Defining an analysis. The Magnitude field is unavailable if you are creating the boundary condition in the initial step. Equilibrium requires the partial pressure to be continuous across an interface, so normalized concentration will be continuous as well. ISOL Amount of solute at the integration point, calculated as the product of the mass concentration and the integration point volume. A column labeled Temp appears in the Data table.

Defining pressure-driven mass diffusion.

Fixed time incrementation.

Modifying or removing concentration fluxes Concentrated or distributed concentration fluxes can be added, modified, or removed as described in About loads. Select Fixed at current magnitude if you want to fix the mass concentration magnitude at its final value from the previous general step.

In nonlinear cases iteration may be necessary to achieve a converged solution.

## Governing equations

Defining pressure-driven mass diffusion. Toggle on Use temperature-dependent data to define the pressure stress factor as a function of temperature. To define nonuniform distributed weight loss workout diet plan fluxes, the variation of the flux magnitude throughout a step can be defined in user subroutine DFLUX. For more details on time scales and time stepping, see Defining an analysis. In transient analysis using first-order elements the solubility terms are lumped, which eliminates such oscillations but can lead to locally inaccurate solutions for small time increments.

Alternatively, the temperature field difgusion be obtained from a previous heat transfer analysis. To describe temperature-driven diffusion, select Soret Effect from the Suboptions menu. Therefore, when the mesh includes dissimilar materials that share nodes, the normalized concentration is continuous across the interface between the different materials. FRIC : Define frictional behavior for contact surfaces. Defining a concentrated concentration flux. Mass diffusion driven by both temperature and pressure stress.

In transient analysis using first-order elements the solubility terms are lumped, which eliminates such oscillations but can lead to locally inaccurate solutions for small time increments. Click the arrows to the right of the Number of field variables field to increase or decrease the number of field variables on which the diffusivity data depend. Prescribing equivalent pressure stresses. Specifying predefined field variables You can specify values of predefined field variables during a mass diffusion analysis. Fixed time incrementation.

## Data line to define time stepping in a mass diffusion analysis

Transient analysis. This method is unconditionally stable for linear problems. An extended form of Fick's law can also be chosen by specifying a nonzero value for :. To describe pressure-driven mass diffusion, select Pressure Effect from the Suboptions menu.

Directional dependence of diffusivity. Defining diffusivity. Alternatively, the temperature field can be obtained from a previous heat transfer analysis. To define nonuniform distributed concentration fluxes, the variation of the flux magnitude throughout a step can be defined in user subroutine DFLUX. For isotropic diffusivity only one value of diffusivity is needed at each concentration, temperature, and field variable value.

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Spurious ana,ysis due to small time increments In transient mass diffusion analysis with workout diet elements there is a relationship between the minimum usable time step and the element size. You can create a body concentration flux load to define a concentration flux over a body in a mass diffusion analysis. Type History data. The first step establishes an initial steady-state concentration distribution of a diffusing material. Material options Both diffusivity Diffusivity and solubility Solubility must be defined in a mass diffusion analysis. Defining general temperature-driven mass diffusion.

In the second step equivalent pressure stresses are read from a fully diffusoon temperature-displacement analysis and the transient mass diffusion response is obtained for the case of mechanical loading of the body. Select Fixed at current magnitude if you want to fix the mass concentration magnitude at its final value from the previous general step. Toggle on Use temperature-dependent data to define the pressure stress factor as a function of temperature. Regardless of the manner in which they are specified, pressures should be entered according to the Abaqus convention that equivalent pressure stresses are positive when they are compressive.

## Optional parameters

Time-dependent temperature variations are possible with either approach. In practical cases the dependence on concentration is abxqus strong, so the nonsymmetric matrix storage and solution scheme is invoked automatically when a mass diffusion analysis is performed see Defining an analysis. An example problem that follows this template is Thermomechanical diffusion of hydrogen in a bending beam. An extended form of Fick's law can be used as an alternative to the general chemical potential:. The units of concentration are commonly given as parts per million P.

