An integrated micromechanics and statistical continuum thermodynamics approach for studying the fracture behaviour of microcracked heterogeneous materials with delayed response

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Cracking, damaging and fracture phenomena in strongly heterogeneous materials with delayed response and random microstructure are considered. The deterministic background which governs these phenomena is described in the first part of the paper on the basis of methods previously introduced by the author. It is shown how an integrated micromechanics approach using modern observation and image processing tools may provide the necessary information about the internal mechanisms and variables involved. Then a hybrid continuum thermodynamics formalism is recalled which combines discrete internal parameters — such as the ones defining cracks or microcracks — with other dissipative mechanisms involving continuous spectra of response, as is the case for most real viscoelastic materials. From this are derived tensor generalisations of the Griffith criterion to bodies exhibiting dissipative behaviour of any kind. The case of viscoelastic materials satisfying the Boltzmann superposition principle is then detailed. Formulae for the energy release rates in terms of external loading conditions that are pseudo-convolutive generalisations of the classical algebraic ones widely used in linear elastic fracture mechanics are presented. They involve at will viscoelastic expressions for the potential energy or complementary energy of the body. The second and third parts of the paper develop the theoretical study for the case of heterogeneous bodies with random internal constitution. As a starting point, the second part recalls several previous results recently obtained by the author and relating to undamaged elastic and viscoelastic materials. A few numerical simulations are presented, which confirm the theoretical prediction. the case of damaged heterogeneous bodies with random microstructures and random distribution of microcracks is studied in the third part. Apparent variables and apparent overall properties for elastic and viscoelastic damaged bodies which can be smaller than the representative volume are defined. Two-sided bounds and statistical hierarchies for these apparent properties are then established, first for the apparent compliances and moduli of the elastic case, second for the apparent relaxation and creep function tensors in the time domain for the viscoelastic case. Then, order relationships between the apparent properties for the damaged and undamaged cases are provided. Explicit expressions for the energy release rates in terms of the apparent properties and external apparent variables are derived. Some practical consequences of the obtained results are discussed, especially from the viewpoint of size and boundary condition effects.