Multiscale Cohesive Modeling of Heterogeneous Material Layers

Wednesday, October 7, 2009
4:00 - 5:15 PM
190 Holden Auditorium

Dr. Karel Matous
Department of Aerospace and Mechanical Engineering
University of Notre Dame, Notre Dame, IN 46556

With concentrated efforts from the material science community over the past several decades to develop new multi-functional materials, that inherently span several length scales due to the presence of disparate phases, the need for modeling tools that accurately describe the physical phenomena at each scale has only further been emphasized.

In this lecture, I will present a multiscale theoretical and computational framework for modeling the macroscopic/microscopic behavior of heterogeneous material layers, such as heterogeneous adhesives, where the macroscopic response is consistently driven by the physical processes occurring at the micro-scale. This novel computational multiscale cohesive model is based on the variational energy equivalence, Hill's Lemma, and is capable of coupling physical processes at the micro-scale to the macroscopic response in order to derive a homogenized cohesive law with a point-wise attached heterogeneous micro-continuum. The multiscale model can account in a natural way for mode mixity and provide the complex coupling of normal and shear effects. The finite element method is used to solve both the macro- and micro-scale boundary value problems. Moreover, the presence of damage at the micro-scale renders both the macro- and micro-scale partial differential equations highly non-linear. To remedy this problem and to devise a computationally attractive scheme, we adopt a nested Newton-Raphson iterative solution procedure to solve a copuled set of the Euler-Lagrange equations. The damage behavior is described by a simple isotropic damage mechanism and a rate-dependent formulation is employed to eliminate mesh bias due to the loss of the strong material ellipticity. The proposed multiscale cohesive framework is capable of predicting the non-homogeneous micro-fields, the damage nucleation and propagation in the interfacial layer as well as the macroscopic response of the damaged system.

Finally, I will present several examples involving various unit cells and a range of macroscopic deformation histories to predict the microscale inhomogeneous fields, the damage evolution, and the macroscopic behavior of a reinforced epoxy-based adhesive. I will also feature a convergence analysis for the nested iterative scheme and the upper and lower bounds on the mechanical traction-separation law will be presented to demonstrate mathematical validity of the multiscale cohesive framework.

BIOSKETCH

Dr. Karel Matous is an Associate Professor at the Aerospace & Mechanical Engineering Department at the University of Notre Dame. He received his M.S. and Ph.D. in the Theoretical & Applied Mechanics from the Czech Technical University in Prague. Before coming to the University of Notre Dame he was a principal research scientist and a lead of the computational physics team, as the part of the DOE/NNSA Advanced Simulation and Computing Program, at the Computational Science and Engineering at the University of Illinois. His research group focuses on computational science and engineering, computational materials science, computational mechanics and physics, advanced numerical methods and multiscale/multitime/multiphysics modeling of complex heterogeneous materials and systems, such as solid propellants, metal alloys and advanced self-healing adhesives. He has authored or co-authored more than 60 journal or conference papers. He is involved in several interdisciplinary research programs with funding from various agencies and private companies. Dr. Matous received the Rector's Award for the best Ph.D. students from the Czech Technical University in Prague, and in return his student, Mohan Kulkarni (Ph.D. AE, UIUC, Prof. Geubelle co-adviser), won the student presentation competition in the material modeling specialty area at the 9th US National Congress on Computational Mechanics (USNCCM9) in San Francisco. Recently an article from Dr. Matous' group entitled Multiscale cohesive failure modeling of heterogeneous adhesives published in Journal of the Mechanics and Physics of Solids has been featured on ScienceDirect Top 25 Hottest articles in April-June 2008. He is a member of ASME, ASCE, AIAA, USACM, and IACM.

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