Select a Law option to specify how you want to define diffusivity behavior: Select General to choose general mass diffusion behavior. Specifying time-dependent concentration fluxes The magnitude of a concentrated or a distributed concentration flux can be controlled by referring to an amplitude curve see Amplitude Curves. If a steady-state analysis step is to be followed by a transient analysis step and total time is used in amplitude definitions Amplitude Curvesthe time period should be defined to be negligibly small in the steady-state step. By default, the analysis will end when the given time period has been completed. Loads Concentration fluxes are the only loads that can be applied in a mass diffusion analysis step. Predefined temperatures, equivalent pressure stresses, and field variables can be specified in a mass diffusion analysis. Click OK to save your data and to exit the editor.

Diffusivity defines the diffusion, or movement, of one material through another. Anslysis predefined field variables You can specify values of predefined field variables during a mass diffusion analysis. Units The units of concentration are commonly given as parts per million P. The Method option appears in the editor only if both methods are valid for the selected step.

## Governing equations

Directional dependence of diffusivity. Use both of the following options to specify diffusion driven by the extended form of Fick's law:. Select Fick to choose Fick's diffusion law. Alternatively, you can specify that the analysis will end when steady state is reached or the time period ends, whichever comes first.

An analyeis problem that follows this template is Thermomechanical diffusion of hydrogen in a bending beam. Enter the following data in the Data table: Solubility Solubility. VUHARD : Define the yield surface size and hardening parameters for isotropic plasticity or combined hardening models. Prescribing temperatures Temperatures are applied to nodes in temperature-driven mass diffusion analyses by defining a temperature field; absolute zero on the temperature scale used is defined as described in Specifying the value of absolute zero. For isotropic diffusion.

Diffusivity is the relationship between the concentration flux,of the diffusing material and the gradient of the chemical potential that is assumed to drive the mass diffusion process.

To describe pressure-driven mass diffusion, select Pressure Effect from the Suboptions menu.

Magnitude data that you enter in the editor are passed into the user subroutine. Orthotropic diffusivity.

The concentration flux,then has units of ; and the concentration volumetric flux,has units of. These values affect only field-variable-dependent material properties, if any.

Transient mass diffusion analysis can be terminated by completing a specified time period, or it can be continued until steady-state conditions are reached.

Generally there is no upper limit on the time increment because the integration procedure is unconditionally stable unless nonlinearities cause numerical problems. Automatic or fixed time incrementation can be abauqs for transient analysis. If different magnitude variations are needed for different fluxes, the flux definitions can be repeated, with each referring to its own amplitude curve. This time scale is often convenient for output identification and for specifying prescribed normalized concentrations and fluxes with varying magnitudes. Modifying or removing concentration fluxes Concentrated or distributed concentration fluxes can be added, modified, or removed as described in About loads. Spurious oscillations due to small time increments.

Click the arrow to the right of the Diffjsion field, and specify the directional dependence of the masx. Enter the following data in the Data table: Solubility Solubility. Diffusivity is the relationship between the concentration flux,of the diffusing material and the gradient of the chemical potential that is assumed to drive the mass diffusion process. Specifying time-dependent concentration fluxes The magnitude of a concentrated or a distributed concentration flux can be controlled by referring to an amplitude curve see Amplitude Curves. Automatic or fixed time incrementation can be used for transient analysis. Input File Usage Use the following option to specify a concentrated concentration flux at a node: CFLUX node number or node set namedegree of freedomconcentrated flux magnitude Use the following option to specify a distributed concentration flux acting on entire elements body flux or just on element faces surface flux : DFLUX element number or element set nameBF or S ndistributed flux magnitude. Related Topics.

## Fick's law

An example problem that follows this template is Thermomechanical diffusion of hydrogen in a bending beam. Predefined fields Predefined abaqks, equivalent pressure stresses, and field variables can be specified in a mass diffusion analysis. The temperature-driven diffusion term in Fick's law is recovered in the general relation if. Click the arrows to the right of the Number of field variables field to increase or decrease the number of field variables included in the definition of the pressure stress factor.

NNC All normalized concentration values at a node. Input File Usage:. Concentrated or distributed concentration fluxes can mass diffusion analysis abaqus user added, modified, or removed as described in About loads. Toggle on Use temperature-dependent data to define solubility as a function of temperature. Note: You can specify the Soret effect factor only if you select general mass diffusion behavior in the diffusivity definition. The diffusion problem is defined from the requirement of mass conservation for the diffusing phase:.

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Directional dependence of diffusivity. Use both of the following options to specify general temperature-driven mass diffusion:. Related Topics. Use both of the following options to specify diffusion driven by the extended form of Fick's law:. Defining pressure-driven mass diffusion. MFLM Magnitude of the concentration flux vector.

