Available featuresΒΆ

Below is a summary of the main features and current limitations of CRATE in the computational multi-scale simulation of heterogeneous materials.

General formulation:

  • Quasi-static deformation processes;

  • Infinitesimal and finite strains;

  • Implicit time integration.

Note

A limitation under finite strains is under investigation, namely the development of a suitable self-consistent scheme for the clustering-based reduced-order models SCA and ASCA. Therefore, enforcing constant reference material properties is currently the only option available to simulate with the previous models under finite strains.

Macro-scale loading path:

  • General monotonic and non-monotonic macro-scale loading paths;

  • Enforcement of macro-scale strain and/or stress constraints;

  • General prescription of macro-scale loading incrementation;

  • Dynamic macro-scale loading subincrementation.

Material constitutive modeling:

  • General nonlinear material constitutive behavior;

  • Interface to implement a new constitutive model;

  • Out-of-the-box constitutive models include:

    • General anisotropic linear elastic constitutive model (infinitesimal strains);

    • von Mises elasto-plastic constitutive model with isotropic strain hardening (infinitesimal and finite strains);

    • General anisotropic Hencky hyperelastic constitutive model (finite strains);

    • General anisotropic St.Venant-Kirchhoff hyperelastic constitutive model (finite strains).

Note

Besides the constitutive models themselves, CRATE also makes available a complete and validated set of computational solid mechanics common procedures as well as a toolkit of tensorial and matricial operations!

Offline-stage DNS methods:

  • Interface to implement a new direct numerical simulation (DNS) multi-scale method;

  • FFT-based homogenization basic scheme (article 1, article 2).

Note

Despite a highly efficient implementation of the FFT-based homogenization basic scheme, the convergence of this method is limited to moderate stiffness ratios between different material phases. Variants of this method or different methods should be implemented to handle some cases of engineering interest (e.g., microstructures with voids or rigid inclusions).

Offline-stage clustering methods:

  • Interface to implement a new clustering algorithm;

  • Wrappers over clustering algorithms available from third-party libraries (e.g., SciPy, Scikit-Learn).

Online-stage clustering-based reduced-order models:

  • Self-Consistent Clustering Analysis (SCA) (article);

  • Adaptive Self-Consistent Clustering Analysis (ASCA) (article).