Multiscale Modelling and Design of New Materials
July 4, 2005 — July 8, 2005
Coordinator:
- Tarek Zohdi (University of California, Berkeley, CA, USA)
The event is part of the program elaborated for the European Atelier for Engineering and Computational Sciences (EUA4X – Marie Curie program). Some of the lectures will be also available on line.
Please check available Marie Curie fellowships under “Admission and Accommodation”
Scope
In many modern engineering systems, materials with highly complex microstructures are now in use. The macroscopic response of such materials is the aggregate behavior of microscale interaction.
The focus of this CISM lecture series is to address recent advances in modeling and computational issues describing multiscale system behavior. The themes to be addressed are: 1) Multiscale- multifield behavior, 2) Nonlinear micro-macro scale relationships, 3) Phase transformations and 4) Inverse multiscale problems. The lectures are suitable for graduate students of applied mathematics, mechanics, engineerings and physics with interests in computer simulation of multiscale materials science problems. The objective is to illustrate techniques which enable fast and accurate predictions of new high performance micro-macro material behavior by direct numerical simulation, with the goal being to reduce costly, time consuming, trial and error laboratory analyses. The specific topics include:
Sequential and embedded multiscale-multiphysics computational techniques in solid mechanics. In the embedded approach both the fine and coarse scales are simultaneously resolved, whereas in the sequential multiscale methods, fine scales are modeled and their gross response is infused into the coarse scale. Among the sequential techniques, both the mathematical homogenization and the variational multiscale methods will be described. Mathematical homogenization theory in space will be applied to elasticity, plasticity, damage and fatigue. A unified continuum-to-continuum and continuum-to-discrete (atomistic) scale bridging methodology based on the generalization of the space-time mathematical homogenization will be presented.
Temporal homogenization theory will be derived and applied to problems of viscoelasticity, viscoplasticity and fatigue. Among the embedded multiscale computational techniques to be described are: the multigrid (multilevel), the composite grid and the mesh superposition approaches. For multiphysics applications multiscale staggering methods will be discussed.
(1) Averaging and integral procedures in homogenisation (2) Micro-macro homogenisation within a geometrically and physically nonlinear framework (3) Multi-scale FE-solution of nested boundary value problems and (4) Some issues on higher-order continua within computational homogenization, extensions toward the Mindlin second gradient continua.
1) Multiscale damage material modeling of composites (general tools and examples: laminate composites, CMCs, 3D composites), 2) Multiscale computational strategies and homogeneization in space and in time for highly heterogeneous media under quasi-static conditions multiphysics problems and 3) Multiscale computational approaches and others for LF-MF-HF dynamics.
Multiscale finite element analysis of composites using mixing theory. Fatigue analysis of composite materials and structures using FEM. Combination of particle and finite element methods for multiscale material analysis and design. Application to mechanical, civil and geotechnical engineering.
Constitutive modeling and simulation of the superelastic effect in shape-memory alloys. The proposed methodology centers around the inclusion of microstructural-level austenite-martensite phase transition in a continuum framework. Also, computational aspects of texture modeling are discussed in connection with experimental measurements.
Micro-macro homogenization and related algorithms for three-dimensional large scale computations including damage and contact algorithms. ALE approach in micromechanical simulations for multi-material applications and multi-scale methods for contact problems at finite strains.
Multiphysics inverse problems in micro-macro mechanics, with emphasis on microstructures comprised of randomly dispersed particles. General nonconvex-nonderivative stochastic optimization strategies are developed for two classes of particulate systems: 1) The design of materials composed of randomly dispersed particulates suspended in a homogeneous binding matrix, where the objectives are to deliver prescribed macroscopic effective responses while simultaneously obeying local constraints that reject restrictions on micro-scale stress fields and 2) Inverse problems involving particulate flows in multifield environments, for example particle impacts, coupled with thermochemical reactions and near-field forces. Staggering methods are also developed. Problems in light scattering are considered as well. Applications include problems in aerosols, epitaxy and astro- and geo-pyhsics.