Note: You can specify only one user subroutine file in the job editor; if your analysis involves more than one user subroutine, diffuusion must combine the user subroutines into one file and then specify that file. FLOW : Define nonuniform seepage coefficient and associated sink pore pressure for consolidation analysis. The Magnitude field is unavailable if you are creating the boundary condition in the initial step. Defining diffusivity.

Alternatively, you can specify that the analysis will end when steady state is reached or the time period ends, whichever comes first. Click OK to save your data and to exit the editor. The following template is representative of a three-step mass diffusion analysis. Isotropic diffusivity. Specifying the value of absolute zero.

## Fick's law

The two terms in this equation describe the normalized concentration and temperature-driven diffusion, respectively. Loads Concentration fluxes are the only loads that can be applied in a mass diffusion analysis step. A listing and explanations of associated utility routines also appear in that guide. To describe pressure-driven mass diffusion, select Pressure Effect from the Suboptions menu.

Predefined fields Predefined temperatures, equivalent pressure stresses, and field variables can be specified in a mass diffusion analysis. In transient analysis using first-order elements the solubility terms are lumped, which eliminates such abaqus user but can lead to locally inaccurate solutions for small time increments. A mass diffusion analysis: models the transient or steady-state diffusion of one material through another, such as the diffusion of hydrogen through a metal. Spurious oscillations due to small time increments. If a steady-state analysis step is to be followed by a transient analysis step and total time is used in amplitude definitions Amplitude Curvesthe time period should be defined to be negligibly small in the steady-state step.

TEMP Magnitude of the applied temperature field. The Soret effect factor,governs uer mass diffusion. Toggle on Use temperature-dependent data to define the pressure stress factor as a function of temperature. In the final step a temperature field is read from a fully coupled temperature-displacement analysis and the transient mass diffusion response is calculated for the case of heating and cooling the body in which diffusion occurs. To establish the relationship between Fick's law and the general chemical potential, we write Fick's law as.

The analysia terms in this equation describe the normalized concentration and temperature-driven diffusion, respectively. If smaller time increments are required, a finer mesh should be used in regions where the normalized concentration changes occur. Creating and modifying prescribed conditions. Whenever D, or depends on concentration, the problem becomes nonlinear and the system of equations becomes nonsymmetric. You can create a body concentration flux load to define a concentration flux over a body in a mass diffusion analysis. By default, the analysis will end when the given time period has been completed.

Modifying or removing concentration fluxes Concentrated or distributed concentration fluxes can be mass diffusion analysis abaqus user, modified, or removed as described diffysion About loads. Time integration in transient diffusion analysis is done with the backward Euler method also referred to as the modified Crank-Nicholson operator. If automatic stepping is used, this value should be a reasonable suggestion for the initial step and will be adjusted as necessary.

MFL Magnitude and components of the concentration flux vector excluding the terms due to pressure and temperature gradients. By default, the analysis will end when the given time period has been completed.

This method is unconditionally stable for linear problems. A simple guideline is.

A column labeled Temp appears in the Data table. For more details on time scales and time stepping, see Defining an analysis.

Steady-state mass diffusion analysis provides the steady-state solution directly: the rate of change of concentration with respect to time is omitted from the governing diffusion equation in steady-state analysis.

For orthotropic diffusivity three values of diffusivity, are needed at each concentration, temperature, and field variable value.

The governing equations for mass diffusion are an extension of Fick's equations: they allow for nonuniform solubility of the diffusing substance in the base material and for mass diffusion driven by gradients of temperature and pressure. Units The units of concentration are commonly given as parts per million P. As a result, any amplitude reference in the flux definition is also ignored. Predefined temperatures, equivalent pressure stresses, and field variables can be specified in a mass diffusion analysis. Generally there is no upper limit on the time increment because the integration procedure is unconditionally stable unless nonlinearities cause numerical problems. Steady state is defined as the point in time when all normalized concentrations change at less than a user-defined rate.

Loads Concentration fluxes are the only loads that can be applied in a mass diffusion analysis step. Defining a concentrated concentration flux. The governing equations for mass diffusion are an extension of Fick's equations: they allow for nonuniform solubility of the diffusing substance in the base material and for mass diffusion driven by gradients of temperature and pressure. Prescribing temperatures Temperatures are applied to nodes in temperature-driven mass diffusion analyses by defining a temperature field; absolute zero on the temperature scale used is defined as described in Specifying the value of absolute zero.

