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
• Hyper ROM approach - with data generation and evaluation
• Parallelizable computations (also across multiple computer nodes)
• Periodic boundary conditions on the micro-scale
• Small and large deformation theory
• UMAT interface to Abaqus on the macro-scale
• Modular concept: UEL, UMAT and UHARD interfaces on the microscale for easy extensibility
• Various element types available:
  • Plane stress, plain strain and 3D
  • Various element shapes: quadrilateral, triangular, tetrahedral, hexagonal
  • Linear and quadratic shape functions with full or reduced integration
  • The included library UELlib can also be used to develop 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 on the micro-scale with plane strain/axisymmetric elements on the macro-scale
• PARDISO solver from Intel MKL for the micro-scale FE problem (unreduced Simulation)
• Intel MKL LAPACK solver on the microscale (ROM simulation)

• N. Lange, G. Hütter, B. Kiefer: A monolithic hyper ROM FE² method with clustered training at finite deformations,  Computer Methods in Applied Mechanics and Engineering 418 (2023), 116522
• N. Lange, M. Abendroth, E. Werzner, G. Hütter, B. Kiefer: Influence of the Foam Morphology on the Mechanical Behavior of Flow-Through Foam Filters During Filtration Processes, Advanced Engineering Materials 24 (2021), 2100784
• N. Lange, G. Hütter, B. Kiefer: An efficient monolithic solution scheme for FE² problems, Computer Methods in Applied Mechanics and Engineering 382 (2021), 113886