INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Int. J. Numer. Meth. Engng 2010; 82:464–504 Published online 30 October 2009 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/nme.2773 Multiscale modeling of impact on heterogeneous viscoelastic solids containing evolving microcracks Flavio V. Souza and David H. Allen ∗, † Department of Engineering Mechanics, University of Nebraska-Lincoln, W317.4 Nebraska Hall, Lincoln, NE 68588-0526, U.S.A. SUMMARY Multiscale computational techniques play a major role in solving problems related to viscoelastic compos- ites due to the complexities inherent to these materials. In this paper, 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 viscoelastic incremental constitutive equations, but the homogenized tangent constitu- tive tensor and the homogenized incremental history-dependent stress tensor at the global scale 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 viscoelastic solids containing evolving cracks (and other kinds of heterogeneities) by solving the micromechanical problem only once at each material point and each time step. 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 the approach and demonstrate the model capabilities. Copyright 2009 John Wiley & Sons, Ltd. Received 12 May 2009; Revised 2 September 2009; Accepted 21 September 2009 KEY WORDS: multiscale model; impact; tangent constitutive tensor; viscoelastic media; evolving cracks 1. INTRODUCTION Essentially all materials exhibit more than one length scale, at least one molecular scale and a continuum scale. Most materials, natural or engineered, exhibit more than one continuum length scale. Examples of multiscale materials found in nature are rocks, soils, geological salt and ∗ Correspondence to: David H. Allen, College of Engineering, University of Nebraska-Lincoln, 114 Othmer Hall, Lincoln, NE 68588-0642, U.S.A. † E-mail: dhallen@unl.edu Contract/grant sponsor: U.S. Army Research Laboratory; contract/grant number: W911NF-04-2-00-11 Contract/grant sponsor: Conselho Nacional de Desenvolvimento Cientifico e Tecnologico—CNPq/Brazil; contract/grant number: 200372/2006-8 Copyright 2009 John Wiley & Sons, Ltd.