Efficient Computational Micromechanics of Composites with Weak Interfaces

• Applicant: Professor Dr. Matti Schneider
• Subject Area: Mechanics
• Term: since 2026
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 571975633

For composite materials, the significant influence of the mechanical properties of the interface between the constituents on the compound’s mechanical performance is well-known and documented. However, more often than not a perfect bonding between the phases is assumed in computational models of micromechanics, in particular for complex microstructures. In fact, prescribing a specific interface behavior requires resolving the interfaces. Conventional voxel-based methods - which are widely appreciated for their computational prowess - are not capable of resolving the interfaces. The goal of the proposed project is to provide a robust computational approach to the micromechanics of composites with strong discontinuities across internal interfaces. More precisely, we target a computational method based on the Fast Fourier Transform (FFT) which accounts for displacement jumps across the interfaces both for spring-type (elastic) laws and nonlinear traction-separation laws, converges under grid refinement (for elastic interfaces) and shows a grid-independent, efficient convergence behavior of FFT solvers. From a technological point of view, we build upon recent ideas for joining the eXtended finite element method (X-FEM) and FFT-based computational micromechanics: the X-FFT method, developed for weak discontinuities (strain/stress jumps). We also target dealing with non-smooth interfaces, e.g., for cylindrical inclusions. The proposed methodology will close a serious shortcoming of current voxel-based methods prevalent in micromechanics, enabling its users to investigate the influence of the interface adhesion on the effective mechanical behavior of matrix-inclusion composites, also shedding light on the size-dependent response of nanocomposites.

• DFG Programme: Research Grants