Info<< "Reading field DU\n" << endl;
    volVectorField DU
    (
        IOobject
        (
            "DU",
            runTime.timeName(),
            mesh,
            IOobject::MUST_READ,
            IOobject::AUTO_WRITE
        ),
        mesh
    );

//volTensorField gradDU = fvc::grad(DU);
    volTensorField gradDU
    (
        IOobject
        (
            "grad(DU)",
            runTime.timeName(),
            mesh,
            IOobject::NO_READ,
            IOobject::NO_WRITE
        ),
        mesh,
        dimensionedTensor("zero", dimless, tensor::zero)
    );
    surfaceVectorField snGradDU
    (
        IOobject
        (
            "snGrad(DU)",
            runTime.timeName(),
            mesh,
            IOobject::NO_READ,
            IOobject::NO_WRITE
        ),
        mesh,
        dimensionedVector("zero", dimless, vector::zero)
    );

    Info<< "Creating field U\n" << endl;
    volVectorField U
    (
        IOobject
        (
            "U",
            runTime.timeName(),
            mesh,
            IOobject::READ_IF_PRESENT,
            IOobject::AUTO_WRITE
        ),
        mesh,
        dimensionedVector("zero", dimLength, vector::zero)
    );

    volSymmTensorField DEpsilon
    (
        IOobject
        (
            "DEpsilon",
            runTime.timeName(),
            mesh,
            IOobject::READ_IF_PRESENT,
            IOobject::AUTO_WRITE
        ),
        mesh,
        dimensionedSymmTensor("zero", dimless, symmTensor::zero)
    );

    volSymmTensorField DSigma
    (
        IOobject
        (
            "DSigma",
            runTime.timeName(),
            mesh,
            IOobject::READ_IF_PRESENT,
            IOobject::AUTO_WRITE
        ),
        mesh,
        dimensionedSymmTensor("zero", dimForce/dimArea, symmTensor::zero)
    );

    volSymmTensorField epsilon
    (
        IOobject
        (
            "epsilon",
            runTime.timeName(),
            mesh,
            IOobject::READ_IF_PRESENT,
            IOobject::AUTO_WRITE
        ),
        mesh,
        dimensionedSymmTensor("zero", dimless, symmTensor::zero)
    );

    volSymmTensorField sigma
    (
        IOobject
        (
            "sigma",
            runTime.timeName(),
            mesh,
            IOobject::READ_IF_PRESENT,
            IOobject::AUTO_WRITE
        ),
        mesh,
        dimensionedSymmTensor("zero", dimForce/dimArea, symmTensor::zero)
    );

    volVectorField divDSigmaExp
    (
        IOobject
        (
            "divDSigmaExp",
            runTime.timeName(),
            mesh,
            IOobject::NO_READ,
            IOobject::NO_WRITE
        ),
        mesh,
        dimensionedVector("zero", dimForce/dimVolume, vector::zero)
    );

    constitutiveModel rheology(sigma, DU);
    //solidInterface interface(mesh, rheology);
    //solidInterface* interfacePtr = new solidInterface(mesh, rheology);

    surfaceVectorField traction
    (
        IOobject
        (
            "traction",
            runTime.timeName(),
            mesh,
            IOobject::NO_READ,
            IOobject::NO_WRITE
        ),
        mesh,
        dimensionedVector("zero", dimForce/dimArea, vector::zero)
    );

    // for aitken relaxation
    volVectorField aitkenDelta
    (
        IOobject
        (
            "aitkenDelta",
            runTime.timeName(),
            mesh,
            IOobject::NO_READ,
            IOobject::NO_WRITE
        ),
        mesh,
        dimensionedVector("zero", dimLength, vector::zero)
    );

    // aitken relaxation factor
    scalar aitkenInitialRes = 1.0;
    scalar aitkenTheta = 0.1;