Multiscale Modeling of Impact on Heterogeneous Viscoelastic Solids with Evolving Microcracks

Multiscale computational techniques play a major role in solving problems related to viscoelas-tic composite materials due to the complexities inherent to these materials. In the present work, a numerical procedure for multiscale modeling of impact on heterogeneous viscoelastic solids containing evolving microcracks is proposed in which the (global scale) homogenized viscoelastic incremental constitutive equations have the same form as the local scale vis-coelastic incremental constitutive equations, but the homogenized tangent constitutive tensor and the homogenized incremental history dependent stress tensor depend on the amount of damage accumulated at the local scale. Furthermore, the developed technique allows the computation of the full anisotropic incremental constitutive tensor of solids containing evolving cracks (and other kinds of heterogeneities) by solving the micromechanical problem only once. The procedure is basically developed by relating the local scale displacement field to the global scale strain tensor and using first order homogenization techniques. The finite element formulation is developed and some example problems are presented in order to verify and demonstrate the model capabilities. A two-scale analytical solution for a functionally graded elastic material subject to dynamic loads is also derived in order to verify the multiscale computational model and additional code verification is also performed. Even though the presented model has been implemented in an explicit time integration algorithm, it can be especially useful when the global scale problem is solved by an implicit finite element algorithm, which requires the knowledge of the global tangent constitutive tensor in order to assemble the corresponding stiffness matrix. iii DEDICATION I dedicate this dissertation to my dear wife Isabela, to my parents, Januario de Souza Neto and to my sister, Fabiola V. Souza, for their unconditional love and support. iv ACKNOWLEDGMENTS I would like to express my deepest gratitude to my Ph. who has by all means been providing me with wise advising and guidance, which helped me to better understand the physics behind the mathematics. I am also indebted to Professor Jorge B. Soares, my Master's advisor, who was the first to introduce me to the challenging world of research and has continuously been part of my academic career. for many valuable discussions on the various topics of mechanics. I am also very grateful to Professor Jean-François Molinari for his help on both practical and theoretical issues of Mechanics and for his kind reception during my visits to LMT/France and EPFL/Switzerland. Special thanks are due to my friends …