Advanced Numerical Methods for Generalized Continuum Models
Fundamental Research Project, FWF 10.55776/PAT1342523
Anticipated start: January 2025
Cohesive-frictional materials, characterized by highly nonlinear mechanical behavior and complex failure modes, are prevalent in essentially all engineering disciplines. Examples comprise concrete, rock, tough ceramics or biological materials like bone. In numerical simulations, e.g., using the Finite Element Method (FEM), generalized continuum theories such as gradient-enhanced or micropolar continua are a promising approach for modeling localized failure in cohesive-frictional materials, associated with large inelastic deformations. Particular examples comprise the formation and propagation of cracks, shear bands or fault zones. However, in the presence of strongly localized deformations, the classical FEM suffers from excessive mesh distortion, which severely deteriorates the numerical performance. Among alternative numerical methods, a particularly promising approach is the implicit Material Point Method (iMPM), a Lagrangian particle method using a fixed background mesh for computing spatial derivatives and for assembling the global equation system, thus overcoming these problems. Nevertheless, the original iMPM has not yet been formulated and applied for generalized continua, including gradient-enhanced and micropolar media.
Motivated by this fact, the proposed project aims at an efficient and robust extension of the iMPM to gradient-enhanced micropolar continua, able to simulate complex and extreme deformations under localized material failure in a geometrically exact, 3D setting. The developed method will overcome limitations of the classical FEM, and it represents a suitable framework for simulations involving localized inelastic deformations in cohesive-frictional materials.
