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Center for Nonlinear Studies |
For many problems in science and engineering, it is necessary to describe the emerging macro-scale behavior of materials formed of a very large number of grains by accounting for the micro-scale phenomena. Such materials are ubiquitous and impact diverse areas of engineering and science ranging from material development to biomaterials to geophysics. For such problems, continuum models are a preferred approach. Classical continuum theory is unable to take into account the effects of complex kinematics and distribution of elastic energy in internal deformation modes within the continuum material point. Therefore, there is a need for microstructure informed continuum models accounting properly for the deformation mechanisms identifiable at the micro-scale. Thus, mathematical description of their mechanical response must begin from the conception of grain-interactions. From this point of departure, either discrete or continuum descriptions can be elaborated. The question remains though how these materials with complex micro-structures and grain-interactions be analyzed efficiently? Even more importantly, how their granular structure and grain-scale mechanics be predefined to produce predictable material behavior?
The granular micromechanics approach (GMA), provides such a paradigm for obtaining effective continuum models. The key aspect of the presented approach is the identification of relevant kinematic measures that describe the deformation of the continuum body and link it to the micro-scale deformation. The methodology, therefore, has the ability to reveal the connections between the micro-scale mechanisms that store/dissipate elastic energy and lead to particular emergent behavior at the macro-scale. In this presentation, we will describe the approach and illustrate with examples of recently synthesized metamaterials and simulation of mesh independent damage localization.
Host: Eric Bryant