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¶
| 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¶
| 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
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