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A thermodynamically consistent framework to couple damage and plasticity microplane-based formulations for fracture modeling: development and algorithmic treatment

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Abstract

For a wide variety of quasi-brittle materials, the constitutive microplane models of damage are capable of describing the anisotropic development and growth of microcracks when materials exhibit inelastic response. Damage development in solids leads to the degradation of the macroscopic material stiffness and results in different response in loading and unloading. On the other hand, the constitutive microplane models of plasticity describe the anisotropic plastic sliding that originates macroscopic permanent deformation and remains upon unloading. For realistic modeling of these materials, in which both damage and plasticity mechanisms can evolve simultaneously, the microplane damage and plasticity models can be coupled in a systematic and robust manner. This work presents a theoretical formulation of a consistent framework to couple both microplane damage and plasticity models for triggering inelastic behavior (damage and plastic effects) in engineering materials. Throughout the derivation, it is specifically shown that the proposed derivation complies with the thermodynamical restrictions with regard to the assessment of the local energy dissipation based on the Clausius–Duhem inequality. Finally, the algorithmic treatment of the developed constitutive framework is outlined for its incorporation into incremental-iterative solution procedures using Newton–Raphson schemes and examined by means of simple benchmark examples.

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Acknowledgments

RR and AD would like to acknowledge the German Research Foundation (DFG) for the financial support through the priority Program 1640 forming by plastic deformation’ with contract No. RO 706/6-1. JR is grateful to the financial support of the Andalusian Government (Project of Excellence No. TEP-7093) and the Spanish Ministry of Economy and Competitiveness/FEDER (DPI2012-37187).

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Authors and Affiliations

  1. Institute of Structural Analysis, Leibniz Universität Hannover, Appelstr. 9A, 30167, Hannover, Germany

    A. Dean, S. Sahraee & R. Rolfes

  2. Institute for Structural Analysis, Technische Universität Dresden, 01062, Dresden, Germany

    K. Özenc & M. Kaliske

  3. Elasticity and Strength of Materials Group, School of Engineering, University of Seville, Camino de los Descubrimientos s/n, 41092, Seville, Spain

    J. Reinoso

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  1. A. Dean
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  2. S. Sahraee
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  3. K. Özenc
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  4. J. Reinoso
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  5. R. Rolfes
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  6. M. Kaliske
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Correspondence to J. Reinoso.

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Dean, A., Sahraee, S., Özenc, K. et al. A thermodynamically consistent framework to couple damage and plasticity microplane-based formulations for fracture modeling: development and algorithmic treatment. Int J Fract 203, 115–134 (2017). https://doi.org/10.1007/s10704-016-0131-9

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  • DOI: https://doi.org/10.1007/s10704-016-0131-9

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