.. _auto_prony_analytical_solver:

*PRONYANALYTICALSOLVER*
=======================

Computes the analytical stress-strain response of an elastomer using a Prony series viscoelastic representation. Given Prony terms (shear relaxation coefficients g_i or β_i) and a prescribed strain rate or velocity, it integrates the constitutive equations over a user-defined time window to produce a predicted force-displacement or stress-strain curve. Use this worker to validate fitted Prony parameters against expected material behaviour before embedding them in an LS-DYNA deck.

When to use
-----------

Tagged: ``analytical_solution``, ``elastomer``, ``material_model``, ``prony``, ``relaxation``, ``simulation``, ``strain_rate``, ``viscoelastic``.

Inputs
------

.. list-table::
   :header-rows: 1
   :widths: 20 20 20 20 20 20

   * - Label
     - ID
     - Type
     - Default
     - Required
     - Description
   * - Dataset with Prony Terms
     - experiments
     - dataset
     - —
     - ✓
     - Dataset containing fitted Prony series terms; column names must begin with 'g' (shear relaxation moduli) or 'beta' (relaxation time constants) — one row per Prony term set to be evaluated.
   * - Strain-rate Input Type
     - strain_rate_input_type
     - select
     - strain-rate
     - ✓
     - Selects how the loading rate is specified: 'strain-rate' (dimensionless s⁻¹) or 'velocity' (length/time consistent with input curves); defaults to 'strain-rate'.
   * - Strain-rate or velocity
     - strain_rate
     - scalar
     - 1e-05
     - 
     - Numerical value of the strain rate (s⁻¹) or crosshead velocity (length/time) used to drive the analytical solution; units must match those of the Prony term curves (default 1×10⁻⁵).
   * - Initial Length
     - initial_length
     - scalar
     - 10.0
     - 
     - Gauge length of the specimen at t = 0 in the same length unit as the input curves; required for the Analytical method to convert velocity to strain (default 10.0 mm).
   * - Initial Velocity
     - initial_velocity
     - scalar
     - 0.0
     - 
     - Initial crosshead velocity at t = 0; set to 0.0 for a step strain-rate load, or supply a non-zero value when a velocity ramp is needed (default 0.0).
   * - Time Increment
     - time_increment
     - scalar
     - 0.001
     - 
     - Fixed time step Δt used for the analytical integration; choose a value small enough to resolve the shortest Prony relaxation time (default 0.001 s).
   * - Number of Timesteps
     - num_timesteps
     - scalar
     - 100
     - ✓
     - Total number of time steps to integrate; the simulation end-time equals num_timesteps × time_increment (required, default 100).

Outputs
-------

.. list-table::
   :header-rows: 1
   :widths: 20 20 20 20

   * - Label
     - ID
     - Type
     - Description
   * - Experiments with Analytical Solution
     - experiments
     - dataset
     - Augmented dataset containing the original Prony term rows plus computed analytical stress (or force) vs. time/strain columns, one result curve per input Prony term set.

Disciplines
-----------

- data.curve.transform
- engineering.material.calibration
- engineering.material.characterization

.. raw:: html

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   Auto-generated from <code>platform</code> schema. Worker id: <code>prony_analytical_solver</code>. Schema hash: <code>20fbdae6bf94</code>. Hand-curated docs in <code>workerexamples/</code> override this page when present.
   </p>