autopdex.models.hyperelastic_steady_state_fos

autopdex.models.hyperelastic_steady_state_fos(strain_energy_fun, youngs_mod_fun, poisson_ratio_fun, mode, spacing, volume_load_fun=None)[source]

Constructs a first-order PDE system for given strain energy function

This function is based on equation (28) in https://doi.org/10.1002/nme.5951 and returns a function representing the first-order PDE system for steady-state hyperelasticity.

Parameters:

  • strain_energy_fun (function) – Function that returns the strain energy given the deformation gradient and Lame parameters.

  • youngs_mod_fun (function) – Function to compute Young’s modulus given spatial coordinates.

  • poisson_ratio_fun (function) – Function to compute Poisson’s ratio given spatial coordinates.

  • mode (str) – Specifies the mode of the elasticity problem. It can be ‘plain strain’ or ‘3d’.

  • spacing (float) – The spatial spacing parameter used to scale the augmented conditions.

  • volume_load_fun (function, optional) – Function to compute volume load given spatial coordinates. Default is None.

Returns:

A function that evaluates the first-order PDE system for hyperelasticity.

Return type:

function

Notes

  • The volume load function, if provided, must be volume-specific.

  • This models works for DOFs as a jnp.ndarray.