Additional reference. Spurious oscillations due to small time increments. Transient mass diffusion analysis can be terminated by completing a specified time period, or it can be continued until steady-state conditions are reached. All reaction flux values conjugate to normalized concentration.

Related Topics. MFL Magnitude and components of the concentration flux vector excluding the terms due to pressure and temperature gradients.

Amount of solute in the model or specified element set, calculated as the sum of ESOL over all the elements in the model or set.

D11, D22, and D33 Orthotropic diffusivity terms.

Defining a surface concentration flux.

ORIENT : Provide an orientation for defining local material directions or local directions for kinematic coupling constraints or local rigid body directions for inertia relief. Generally there is no upper limit on the time increment because the integration procedure is unconditionally stable unless nonlinearities cause numerical problems.

Defining solubility. UAMP : Specify amplitudes. Note: You can specify only one user subroutine file in the job editor; if your analysis involves more than one user subroutine, you must combine the user subroutines into one file and then specify that file. Anisotropic diffusivity.

D11, D22, and Analysis abaqus user Orthotropic diffusivity terms. If you usfr fixed time incrementation, fixed time increments equal to the size of the user-specified initial time increment,will be used. Predefined fields Predefined temperatures, equivalent pressure stresses, and field variables can be specified in a mass diffusion analysis. Alternatively, the temperature field can be obtained from a previous heat transfer analysis. Prescribing equivalent pressure stresses.

Toggle on Use temperature-dependent data to define solubility as a function of temperature. Diffusiob Magnitude of the concentration flux vector. VUEL : Define an element. In practical cases the dependence on concentration is quite strong, so the nonsymmetric matrix storage and solution scheme is invoked automatically when a mass diffusion analysis is performed see Defining an analysis. Information on writing user subroutines and detailed descriptions of each subroutine appear online in the Abaqus User Subroutines Guide.

You can create a body concentration flux uuser to define a concentration flux over a body in a mass diffusion analysis. Defining pressure-driven mass diffusion. This value is used only for automatic time incrementation. Enter the Job module and display the job editor for the analysis job of interest. Nodal variables: CFL.

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Defining general temperature-driven mass diffusion. If a Distribution field appears in the editor, click the arrow to the right of user field, and select one of the following: Select Uniform to define a uniform boundary condition. Both diffusivity Diffusivity and solubility Solubility must be defined in a mass diffusion analysis. Steady state is defined as the point in time when all normalized concentrations change at less than a user-defined rate. GAPCON : Define conductance between contact surfaces or nodes in a fully coupled temperature-displacement analysis, a fully coupled thermal-electrical-structural analysis, or a pure heat transfer analysis.

Transient analysis Time integration in transient diffusion analysis naalysis done with the backward Euler method also referred to as the modified Crank-Nicholson operator. Toggle on Use temperature-dependent data to define diffusivity data as a function of temperature. The concentration flux,then has units of ; and the concentration volumetric flux,has units of. Steady state is defined as the point in time when all normalized concentrations change at less than a user-defined rate.

For isotropic diffusion.

The Soret effect factor,governs temperature-driven mass diffusion. Optionally, a Soret effect factor and a pressure stress factor can be defined to introduce mass diffusion caused by temperature and pressure gradients, respectively.

Click the arrows to the right of the Number of field variables field to increase or decrease the number of field variables included in the definition of the Soret effect factor. Anisotropic diffusivity.

TEMP Magnitude of the applied temperature field.

If a Method field abaqud toward the top of the editor, click the arrow to the right of the field, and select one of the following: Select Specify magnitude if you want to specify a value for the mass concentration. A listing and explanations of associated utility routines also appear in that guide.

The Method option appears in the editor only if both methods are valid for the selected step. Abaqus user example problem that follows this template is Thermomechanical diffusion of hydrogen in a bending beam. Optionally, a Soret effect factor and a pressure stress factor can be defined to introduce mass diffusion caused by temperature and pressure gradients, respectively. User subroutines allow advanced users to customize a wide variety of Abaqus capabilities. Defining a body concentration flux. Specifying the value of absolute zero. Alternatively, the temperature field can be obtained from a previous heat transfer analysis.

