Morphogenesis and Propagation of Complex Cracks Induced by Thermal Shocks

Bourdin, Blaise; Marigo, Jean‐Jacques; Maurini, Corrado; Sicsic, Paul

doi:10.1103/physrevlett.112.014301

Cited by 239 publications

(168 citation statements)

References 30 publications

(64 reference statements)

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“…The functions (21) are different from those considered in [4], where they were chosen to allow for explicit analytical results. The present model reduces to the ones commonly used in a phase-field regularisation of brittle fracture [55,47,24] when neglecting plasticity (σ p → ∞). The underlying damage model is that of a strongly brittle material [58], for which the energy necessary to break the material is finite, while the underlying plastic model is that of perfect plasticity.…”

Section: Specific Modelsmentioning

confidence: 99%

“…This can be considered as an extension of the consolidated alternate minimization scheme used in the regularised models of brittle fracture, [22,21,23,12,24] and fits the incremental energy minimization framework [54,59]. Similar algorithms have been used for coupled plasticity-damage problems also by [9,50,60].…”

Section: Numerical Solution Algorithmmentioning

confidence: 99%

“…10 highlights the force-displacement response for the E-P-PD model and for different values of the critical accumulated plastic strainp c , that is, the accumulated plastic strain at which damage is triggered and given by the relation w 1 = 2p c . By increasing w 1 , one increases the initial damage yield stress (24) and, therefore, postpones the triggering of the localisation. We note then, that the more the plastic strain is accumulated before damage is triggered, the less the snap-back phenomenon is accentuated.…”

Section: E-p-pd Responsementioning

confidence: 99%

“…The variational approach of brittle fracture and the associated regularised formulations [22,21,23,38] are nowadays widely adopted in computational mechanics. The mechanical interpretation of the regularised models as damage models added a further insight on the prediction of crack nucleation in the quasi-brittle setting, giving a precise connection between the regularising length-scale and the maximum allowable stress before failure [55,24].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Coupling damage and plasticity for a phase-field regularisation of brittle, cohesive and ductile fracture: One-dimensional examples

Alessi

Marigo

Maurini

et al. 2018

International Journal of Mechanical Sciences

Self Cite

104

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Plasticity and damage are two fundamental phenomena in nonlinear solid mechanics associated to the development of inelastic deformations and the reduction of the material stiffness. Alessi et al. [4] have recently shown, through a variational framework, that coupling a gradient-damage model with plasticity can lead to macroscopic behaviours assimilable to ductile and cohesive fracture. Here, we further expand this approach considering specific constitutive functions frequently used in phase-field models of brittle fracture. A numerical solution technique of the coupled elastodamage-plasticity problem, based on an alternate minimisation algorithm, is proposed and tested against semi-analytical results. Considering a one-dimensional traction test, we illustrate the properties of four different regimes obtained by a suitable tuning of few key constitutive parameters. Namely, depending on the relative yield stresses and softening behaviours of the plasticity and the damage criteria, we obtain macroscopic responses assimilable to (i) brittle fracturè a la Griffith, (ii) cohesive fractures of the Barenblatt or Dugdale type, and (iii) a sort of cohesive fracture including a depinning energy contribution. The comparisons between numerical and analytical results prove the accuracy of the proposed numerical approaches in the considered quasi-static time-discrete setting, but they also emphasise some subtle issues occurring during time-discontinuous evolutions.

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Section: Specific Modelsmentioning

confidence: 99%

Section: Numerical Solution Algorithmmentioning

confidence: 99%

Section: E-p-pd Responsementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Coupling damage and plasticity for a phase-field regularisation of brittle, cohesive and ductile fracture: One-dimensional examples

Alessi

Marigo

Maurini

et al. 2018

International Journal of Mechanical Sciences

Self Cite

104

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show abstract

“…Hence, it is suitable for measuring physical properties of a deformable object due to its ability to detect the displacements of points. The moiré interferometry has been employed in many types of materials such as solids, films and composites in measurement of mechanical properties, such as stress and strain, as well as in the study of crack propagation and morphogenesis [2][3][4][5][6].…”

Section: Introductionmentioning

confidence: 99%

Stress-Strain Measurement of Rubber with Optical Moiré Fringes

Sriklin

Sriwipat²,

Suwanna

et al. 2017

J. Phys.: Conf. Ser.

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Abstract. We use the moiré fringes to measure true stress and true strain of a rubber specimen in tension, and analyze the stress-strain relationship. With the printed straight-line pattern on a specimen, the moiré patterns appear when the specimen is stretched. The geometrical relationship of bright and dark fringes is used to calculate the strain values both in the axial and transverse directions. Together with optical image processing, which can also be used to obtain the instantaneous cross sectional area, we can determine true stress and true strain. The results from the moiré method yield the true stress and true strain in good agreement with those calculated from the standard engineering measurement. Additional benefits of the method include simultaneous measurement of stress and strain, their inhomogeneity, and shear strain.

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A length scale insensitive phase‐field model for fully coupled thermo‐mechanical fracture in concrete at high temperatures

Chen

Zhou

2022

Num Anal Meth Geomechanics

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Fracture in concrete at high temperatures involves complex thermo‐mechanical couplings and arbitrary crack evolution, imposing great challenges to its computational modeling. This work addresses a length scale insensitive phase‐field cohesive model for fully coupled thermo‐mechanical fracture in concrete at high temperatures. Both the thermal expansion and transient creep strain are accounted for in the kinematics. Based on the underlying phase‐field cohesive model for fracture in solids at ambient temperature, the temperature‐dependent mechanical properties of concrete, that is, Young's modulus, tensile and compressive strengths and fracture energy, and so forth, are all incorporated. In addition to the cracking‐induced mechanical damage mechanism represented by the crack phase‐field, the thermal deterioration mechanism is also considered by a temperature‐dependent thermal damage variable. The numerical implementation of the proposed model into the multi‐field finite element method is then briefly addressed. Several representative numerical examples, for example, thermally induced cracking in energy storage structures, thermal shock in quenched concrete plates, mode‐I and mixed‐mode failure of notched beams at high temperatures, and so forth, are presented for the validation. The effects of various expressions for the transient creep strain (TCS) on the global behavior of concrete structures are also studied. As in those purely mechanical problems, both the predicted crack pattern and global responses for all examples are insensitive to the incorporated phase‐field length scale. Being able to capture the fully coupled thermo‐mechanical fracture in concrete, the proposed phase‐field cohesive model, combined with a reliable hydro‐chemo‐thermal analysis, is promising in assessing the integrity and safety of concrete structures at high temperatures like fire scenarios.

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Morphogenesis and Propagation of Complex Cracks Induced by Thermal Shocks

Cited by 239 publications

References 30 publications

Coupling damage and plasticity for a phase-field regularisation of brittle, cohesive and ductile fracture: One-dimensional examples

Coupling damage and plasticity for a phase-field regularisation of brittle, cohesive and ductile fracture: One-dimensional examples

Stress-Strain Measurement of Rubber with Optical Moiré Fringes

A length scale insensitive phase‐field model for fully coupled thermo‐mechanical fracture in concrete at high temperatures

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