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Microstructural inelastic fingerprints and data-rich predictions of plasticity and damage in solids

Abstract

Inelastic mechanical responses in solids, such as plasticity, damage and crack initiation, are typically modeled in constitutive ways that display microstructural and loading dependence. Nevertheless, linear elasticity at infinitesimal deformations is used for microstructural properties. We demonstrate a framework that builds on sequences of microstructural images to develop fingerprints of inelastic tendencies, and then use them for data-rich predictions of mechanical responses up to failure. In analogy to common fingerprints, we show that these two-dimensional instability-precursor signatures may be used to reconstruct the full mechanical response of unknown sample microstructures; this feat is achieved by reconstructing appropriate average behaviors with the assistance of a deep convolutional neural network that is fine-tuned for image recognition. We demonstrate basic aspects of microstructural fingerprinting in a toy model of dislocation plasticity and then, we illustrate the method’s scalability and robustness in phase field simulations of model binary alloys under mode-I fracture loading.

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Notes

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    In the context of elasticity, it is natural to neglect all intrinsic timescales and view the loading process of a mechanical system as a non-linear dynamical system with “time” defined by the applied load. In this definition, the dynamics in-between loading steps is considered fully dissipative, and thus is neglected.

  2. 2.

    Here, we assume a square grid, which could be generalized to any grid in a straightforward manner

  3. 3.

    A relation of plasticity/damage to elastic fields is derived through the elastic fields generated by corresponding defects (eg. dislocations or voids)

  4. 4.

    The subtraction, in this case, amounts to neglecting the average mechanical response. The subtraction may be done locally, by subtracting the expected elastic solution in the microstructure. The investigation of the local subtraction approach is beyond the purposes of the current work.

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Acknowledgements

This work is supported by the National Science Foundation, DMR-MPS, Award No. #1709568. This work benefited from the facilities and staff of the Super Computing System (Spruce Knob) at West Virginia University.

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Correspondence to Stefanos Papanikolaou.

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Papanikolaou, S. Microstructural inelastic fingerprints and data-rich predictions of plasticity and damage in solids. Comput Mech 66, 141–154 (2020). https://doi.org/10.1007/s00466-020-01845-x

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Keywords

  • Mechanical property
  • Fracture
  • Plasticity
  • Elastic-plastic solids
  • Damage criteria