This option is valid only if you selected Diffusioh in Step 3. By default, the analysis will end when the given time period has been completed. Magnitude and components of the concentration flux vector excluding the terms due to pressure and temperature gradients. If time increments smaller than this value are used, spurious oscillations can appear in the solution. Diffusion is assumed to be driven by the gradient of a general chemical potential, which gives the behavior. In the second step equivalent pressure stresses are read from a fully coupled temperature-displacement analysis and the transient mass diffusion response is obtained for the case of mechanical loading of the body. The units of concentration are commonly given as parts per million P.

Input Mass diffusion analysis abaqus user Usage:. Click the arrows to the right of the Number of field variables field to increase or decrease the number of field variables included in the definition of the Soret effect factor. Amount of solute in the element, calculated as the sum of ISOL over all the element integration points. Element integration point variables: CONC. An extended form of Fick's law can also be chosen by specifying a nonzero value for :.

To establish the relationship between Fick's law and the general chemical potential, we write Fick's law as. Note: You can specify the Soret effect factor only if you select general mass diffusion behavior in the diffusivity definition. Configuring a mass diffusion procedure. Creating and modifying prescribed conditions. Equilibrium requires the partial pressure to be continuous across an interface, so normalized concentration will be continuous as well. A simple guideline is.

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For isotropic diffusion. Temperatures are applied to nodes in temperature-driven mass diffusion analyses usr defining a temperature field; absolute zero on the temperature scale used is defined as described in Specifying the value of absolute zero. Amount of solute in the element, calculated as the sum of ISOL over all the element integration points. Transient analysis. All reaction flux values conjugate to normalized concentration. Use the following input to define a distributed concentration flux acting on entire elements body flux or just on element faces surface flux :.

Defining general temperature-driven mass diffusion.

Automatic or fixed time incrementation can be used for transient analysis.

This option is valid only if you selected General in Step 3.

UTRS : Define a reduced time shift function for a viscoelastic material.

Configuring a mass diffusion procedure.

In the final step a temperature field is read from a fully coupled temperature-displacement analysis and the transient mass diffusion response is calculated for the case of heating and cooling the body in which diffusion occurs. Specifying the value of absolute zero.

If different magnitude variations are needed for different fluxes, the flux definitions can be repeated, with each referring to its own amplitude curve. Mass diffusion analysis abaqus user temperature variations are maass with either approach. The automatic time incrementation scheme is generally preferred because the response is usually simple diffusion: the rate of change of normalized concentration varies widely during the step and requires different time increments to maintain accuracy in the time integration. In nonlinear cases iteration may be necessary to achieve a converged solution. Click OK to close the Edit Material dialog box. The concentration flux,then has units of ; and the concentration volumetric flux,has units of. Equilibrium requires the partial pressure to be continuous across an interface, so normalized concentration will be continuous as well.

For isotropic diffusion. If you selected the Uniform or analytical field distribution option, perform the following steps:. Related Topics. Orthotropic diffusivity.

Diffusion is assumed to be driven by the gradient of a general chemical potential, which gives the behavior. The normalized concentration-driven diffusion term is identical to that given in the general relation. Time-dependent temperature variations are possible with either approach. As a result, any amplitude reference in the flux definition is also ignored. Level Step.

Set this parameter equal to the masss normalized concentration change to be allowed in an increment. Predefined fields. In transient analysis using first-order elements the solubility terms are lumped, which eliminates such oscillations but can lead to locally inaccurate solutions for small time increments. Modifying or removing concentration fluxes. For specific details on prescribing temperatures, see Predefined temperature.

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The diffusivity,abqqus units ofwhere T is time. To describe pressure-driven mass diffusion, select Pressure Effect from the Suboptions menu. Type User data. Input File Usage Use the following option to specify a concentrated concentration flux at a node: CFLUX node number or node set namedegree of freedomconcentrated flux magnitude Use the following option to specify a distributed concentration flux acting on entire elements body flux or just on element faces surface flux : DFLUX element number or element set nameBF or S ndistributed flux magnitude. This time scale is often convenient for output identification and for specifying prescribed normalized concentrations and fluxes with varying magnitudes.

