Computational homogenization of inelastic conventional and gradient-extended microstructures by a shear band approach
Final Report Abstract
This project was dedicated to a numerically efficient approach for the computation of the average stress response of periodic microstructures. The developed methods exploit the fact that many heterogeneous microstructures with and without gradient effects mainly deform by the formation of shear band-like deformation patterns. By introducing a small number of clusters of material points derived from these bands, a computationally cheap model is obtained being surprisingly accurate for a wide range of microstructures. Thus, the approach allows for efficient two-scale simulations, where a microstructural model is attached to each integration point of a macroscopic finite element model. In contrast to the classical FE2 -method, the microscopic model has significantly less degrees of freedom. This makes the fast two-scale simulation of complex macroscopic structures possible. The microscopic strains of the model are piecewise constant. Thus, the number of stress computations within the microstructure is significantly smaller than in many other order reduction methods being, e.g., based on the proper orthogonal decomposition (POD). As another advantage, the implementation of the method is rather simple and does not require the input of certain data objects like the finite element stiffness matrix or the residual vector, which are needed for the POD but are not always easy to access in finite element programs. Since size effects play a significant role in many microstructures, aspects of grain boundary modeling in gradient plasticity are also considered. In this part of the project, the main goal was to develop a micro-scale plasticity theory with a new grain boundary model. To achieve this goal, three steps were considered using continuum theory of plasticity. In the first step, a gradient-extended crystal plasticity model using the linear momentum balance equation and surface related considerations was developed. The second step was to incorporate a grain boundary yield criterion via an appropriate assumption on the grain boundary free energy density which leads to a grain boundary yield criterion with isotropic and kinematic hardening. Implementation of finite element method into the crystal plasticity framework was the third step in the project, which allowed to investigate the shear band formation in related microstructures as a function of the grain boundary model.
Publications
- An efficient reduced computational method for nonlinear homogenization problems: the Hashin–Shtrikman type Finite Element method (HSFE), PAMM 18, Sec. 8, 2018
F. Cavaliere, S. Wulfinghoff, S.Reese
(See online at https://doi.org/10.1002/pamm.201800146) - Model order reduction of nonlinear homogenization problems using a Hashin–Shtrikman type finite element method, Computer Methods in Applied Mechanics and Engineering 330, pp. 147-179, 2018
S. Wulfinghoff, F. Cavaliere, S. Reese
(See online at https://doi.org/10.1016/j.cma.2017.10.019) - A grain boundary model considering the grain misorientation within a geometrically nonlinear gradient-extended crystal viscoplasticity theory, Proceedings of the Royal Society A 476, 2020
A. Alipour, S. Reese, B. Svendsen, S. Wulfinghoff
(See online at https://doi.org/10.1098/rspa.2019.0581) - Efficient two–scale simulations of engineering structures using the Hashin–Shtrikman type finite element method, Computational Mechanics 65, pp. 159- 175, 2020
F. Cavaliere, S. Reese, S. Wulfinghoff
(See online at https://doi.org/10.1007/s00466-019-01758-4)
