A dissipation‐based path‐following technique for the phase‐field approach to brittle and ductile fracture

Wambacq, Jef; Ulloa, Jacinto; Lombaert, Geert; François, Stijn

doi:10.1002/nme.6687

Cited by 6 publications

(3 citation statements)

References 55 publications

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“…We note that another possibility to deal with numerical difficulties associated with brutal crack propagation is the use of a dissipation-based path-following constraint [123], a topic worth considering in future research.…”

Section: Viscous Regularizationmentioning

confidence: 99%

A micromechanics-based variational phase-field model for fracture in geomaterials with brittle-tensile and compressive-ductile behavior

Ulloa

Wambacq

Alessi

et al. 2022

Journal of the Mechanics and Physics of Solids

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Section: Viscous Regularizationmentioning

confidence: 99%

A micromechanics-based variational phase-field model for fracture in geomaterials with brittle-tensile and compressive-ductile behavior

Ulloa

Wambacq

Alessi

et al. 2022

Journal of the Mechanics and Physics of Solids

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“…Nikolaevskij (1987) and later Slepyan (1993) were among the first authors who applied the maximum dissipation rate for studying crack growth in elastic bodies. Dissipation-based paths are also followed in ductile fracture (Verhoosel et al 2009;Wambacq et al 2021). An according variational treatment of thermo-chemomechanical processes has been published recently (Romero et al 2021).…”

Section: Energetics Of the Processmentioning

confidence: 99%

Evolution of chemically induced cracks in alkali feldspar: thermodynamic analysis

et al. 2022

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A system of edge cracks was applied to polished (010) surfaces of K-rich gem-quality alkali feldspar by diffusion-mediated cation exchange between oriented feldspar plates and a Na-rich NaCl–KCl salt melt. The cation exchange produced a Na-rich layer at and beneath the specimen surface, and the associated strongly anisotropic lattice contraction lead to a tensile stress state at the specimen surface, which induced fracturing. Cation exchange along the newly formed crack flanks produced Na-enriched diffusion halos around the cracks, and the associated lattice contraction and tensile stress state caused continuous crack growth. The cracks nucleated with non-uniform spacing on the sample surface and quickly attained nearly uniform spacing below the surface by systematic turning along their early propagation paths. In places, conspicuous wavy cracks oscillating several times before attaining their final position between the neighboring cracks were produced. It is shown that the evolution of irregularly spaced towards regularly spaced cracks including the systematic turning and wavyness along the early propagation paths maximizes the rate of free energy dissipation in every evolutionary stage of the system. Maximization of the dissipation rate is suggested as a criterion for selection of the most probable evolution path for a system undergoing chemically induced diffusion mediated fracturing in an anisotropic homogeneous brittle material.

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“…We note that another possibility to deal with numerical difficulties associated with brutal crack propagation is the use of a dissipation-based path-following constraint [122], a topic worth considering in future research.…”

Section: Viscous Regularizationmentioning

confidence: 99%

A micromechanics-based variational phase-field model for fracture in geomaterials with brittle-tensile and compressive-ductile behavior

Ulloa,

Wambacq,

Alessi

et al. 2021

Preprint

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This paper presents a framework for modeling failure in quasi-brittle geomaterials under different loading conditions. A micromechanics-based model is proposed in which the field variables are linked to physical mechanisms at the microcrack level: damage is related to the growth of microcracks, while plasticity is related to the frictional sliding of closed microcracks. Consequently, the hardening/softening functions and parameters entering the free energy follow from the definition of a single degradation function and the elastic material properties. The evolution of opening microcracks in tension leads to brittle behavior and mode I fracture, while the evolution of closed microcracks under frictional sliding in compression/shear leads to ductile behavior and mode II fracture. Frictional sliding is endowed with a non-associative law, a crucial aspect of the model that considers the effect of dilation and allows for realistic material responses with non-vanishing frictional energy dissipation. Despite the non-associative law, a variationally consistent formulation is presented using notions of energy balance and stability, following the energetic formulation for rate-independent systems. The material response of the model is first described, followed by several benchmark finite element simulations. The results highlight the ability of the model to describe tensile, shear, and mixed-mode fracture, as well as responses with brittle-to-ductile transition. A key result is that, by virtue of the micromechanical arguments, realistic failure modes can be captured, without resorting to the usual heuristic modifications considered in the phase-field literature. The numerical results are thoroughly discussed with reference to previous numerical studies, experimental evidence, and analytical fracture criteria.

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A dissipation‐based path‐following technique for the phase‐field approach to brittle and ductile fracture

Cited by 6 publications

References 55 publications

A micromechanics-based variational phase-field model for fracture in geomaterials with brittle-tensile and compressive-ductile behavior

A micromechanics-based variational phase-field model for fracture in geomaterials with brittle-tensile and compressive-ductile behavior

Evolution of chemically induced cracks in alkali feldspar: thermodynamic analysis

A micromechanics-based variational phase-field model for fracture in geomaterials with brittle-tensile and compressive-ductile behavior

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