HTML is the primary format for the Abaqus documentation. The HTML manuals. This section contains information on using the Advanced Search options. Execution procedure for fetching sample input files. Products.

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A mass diffusion analysis: The governing equations for mass diffusion are an extension of Fick’s equations: Therefore, when the mesh includes dissimilar materials that share nodes, the normalized concentration is continuous across the interface between the different materials. For example, a diatomic gas that dissociates during diffusion can be described using Sievert’s law: Combining Sievert’s law with the definition of normalized concentration given earlier.

Equilibrium requires the partial pressure to be continuous across dcoumentation interface, so normalized concentration will be continuous as well.

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. The diffusion problem is defined from the requirement of mass conservation for the diffusing phase: Diffusion is assumed to be driven by the gradient of a general chemical potential, which gives the behavior.

Whenever D, or depends on concentration, the problem becomes nonlinear and the system of equations becomes nonsymmetric. Mass diffusion behavior is often described by Fick’s law Crank, The two terms in this equation describe the normalized concentration and temperature-driven diffusion, agaqus. The normalized concentration-driven diffusion term is identical to that given in the general relation.

The temperature-driven diffusion term in Fick’s law is recovered in the general relation if. An extended form of Fick’s law can also be chosen by specifying a nonzero value for: The units of concentration are commonly given as parts per million P. On the basis of the applicability of Sievert’s law to the mass diffusion, the units of solubility arewhere F is force and L is length. The units of the Soret effect factor are. The units of the pressure stress factor areand the units of equivalent pressure stress are.

The diffusivity,has units ofwhere T is time. The concentration flux,then has units of ; and the concentration volumetric flux,has units of. Steady-state mass diffusion analysis provides the steady-state solution directly: In nonlinear cases iteration may be necessary to achieve a converged solution. This time scale is often convenient for output identification and for specifying prescribed normalized concentrations and fluxes with varying magnitudes. Time integration in transient diffusion analysis is done with the backward Euler method also referred to as the modified Crank-Nicholson operator.

This method is unconditionally stable for linear problems. Automatic or fixed time incrementation can be used for transient analysis.

The automatic abaqsu incrementation scheme is generally preferred because the response is usually simple diffusion: In transient mass diffusion analysis with second-order elements there is a relationship between the minimum usable time step and the element size.

A simple guideline is. 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.

If smaller time increments are required, a finer mesh should be used in regions where the normalized documentationn changes occur. Generally there is no upper limit on the time increment because the integration procedure is unconditionally stable unless nonlinearities cause numerical problems. The automatic time incrementation scheme for abaqqus diffusion problems is based on the user-specified maximum normalized concentration change allowed at any node during an increment.

If you choose fixed time incrementation, fixed time increments equal to the size of the documentatuon initial time increment,will be used. FixedIncrement size: Transient mass diffusion analysis can be terminated by completing a specified time period, or it can be continued until steady-state conditions are reached.

By default, the analysis will end when the given time period has been completed. Alternatively, you can specify that the analysis will end when steady state is reached or the time period ends, whichever comes first.

Steady state is defined as the point documetnation time when all normalized concentrations change at less than a user-defined rate. End step when normalized concentration change rate is less than.

Such values can be specified as functions of time.

## Abaqus 6.9 Supported Platforms & Products

Use the following option to specify a distributed concentration flux acting on entire elements body flux or just on element faces surface flux:. Use the following input to define a distributed concentration flux acting on entire elements body flux or just on element faces surface flux:. Uniform or select an analytical field, Magnitude: If different magnitude variations are needed for different fluxes, the flux documenfation can be repeated, with each referring to its own amplitude curve.

To define nonuniform distributed concentration fluxes, the variation of the flux magnitude throughout a step can be defined in user subroutine DFLUX.

### Execution procedure for fetching sample input files

If a reference flux magnitude is specified directly, it will be ignored. As a result, any amplitude reference in the flux definition is also ignored. Predefined temperatures, equivalent pressure stresses, and field variables can be documentatjon in a mass diffusion analysis. Alternatively, the temperature field can be obtained from a previous heat transfer analysis. Time-dependent temperature variations are possible with either approach. Values in the results file are ignored doxumentation 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.

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. 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.

Documenttion values affect only field-variable-dependent material properties, if any. Optionally, a Soret effect factor and a pressure stress factor can be defined to introduce mass diffusion caused by temperature and pressure gradients, respectively. The use of Fick’s law also introduces temperature-driven mass diffusion since a Soret effect factor is calculated automatically. Element integration point variables: Amount of solute at the integration point, calculated as the product agaqus the mass concentration and the integration point volume.

Magnitude and components of the concentration flux vector excluding the terms due to pressure and temperature gradients. Amount of solute in the element, calculated as the sum of ISOL over all the element integration points. 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.

The following template is representative of a three-step mass diffusion analysis. The first step establishes an initial steady-state concentration distribution of a diffusing material.

In the second step equivalent pressure stresses are read from a fully coupled dochmentation analysis and the transient mass diffusion response is obtained for the case of mechanical loading of the body. In the documenttaion 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 abaqu which diffusion occurs.

Abaqus Analysis User’s Manual. Spurious oscillations due to small time increments. Ending a transient analysis. Use the following option to end the analysis when the time period is reached: Use the following options: Use the following option to specify a concentrated concentration flux at a node: Use the following input to define a concentrated concentration flux at a node: Modifying or removing concentration fluxes.

Specifying time-dependent concentration fluxes. Defining nonuniform distributed concentration fluxes in a user subroutine. Use the following option to define a nonuniform distributed concentration body flux: Use the following input to define a nonuniform distributed concentration body flux: User-defined Use the following input to define a nonuniform distributed concentration surface flux: Prescribing equivalent pressure stresses.

Specifying predefined field variables. Whole or partial model cocumentation Fluxes at the nodes of the element caused by mass diffusion in the element. All reaction flux values conjugate to normalized concentration.