GentElastic

This page documents the Gent-Flory elastic law for microgel behaviour. The runtime type is:

GentElastic

User Guide

What it computes

The law updates the deformation gradient and evaluates the following stress at cell centres or faces:

J     = det(F)
B     = symm(F & F.T())
C     = symm(F.T() & F)
omega = Vs/Na
Nv    = N/omega

sigma = kb*temperature*(Nv/J)
      * ((ilim/(ilim - tr(B) + 3))*C - I)

Here Na is fixed at 6.022141e23 and dimensionless, while kb is fixed at 1.38064852e-23 with dimensions [1 2 -2 -1 0 0 0]. The nonlinear stress does not use E, nu, mu or K; those quantities are used by updateF() when the solid model enforces a linear response and by impK().

The volSymmTensorField and surfaceSymmTensorField correct() overloads are implemented. The inherited pointSymmTensorField overload aborts with notImplemented. On OpenFOAM.com and OpenFOAM.org, the inherited CompactListList overload also exists and aborts with notImplemented; that interface is excluded from foam-extend by #ifndef FOAMEXTEND.

Model options

The top-level planeStress switch is also required. It changes the K used for linear enforcement and impK(), but it does not change the nonlinear stress expression. Although the base constructor reads solvePressureEqn and pressureSmoothingScaleFactor, this law never calls updateSigmaHyd(), so neither option changes its computed stress.

No range or positivity checks are applied to the material entries. In particular, the denominator ilim - tr(B) + 3 is not guarded against zero.

Recommended dictionary setup

Illustrative setup for a water-swollen microgel:

planeStress     no;

mechanical
(
    waterSwollenMicrogel
    {
        type            GentElastic;
        rho             rho [1 -3 0 0 0 0 0] 1000;
        E               E [1 -1 -2 0 0 0 0] 3e4;
        nu              nu [0 0 0 0 0 0 0] 0.49;
        temperature     temperature [0 0 0 1 0 0 0] 298;
        ilim            ilim [0 0 0 0 0 0 0] 100;
        Vs              Vs [0 3 0 0 0 0 0] 1.8e-5;
        N               N [0 0 0 0 0 0 0] 1e-4;

        // Optional base-class entries
        // regionName                    region0;
        // solvePressureEqn              no;
        // pressureSmoothingScaleFactor  100;
    }
);

Field glossary

• F_, Ff_: total deformation gradients at cell centres and faces. They are read if present and written for restart.
• relF_, relFf_: relative deformation gradients maintained by updateF().
• mu_<material>, K_<material>: cell fields populated from the uniform derived moduli when the volume correction is used.
• muf_<material>, Kf_<material>: corresponding face fields populated by the surface correction.
• impK: implicit stiffness field returned to the solid model, with value (4/3)*mu + K unless an impK field is read from the current time.
• sigma: stress field supplied by the solid model and overwritten by correct().

Developer Notes

Class role

GentElastic derives directly from mechanicalLaw and is registered in the nonLinGeomMechLaw runtime selection table. It stores ten constant dimensionedScalar members: E_, nu_, mu_, temperature_, ilim_, K_, Na_, kb_, omega_ and N_.

The class itself has no fork guards. The inherited quadrature-point interface is guarded by #ifndef FOAMEXTEND. GentElastic.C appears in both Make/files.openfoam and Make/files.foamextend.

Construction

The base constructor first reads or inserts solvePressureEqn and pressureSmoothingScaleFactor, then reads regionName or detects solid or region0. Failure to find a base mesh region is fatal.

The derived constructor then performs these operations in order:

1. Reads E and nu, and derives mu = E/(2*(1 + nu)).
2. Reads temperature and ilim.

3. Reads the top-level planeStress switch and derives K:

   K = nu*E/((1 + nu)*(1 - nu))     + (2/3)*mu  // plane stress
   K = nu*E/((1 + nu)*(1 - 2*nu))   + (2/3)*mu  // otherwise
   

4. Sets the fixed values of Na and kb.
5. Reads Vs and calculates omega = Vs/Na.
6. Reads N and replaces it internally by N/omega.

Missing or dimensionally inconsistent required entries cause dictionary or dimension errors. The constructor contains no explicit material validation and emits no law-specific fatal error or warning. If solvePressureEqn is enabled, the base constructor only prints an informational message.

Key methods

• impK() returns a cell field equal to (4/3)*mu + K. It is the diffusivity of the solid model's implicit Laplacian term and affects the outer-iteration convergence rate rather than the converged answer.
• Both implemented correct() methods call updateF(sigma, mu, K) first. If it returns true, the linearised stress supplied by updateF() is kept. Otherwise they evaluate the Gent-Flory expression above using F or Ff. updateF() aborts for non-incremental updated-Lagrangian use or an unknown nonlinear-geometry type, and warns when linearity is enforced for stability.
• materialTangent() is not overridden. The inherited implementation aborts with notImplemented, so solid models that request a material tangent cannot use this law.
• setRestart() sets both F and Ff to AUTO_WRITE, constructing either field if it has not already been used.

Extension points

A related law can copy this class, replace both correct() expressions, and update the dimensionedScalar inputs and impK() linearisation. It must use a new TypeName, register in the nonLinGeomMechLaw table, and be added to both build lists when it supports all forks. Implement the point, quadrature-point and material-tangent interfaces if the target solid models require them.

The source is at GentElastic.C.

Tutorials

No tutorial currently selects the GentElastic runtime type.