OOF2: The Manual

B.2. Nonlinearity

The nonlinear solvers in OOF2 have been greatly improved in version 2.1. In Basic Solver mode, a nonlinear solver will be chosen automatically if the material properties are nonlinear. In Advanced mode, the nonlinear solver can be set to Newton, Picard, or None (indicating that a linear solver will be used). The nonlinear solvers are used to solve the finite element matrix equations both in static and time dependent problems.

The only nonlinear Material Property that is built into OOF2 is large strain elasticity (Mechanical:Elasticity:LargeStrain:Isotropic, Mechanical:Elasticity:LargeStrain:Anisotropic:Cubic, etc), which uses the rotationally invariant nonlinear strain. Other nonlinear Properties can be added. The OOFEXTENSIONS package, downloadable separately, contains easily modifiable examples of nonlinear properties.

(WARNING: Using Neumann boundary conditions expressed in normal/tangential coordinates for the force balance equation in the presence of large strains introduces nonlinearities which OOF2 does not yet handle correctly, whether or not large strain elasticity is being used.)

Nonlinear solvers are required when the Material Properties are functions of the Fields that are being solved for. OOF2 can solve nonlinearities that appear in the stiffness matrix (eg, elastic modulus, thermal conductivity) and right-hand side (eg, stress free strain, heat source) terms. It cannot solve nonlinearities that appear in a damping or mass terms (ie, multiplying the time derivatives of the Fields).