Use the following option to mass diffusion analysis abaqus user a concentrated concentration flux at a node:. The units of the pressure stress factor areand the units of equivalent abaqs stress are. Time-dependent temperature variations are possible with either approach. Defining solubility. These values affect only field-variable-dependent material properties, if any. In transient mass diffusion analysis with second-order elements there is a relationship between the minimum usable time step and the element size. When all nodal normalized concentrations are changing at less than this rate, the solution terminates.

Initial conditions. The normalized concentration-driven diffusion term is identical to that given in the general relation. In practical cases the dependence on concentration is quite strong, so the nonsymmetric matrix storage and solution scheme is invoked automatically when a mass diffusion analysis is performed see Defining an analysis. Toggle on Use temperature-dependent data to define diffusivity data as a function of temperature. Click OK to save your data and to exit the editor.

See Predefined field variables.

Load module: Create Load : choose Mass diffusion for the Category and Concentrated concentration fluxSurface concentration fluxor Body concentration flux for the Types for Selected Step. Amount of solute in the element, calculated as the sum of ISOL over all the element integration points.

In the final step a temperature field is read from a fully coupled temperature-displacement analysis and the transient mass diffusion response is calculated for the case of heating and cooling the body in which diffusion occurs.

Defining a surface concentration flux.

RFL n. For specific details on prescribing equivalent pressure stresses, see Predefined pressure stress. Diffusion is assumed to be driven by diffysion gradient of a general chemical potential, which gives the behavior. Steady-state analysis Steady-state mass diffusion analysis provides the steady-state solution directly: the rate of change of concentration with respect to time is omitted from the governing diffusion equation in steady-state analysis. The normalized concentration-driven diffusion term is identical to that given in the general relation.

The magnitude of a concentrated or a distributed concentration flux can be controlled by referring to an amplitude curve see Amplitude Curves. Orthotropic diffusivity. Field n Predefined field variables. Input file template The following template is representative of a three-step mass diffusion analysis. In transient mass diffusion analysis with second-order elements there is a relationship between the minimum usable time step and the element size. VUEL : Define an element. The Magnitude field is unavailable if you are creating the boundary condition in the initial step.

A simple guideline is. Diffusive behavior provides the following general chemical potential:. Diffusoon diffusion analysis. The temperature-driven diffusion term in Fick's law is recovered in the general relation if. To define nonuniform distributed concentration fluxes, the variation of the flux magnitude throughout a step can be defined in user subroutine DFLUX.

Temperatures are applied to nodes in temperature-driven mass diffusion analyses by defining a temperature field; analysis abaqus zero on the temperature scale used is defined as described in Specifying the value of absolute zero. Predefined temperatures, equivalent pressure stresses, and field variables can be specified in a mass diffusion analysis. Mass diffusion behavior is often described by Fick's law Crank, :. Fluxes at the nodes of the element caused by mass diffusion in the element.

Therefore, when the mesh includes dissimilar materials that share nodes, the normalized concentration is continuous across the interface between the different materials. Optional parameters Data line mass diffusion analysis abaqus user define time stepping in a mass diffusion analysis. Use the following option to specify a concentrated concentration flux at a node:. Click the arrows to the right of the Number of field variables field to increase or decrease the number of field variables included in the definition of the Soret effect factor. Regardless of the manner in which they are specified, pressures should be entered according to the Abaqus convention that equivalent pressure stresses are positive when they are compressive. In transient mass diffusion analysis with second-order elements there is a relationship between the minimum usable time step and the element size.

Diffusivity is the relationship between the concentration flux,of the diffusing material and the gradient of the chemical potential that is assumed to absqus the mass diffusion process. The Method option appears in the editor only if both methods are valid for the selected step. Select Fixed at current magnitude if you want to fix the mass concentration magnitude at its final value from the previous general step. The Magnitude field is unavailable if you are creating the boundary condition in the initial step.

Note: You can specify the Soret effect factor only if you select general mass diffusion behavior in the diffusivity definition. Defining general temperature-driven mass diffusion. Defining diffusivity. Magnitude and components of the concentration flux vector excluding the terms due to pressure and temperature gradients.

If an expression other than Sievert's law defines the relationship between concentration and partial pressure for a diffusing material, solubility should be defined accordingly. Use all of the following options to specify general diffusion driven by gradients of temperature and pressure stress:. You can specify values of predefined field variables during a mass diffusion analysis. Defining diffusivity. This method is unconditionally stable for linear problems. The Magnitude field is unavailable if you are creating the boundary condition in the initial step.

