Examples

Below are examples illustrating Simcoon’s main features. These examples are designed to serve as tutorials. In that sense, an effort is made to keep the scripts simple and executable with a low computational cost.

Analysis and processing examples

Below are examples illustrating Simcoon’s capabilities for simulating mechanical and thermomechanical responses and post-processing results.

Increment size convergence study

Effective properties of a cubic material

Numerical vs Analytical Eshelby Tensor Comparison

Parameter Identification for Mooney-Rivlin Hyperelastic Material

Comparison of objective rates

Continuum Mechanics Examples

Below are examples illustrating Simcoon’s main features. These examples are designed to serve as tutorials. In that sense, an effort is made to keep the scripts simple and executable with a low computational cost.

This gallery contains examples demonstrating:

Constitutive relations - Building stiffness and compliance tensors for various material symmetries
Stress measures - Converting between different stress measures (Cauchy, PK1, PK2, etc.)
Rotation operations - Rotating tensors and vectors
Yield criteria - von Mises, Tresca, Drucker, and Hill anisotropic criteria

Constitutive Library Examples

A Neo-Hookean material with the Tensor API

Rotation library Examples

Stress transfer: Cauchy → PKI/PKII/Kirchhoff

Stress transfer library examples

Tensor2 and Tensor4 Examples

Yield Criteria Examples

Heterogeneous materials simulation

Below are examples illustrating Simcoon’s capabilities for simulating heterogeneous materials.

This gallery contains examples demonstrating:

Eshelby tensors - Computing Eshelby and Hill interaction tensors for various inclusion shapes
Micromechanics - Effective properties using Mori-Tanaka and self-consistent schemes, effect of volume fraction and aspect ratio

Composite Parameter Identification using Mori-Tanaka and Self-Consistent

Micromechanics Examples

Eshelby Tensor Examples

2 phase composite homogenization example

Hyperelasticity

Below are examples illustrating Simcoon’s capabilities for simulating materials exhibiting hyperelasticity.

Hyperelastic models - use the API

Hyperelastic models - use the umat

Mooney-Rivlin identification with the MOORI UMAT and the simcoon API

Parameter identification examples

Below are examples illustrating Simcoon’s parameter-identification workflow: calibrating constitutive-model parameters from experimental data with the identification API (sim.identification and sim.calc_cost) on top of the material-point solver and homogenization tools.

This gallery contains examples demonstrating:

Chaboche cyclic plasticity - Identifying 7 elasto-plastic parameters (EPCHA UMAT) from cyclic uniaxial tests, with an NMSE-per-response cost

Note

Two related hyperelastic identification examples live in other galleries: analysis/hyperelastic_parameter_identification.py (hand-rolled analytical stress + manual scipy/sklearn cost) and hyperelasticity/hyperelastic_umat_identification.py (the deployable MOORI UMAT driven through sim.solver with the identification API).

Chaboche Cyclic Plasticity Identification

Mechanical Constitutive Laws

Below are examples illustrating Simcoon’s mechanical constitutive laws library.

Elastic Models:

ELISO - Isotropic elasticity
ELIST - Transversely isotropic elasticity
ELORT - Orthotropic elasticity

Plasticity Models:

EPICP - Plasticity with isotropic hardening (power-law)
EPKCP - Plasticity with combined isotropic and kinematic hardening
EPCHA - Plasticity with Chaboche hardening (cyclic plasticity)

Viscoelastic Models:

ZENER - Poynting-Thomson (Zener) model
ZENER_N - Generalized Zener model (N Kelvin branches)
PRONY_N - Prony series (Generalized Maxwell)

Shape Memory Alloys:

SMA_TR - Superelastic model (transformation only)

Isotropic elasticity examples

Transversely Isotropic Elasticity Example

Orthotropic Elasticity Example

Plasticity with Chaboche Hardening Example

Plasticity with isotropic hardening example

Plasticity with Isotropic and Kinematic Hardening Example

Prony Series Viscoelastic Model (Generalized Maxwell)

Shape Memory Alloy - Superelastic Model

Zener viscoelastic model

Generalized Zener model (N Kelvin branches)

Thermomechanical Constitutive Laws

Below are examples illustrating Simcoon’s thermomechanical constitutive laws. These examples extend the mechanical models with thermal coupling, including temperature evolution, thermal expansion, and dissipation.

Thermoelastic Models:

ELISO - Isotropic elasticity with thermal coupling
ELIST - Transversely isotropic elasticity with thermal coupling
ELORT - Orthotropic elasticity with thermal coupling

Thermoplasticity Models:

EPICP - Plasticity with isotropic hardening and thermal dissipation
EPKCP - Plasticity with kinematic hardening and thermal dissipation

Thermoviscoelastic Models:

ZENER - Zener model with thermal coupling

Shape Memory Alloys:

SMA_T - SMA with full thermomechanical coupling

Isotropic elasticity (thermomechanical)

Transversely isotropic elasticity (thermomechanical)

Orthotropic elasticity (thermomechanical)

Plasticity with isotropic hardening (thermomechanical)

Plasticity with kinematic hardening (thermomechanical)

Shape Memory Alloy - Thermomechanical coupling

Zener viscoelastic model (thermomechanical)

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