Project Details
Projekt
FOR 797: Analysis and Computation of Microstructure in Finite Plasticity
Subject Area
Mechanical and Industrial Engineering
Mathematics
Mathematics
Term
from 2007 to 2019
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 28259266
Plastic material behaviour is a key feature of many materials in science and technology. Examples include metals, geomaterials such as rocks and soils, biomaterials, ice or polymers. The processes studied include metal-forming and ductile fracture as well as deformations in the earth crust and the flow of ice-sheets. A number of phenomenological theories have been developed in order to describe such processes on a macroscopic level. These have been extended in various directions such as finite and crystal plasticity. Moreover, efficient numerical schemes have been developed and a large number of the applications above can today be treated with success. Nowadays, however, these models have reached their limits in various respects.
The main problem is that they exclude a priori the formation of microstructure by requiring rather strong assumptions, such as small strain, large hardening or very strong ad hoc regularising terms. Microstructure is instead crucial, since plastic behaviour typically is the result of the interaction of complex substructures on several length scales. The macroscopic behaviour is determined by appropriate averages over the (evolving) microstructure. Also effects controlling lifetime and deterioration of specimens depend strongly on the microstructure.
The role of microstructure becomes more and more noticeable with decreasing size of the material specimens considered, as is the case in modern micromechanics and micromachining applications. Here size-effects become very prominent and the predictive power of the classical models breaks down. What is needed are models, which are more closely related to physics and materials science and which are able to take into account the microstructural behaviour of the material.
We intend to address the need for a fundamental understanding of the physical origin, the mathematical behaviour and the numerical treatment of models, which include microstructure. This can only be achieved by a joint effort involving mathematical analysis, numerical analysis, computational mechanics, material modelling and experiment. While both purely computational approaches and mathematical analysis are pursued separately at a number of leading centres worldwide, we believe that the integrated approach we propose offers a clear opportunity for Germany to play a key role in this important area.
The main problem is that they exclude a priori the formation of microstructure by requiring rather strong assumptions, such as small strain, large hardening or very strong ad hoc regularising terms. Microstructure is instead crucial, since plastic behaviour typically is the result of the interaction of complex substructures on several length scales. The macroscopic behaviour is determined by appropriate averages over the (evolving) microstructure. Also effects controlling lifetime and deterioration of specimens depend strongly on the microstructure.
The role of microstructure becomes more and more noticeable with decreasing size of the material specimens considered, as is the case in modern micromechanics and micromachining applications. Here size-effects become very prominent and the predictive power of the classical models breaks down. What is needed are models, which are more closely related to physics and materials science and which are able to take into account the microstructural behaviour of the material.
We intend to address the need for a fundamental understanding of the physical origin, the mathematical behaviour and the numerical treatment of models, which include microstructure. This can only be achieved by a joint effort involving mathematical analysis, numerical analysis, computational mechanics, material modelling and experiment. While both purely computational approaches and mathematical analysis are pursued separately at a number of leading centres worldwide, we believe that the integrated approach we propose offers a clear opportunity for Germany to play a key role in this important area.
DFG Programme
Research Units
International Connection
United Kingdom, USA
Projects
- Analysis and computation of microstructure in finite plasticity (Applicant Hackl, Klaus )
- Analytical and numerical aspects of relaxation and regularization in models of crystal plasticity (Applicants Conti, Sergio ; Dolzmann, Georg )
- Discrete and phase field models of dislocations and their macroscopic limits (Applicant Dondl, Patrick )
- Experimental analysis of the orientation dependence of deformation laminates. (Applicant Raabe, Dierk )
- Hybrid Micro-Macro Modeling of Evolving Microstructures in Finite Plasticity (Applicant Miehe, Christian )
- Modeling and computation of time-continuous evolution of microstructures (Applicant Hackl, Klaus )
- Numerical algorithms for the simulation of finite plasticity with microstructures (Applicant Carstensen, Carsten )
- Regularizations and relaxations of time-continiuous problems in plasticity (Applicant Mielke, Alexander )
- Statistically similar representative microstructures in elasto-plasticity (Applicant Schröder, Jörg )
Spokesperson
Professor Dr. Klaus Hackl
