Available nonlinear algorithms

Prediction of the solution

By default, a nonlinear evolution problem uses the solution at the beginning of the time step, modified by applying Dirichlet boundary conditions, as the initial guess of the solution at the end of the time step, see below for details.

This can be changed by using the setPredictionPolicy method, as follows:

mechanics.setPredictionPolicy(
   {.strategy = PredictionStrategy::ELASTIC_PREDICTION});

Available strategies

Default prediction (PredictionStrategy::DEFAULT_PREDICTION)

By default, a nonlinear evolution problem uses the solution at the beginning of the time step, modified by applying Dirichlet boundary conditions, as the initial guess of the solution at the end of the time step.

Warning

In mechanics, this may lead to very high increments of the deformation gradients or the strain in the neighboring elements of boundaries where evolving displacements are imposed.

Elastic prediction (PredictionStrategy::ELASTIC_PREDICTION)

The ElasticPrediction strategy determines the increment of the displacement \(\Delta\,\mathbb{u}\) by solving the following linear system:

\[\mathbb{K}_{e}\,\cdot\,\Delta\,\mathbb{u} = \ets{\mathbb{F}_{e}}-\bts{\mathbb{F}_{i}}\]

where:

  • \(\mathbb{K}_{e}\) denotes the elastic stiffness matrix.

  • \(\bts{\mathbb{F}_{e}}\) denotes the external forces at the beginning of the time step.

  • \(\bts{\mathbb{F}_{i}}\) denotes the inner forces at the beginning of the time step.

  • \(\Delta\,\mathbb{u}\) is submitted to the the increment of the imposed Dirichlet boundary conditions.

Note

Although the wording explicitly refers to mechanics, this equation applies to all physics.