Micro-mechanical Modeling of Brittle Materials under Dynamic Compressive Loading
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Date
2015-02-23
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Johns Hopkins University
Abstract
Micro-mechanical modeling of brittle dynamic failure provides a physical insight into the relationship between microstructure, which dictates key failure mechanisms, and material performance. This dissertation addresses key issues in micromechanical models associated with brittle dynamic failure, in particular damage-induced material anisotropy, efficiency of the micromechanics model to enable larger-scale implementation, and non-local modeling to represent strain softening materials. The dominant failure mechanism for brittle materials under compressive loads is the growth and coalescence of wing-cracks; therefore, the micromechanics model based on wing-cracks is the focus of this work.
Based on a wing-crack RVE model, analytical closed-form solutions for the instantaneous effective anisotropic compliance (or stiffness) of a damaged material under compression are derived through both kinematic and energetic approaches. These solutions are functions of the geometric measurements of the wing-cracks and the friction coefficient. Application of the model to tensile loads is a straightforward simplification of the proposed model. Finite element models of periodic wing-cracks verify the analytical results, confirming the effectiveness of the analytical solution. Combining this anisotropic compliance with an established micro-mechanics model that addresses crack growth, the stress-strain relationship of a brittle material under compressive loading is established.
In upscaling to a macro-scale computational model, this micro-mechanically based constitutive model is evaluated at each individual integration point of the mesh. For models with many integration points, this micromechanical analysis for every integration point at every time step is computationally prohibitive. An upscaling technique is proposed here to tackle this issue. Instead of repeatedly performing the complete constitutive model for each integration point, a Taylor series expansion is applied to approximate the micromechanics damage process. Such a methodology can be deployed to enhance the efficiency of the macro-scale models as well as the statistical estimations of the local stress and strength of the material with heterogeneous nature.
To the end of properly modeling the strain softening behavior at the highly damaged stage, a conventional nonlocal finite element method is investigated by simulating a series of bench mark problems.
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Keywords
Brittle Materials, Dynamic Failure