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Material options Both diffusivity Diffusivity and solubility Solubility must be defined in a mass diffusion analysis. For specific details on prescribing temperatures, see Predefined abzqus. Values in the mass diffusion analysis abaqus user file are ignored at nodes that exist in the heat transfer analysis but not in the mass diffusion analysis, and the temperatures at nodes that did not exist in the heat transfer analysis will not be set by reading the results file. Defining diffusivity. Click OK to return to the Edit Material dialog box. Toggle on Use temperature-dependent data to define the pressure stress factor as a function of temperature. References CrankJ.

Amount of solute in the element, calculated as the doffusion of ISOL over all the element integration points. TEMP Magnitude analysis abaqus user the applied temperature field. Diffusivity: defines the diffusion or movement of one material through another, such as the diffusion of hydrogen through a metal. In the Data table, enter the applicable data: D Isotropic diffusivity. If desired, enter the mass concentration magnitude in the Magnitude field. If a Distribution field appears in the editor, click the arrow to the right of the field, and select one of the following: Select Uniform to define a uniform boundary condition.

Amount of solute in the model or specified element set, calculated as the sum of ESOL xnalysis all the elements in the model or set. To define nonuniform distributed concentration fluxes, the variation of the flux magnitude throughout a step can be defined in user subroutine DFLUX. The Soret effect factor,governs temperature-driven mass diffusion.

When all nodal normalized concentrations are changing at less than this rate, the solution terminates. Analusis Step. Minimum time increment allowed. RFL n. The normalized concentration-driven diffusion term is identical to that given in the general relation. If an expression other than Sievert's law defines the relationship between concentration and partial pressure for a diffusing material, solubility should be defined accordingly. In nonlinear cases iteration may be necessary to achieve a converged solution.

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Temperatures are applied to nodes in temperature-driven mass diffusion diffusiom by defining a temperature field; absolute zero on the temperature scale used is defined as described in Specifying the value of absolute zero. Steady-state analysis Steady-state mass diffusion analysis provides the steady-state solution directly: the rate of change of concentration with respect to time is omitted from the governing diffusion equation in steady-state analysis. Note: You can specify only one user subroutine file in the job editor; if your analysis involves more than one user subroutine, you must combine the user subroutines into one file and then specify that file. This option is used to control uncoupled transient or steady-state mass diffusion analysis. If time increments smaller than this value are used, spurious oscillations can appear in the solution. Configuring a mass diffusion procedure.

Input File Usage Use the following option to specify mass diffusion analysis abaqus user concentrated concentration flux at a node: CFLUX node number or node diiffusion namedegree of freedomconcentrated flux magnitude Use the following option to specify a distributed concentration flux acting on entire elements body flux or just on element faces surface flux : DFLUX element number or element set nameBF or S ndistributed flux magnitude.

In the final step a temperature field is read from a fully coupled temperature-displacement analysis and the transient mass diffusion response is calculated for the case of heating and cooling the body in which diffusion occurs.

Governing equations The governing equations for mass diffusion are an extension of Fick's equations: they allow for nonuniform solubility of the diffusing substance in the base material and for mass diffusion driven by gradients of temperature and pressure.

Values in the results file are ignored at nodes that exist in the mechanical analysis but not in the mass diffusion analysis, and the pressures at nodes that did not exist in the mechanical analysis will not be set by reading the results file. Abaqus Analysis User's Guide.

Therefore, when the mass diffusion analysis abaqus user includes dissimilar materials that share nodes, the normalized concentration is continuous across the interface between the different materials. The Soret effect factor,governs temperature-driven mass diffusion. Amount of solute in the model or specified element set, calculated as the sum of ESOL over all the elements in the model or set. Enter the Job module and display the job editor for the analysis job of interest. Magnitude and components of the concentration flux vector excluding the terms due to pressure and temperature gradients.

Spurious anapysis due to small time increments In transient mass diffusion analysis with second-order elements there is a relationship between the minimum usable time step analysis abaqus user the element size. By default, the analysis will end when the given time period has been completed. Mass diffusion behavior is often described by Fick's law Crank, :. In the Data table, enter the applicable data: D Isotropic diffusivity. Automatic or fixed time incrementation can be used for transient analysis. A simple guideline is.