KLRNucleationMicroForce

@article{Drucker-Prager,
    author = "DRUCKER, D. C. and PRAGER, W.",
    ISSN = "0033569X, 15524485",
    URL = "http://www.jstor.org/stable/43633942",
    journal = "Quarterly of Applied Mathematics",
    number = "2",
    pages = "157--165",
    publisher = "Brown University",
    title = "SOIL MECHANICS AND PLASTIC ANALYSIS OR LIMIT DESIGN",
    urldate = "2023-06-16",
    volume = "10",
    year = "1952"
}

@Article{Kumar2022,
    author = "Kumar, A. and Ravi-Chandar, K. and Lopez-Pamies, O.",
    title = "The revisited phase-field approach to brittle fracture: application to indentation and notch problems",
    journal = "International Journal of Fracture",
    year = "2022",
    month = "Sep",
    day = "01",
    volume = "237",
    number = "1",
    pages = "83-100",
    abstract = "In a recent contribution, Kumar et al. (J Mech Phys Solids 142:104027, 2020) have introduced a comprehensive macroscopic phase-field theory for the nucleation and propagation of fracture in linear elastic brittle materials under arbitrary quasistatic loading conditions. The theory can be viewed as a natural generalization of the phase-field approximation of the variational theory of brittle fracture of Francfort and Marigo (J Mech Phys Solids 46:1319--1342, 1998) to account for the material strength at large. This is accomplished by the addition of an external driving force---which physically represents the macroscopic manifestation of the presence of inherent microscopic defects in the material---in the equation governing the evolution of the phase field. The main purpose of this paper is to continue providing validation results for the theory by confronting its predictions with direct measurements from three representative types of experimentally common yet technically challenging problems: (i) the indentation of glass plates with flat-ended cylindrical indenters and the three-point bending of (ii) U-notched and (iii) V-notched PMMA beams.",
    issn = "1573-2673",
    doi = "10.1007/s10704-022-00653-z",
    url = "https://doi.org/10.1007/s10704-022-00653-z"
}

@article{KUMAR2020104027,
    author = "Kumar, Aditya and Bourdin, Blaise and Francfort, Gilles A. and Lopez-Pamies, Oscar",
    title = "Revisiting nucleation in the phase-field approach to brittle fracture",
    journal = "Journal of the Mechanics and Physics of Solids",
    volume = "142",
    pages = "104027",
    year = "2020",
    issn = "0022-5096",
    doi = "https://doi.org/10.1016/j.jmps.2020.104027",
    url = "https://www.sciencedirect.com/science/article/pii/S0022509620302623",
    keywords = "Fracture, Strength, Energy methods, Configurational forces, Brittle materials",
    abstract = "Twenty years in since their introduction, it is now plain that the regularized formulations dubbed as phase-field of the variational theory of brittle fracture of Francfort and Marigo (1998) provide a powerful macroscopic theory to describe and predict the propagation of cracks in linear elastic brittle materials under arbitrary quasistatic loading conditions. Over the past ten years, the ability of the phase-field approach to also possibly describe and predict crack nucleation has been under intense investigation. The first of two objectives of this paper is to establish that the existing phase-field approach to fracture at large — irrespectively of its particular version — cannot possibly model crack nucleation. This is so because it lacks one essential ingredient: the strength of the material. The second objective is to amend the phase-field theory in a manner such that it can model crack nucleation, be it from large pre-existing cracks, small pre-existing cracks, smooth and non-smooth boundary points, or within the bulk of structures subjected to arbitrary quasistatic loadings, while keeping undisturbed the ability of the standard phase-field formulation to model crack propagation. The central idea is to implicitly account for the presence of the inherent microscopic defects in the material — whose defining macroscopic manifestation is precisely the strength of the material — through the addition of an external driving force in the equation governing the evolution of the phase field. To illustrate the descriptive and predictive capabilities of the proposed theory, the last part of this paper presents sample simulations of experiments spanning the full range of fracture nucleation settings."
}