A Variational Asymmetric ’Phase–Field’ Model for Thermoelastic Fracture of Cementitius Materials
DOI:
https://doi.org/10.70567/mc.v41i13.69Keywords:
Fracture, Phase-field, Thermoelasticity, Energetic formulationAbstract
We derive a phase-field variational model for the thermoeleastic in materials with an asymmetric behaviour at compression and traction. We show that the model can be derived from an energetic formulation of rate–independent processes, where the therno-mechanics fracture is the result of the evolution of the global minimum of a functional which accounts for the elastic energy and the dissipation associated with the thermomechanics process. We will derive energetic bounds that are used to design an algorithm which ensures the consistency of the numerical solution. The modelling and numerical simulation of a shock termic problem validates the formulation.
References
Amor H., Marigo J., y Maurini C. Regularized formulation of the variational brittle fracture with unilateral contact: Numerical experiments. Journal of the Mechanics and Physics of Solids, 57:1209-1229, 2009. https://doi.org/10.1016/j.jmps.2009.04.011
Bourdin B., Marigo J., Maurini C., y Sicsic P. Morphogenesis and propagation of complex cracks induced by thermal shocks. Physical Review Letters, 112:014301, 2014. https://doi.org/10.1103/PhysRevLett.112.014301
Carlson D.E. Linear Thermoelasticity. Springer, 1973. https://doi.org/10.1007/978-3-662-39776-3_2
Frémond M. Non-Smooth Thermomechanics. Springer-Verlag, 2002. https://doi.org/10.1007/978-3-662-04800-9
Geyer J. y Nemat Nasser S. Experimental investigation of thermally induced interacting cracks in brittle solids. International Journal of Solids & Structures, 4:349-356, 1982. https://doi.org/10.1016/0020-7683(82)90059-2
Jiang C.,Wu X., Li J., Song F., Shao Y., Xu X., y Yan P. A study of the mechanism of formation and numerical simulations of crack patterns in ceramics subjected to thermal shock. Acta Materialia, 60:4540-4550, 2012. https://doi.org/10.1016/j.actamat.2012.05.020
Luege M. Análisis de unicidad y estabilidad de la respuesta homogénea de una barra de hormigón modelada con un modelo gradiente de daño. AMCA - Mecánica Computacional, 35:1887-1904, 2017.
Luege M. y Orlando A. A variational asymmetric phase-field model of quasi-brittle fracture: Energetic solutions and their computation. International Journal of Solids & Structures, 225:110940-110965, 2021. https://doi.org/10.1016/j.ijsolstr.2020.12.005
Miehe C., Hofacker M., y Welschinger F. A phase field model for rateindependent crack propagation: robust algorithmic implementation based on operator splits. Computer Methods in Applied Mechanics and Engineering, 199:2765-2778, 2010. https://doi.org/10.1016/j.cma.2010.04.011
Miehe C., Schaenzel L.M., y Ulmer H. Phase field modeling of fracture in multi physics problems. part i. balance of crack surface and failure criteria for brittle crack propagation in thermo-elastic solids. Computer Methods in Applied Mechanics and Engineering, 294:449- 485, 2015. https://doi.org/10.1016/j.cma.2014.11.016
Mielke A. y Roubícek. Rate-Independent Systems. Theory and Application. Springer-Verlag, 2015. https://doi.org/10.1007/978-1-4939-2706-7
Pham K., Marigo J., y Maurini C. The issues of the uniqueness and the stability of the homogeneous response in uniaxial tests with gradient damage models. Journal of the Mechanics and Physics of Solids, 59:1163-1190, 2011. https://doi.org/10.1016/j.jmps.2011.03.010
Sicsic P., Marigo J., y Maurini C. Initiation of a periodic array of cracks in the thermal shock problem: A gradient damage model. Journal of the Mechanics and Physics of Solids, 63:256- 284, 2014. https://doi.org/10.1016/j.jmps.2013.09.003
Downloads
Published
Issue
Section
License
Copyright (c) 2024 Argentine Association for Computational Mechanics
This work is licensed under a Creative Commons Attribution 4.0 International License.
This publication is open access diamond, with no cost to authors or readers.
Only those papers that have been accepted for publication and have been presented at the AMCA congress will be published.
