MonolithFE² is an open-source toolbox for FE² multi-scale simulation in Abaqus. It implements the highly efficient monolithic algorithms, but supports also the conventional staggered algorithm.

The main idea behind the implementation is to use Abaqus/Standard for solving the macro FE problem and a self-written light-weight code for solving the micro problems. The micro-macro data exchange is performed through the muser material routine interface UMAT of Abaqus. At the micro-scale, MonolithFE² employs the element routine interface UEL of Abaqus. For this purpose, an UEL routine is shipped with MonolithFE² which supports the established element types like triangular, quadrilateral, tetragonal or hexahedral shape with linear or quadratic shape functions. It employs the UMAT interface for the material law at the micro-scale. Thus, previously developed UELs and UMATs can be employed directly at the micro-scale and be tested in Abaqus directly independent of MonolithFE². By default, an elastic-plastic MISES material routine UMAT in rate formulation is employed at the microscale. The preprocessing and postprocessing for the micro-scale is done in Abaqus/CAE with aid of a Python plug-in. 


  • monolithic and staggered algorithm
  • parallelizable computations (also over multiple computer nodes)
  • periodic boundary conditions at micro-scale
  • small deformation and large deformation theory
  • UMAT interface to Abaqus at the macroscopic scale
  • modular concept: UEL, UMAT and UHARD interfaces at micro-scale for easy extensibility
  • different element types available:
    • plane stress, plane strain and 3D
    • different element shapes: quadrilateral, triangular, tetrahedral, hexagonal
    • linear and quadratic shape functions with full or reduced integration
    • included library UELlib can be used also for development of other UELs for Abaqus 
  • Python plug-ins for preprocessing and postprocessing of micro-scale models in Abaqus/CAE (meshing, material assignment, convergence parameters etc.)
  • 3D Models at the microscale with plane strain/axisymmetric elements at macro-scale
  • PARDISO solver from Intel MKL for the microscale problem


N. Lange, G. Hütter, B. Kiefer: An efficient monolithic solution scheme for FE² problems, Computer Methods in Applied Mechanics and Engineering 382 (2021), 113886, preprint


Binaries and source files

Version history

v1.02a (current)

  • style of input file for microscale in style of Abaqus *Keyword
  • variable number of node DOFs (if supported by micro-scale UEL)
  • simpliplied integration of micro-scale UMATs


  • added: compilation script and binaries for Windows