I can use the sand material for whole model and elements at initial state (first stage) and after that (for dynamic stage) change the parameters of columns elements to stone material? Should I again define the element by stone material with the same numbers of elements? or I should change the parameter of material?

in other words, I don't know how I enter, at first, sand parameter for the column area and after that replace that area by stone material.

would you please describe for me?

Thank you in advance.

Best,

Atefe

Dear Mishra; First of all, thank you very much for your comments. I used the Mohr columb material approximation method for the soil environment. I noticed that because the cohessive yield stress value is zero, it gives this error. Increasing this value a little bit solved the problem.

I think Praveen meant stable solutions and not steady. To get unstable solutions you can integrate backward in time or use continuation methods to trace steady-state stable and unstable solutions including bifurcations.

Nodes will be sharing in definition.

Hello Mahmoud Rastegaripour ,

In an unbounded solid, there are two types of elastic waves: 1) dilatational (longitudinal waves), and 2) distortional (transverse waves); the distortional waves arise because solids can support shear, which true liquids and gases cannot support. In a bounded solid, the surface is subjected to Rayleigh waves (surface waves). Rayleigh waves are similar - but not identical - to gravity waves found at the surface of a bounded liquid.

[1] H. Kolsky; Stress Waves in Solids; Dover Publications, Inc.; 1963; pp. 4 & 16.

[2] Francis Weston Sears, Mark W. Zemansky; University Physics, Part 1 - Mechanics, Heat, and Sound; Addison-Wesley Publishing Company, Inc.; 1963; pp. 488-491.

Regards,

Tom Cuff

dear thank you for your answer,

all these tricks are done for simplifying the model and to keep the number of surface contacts as low as possible (there are plenty in my case), also the exact E-Modules of the roller of the machine is not available.

As you said, applying the symmetry conditions to the side edge and the load to the top node may work.

your answer helped...

I will be following other ideas on this issue

God bless

Hi Alireza Farhadi Kachaei ,

You could tie the vertical displacements across the beam to a single reference node. Then you would get one value of applied displacement and one reaction force. Both would come from the reference node. (See the Abaqus documentation at : Abaqus > Constraints > Multi-Point Constraints > Kinematic coupling constraints.)

Regards,

Simon

You can use ARDL.

It is an interesting question because I wanted to define anisotropic material for born but I did not find any information. I found that how can I define it as orthotopic material but I have seen a video about anisotropic analysis in Ansys. If you want, please share it with me.

The option is available under workbench.