A continuous – discontinuous approach to simulate physical degradation processes in porous media.

*(English)*Zbl 1202.74158Summary: A macroscopic framework for the simulation of physical degradation processes in quasi-brittle porous materials is proposed. The framework employs the partition of unity (PU) concept and introduces a cohesive zone model, capturing the entire failure process starting from the growth and coalescence of micro-defects until the formation of macro-cracks. The framework incorporates the interaction between the failure process and the heat and mass transfer in the porous medium. As an example, physical degradation of an outside render is studied. The analysis illustrates that both material and interface failure can be investigated with this formulation. Depending on the boundary conditions, either one dominant crack or a network of small cracks is formed.

##### MSC:

74R99 | Fracture and damage |

74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |

74F05 | Thermal effects in solid mechanics |

80A20 | Heat and mass transfer, heat flow (MSC2010) |

##### Keywords:

failure; damage; fracture; cohesive zone model; PU; X-FEM; heat transfer; mass transfer; multi-physics; continuous; discontinuous framework##### Software:

TOUGH
PDF
BibTeX
XML
Cite

\textit{P. Moonen} et al., Int. J. Numer. Methods Eng. 84, No. 9, 1009--1037 (2010; Zbl 1202.74158)

Full Text:
DOI

**OpenURL**

##### References:

[1] | De Boer, Theory of Porous Media-Highlights in the Historical Development and Current State (2000) · Zbl 0945.74001 |

[2] | Roels, Measuring and simulating moisture uptake in a fractured porous medium, Advances in Water Resources 26 (3) pp 237– (2003) |

[3] | Ren, Simulation of progressive fracturing under dynamic loading conditions, Communications in Numerical Methods in Engineering 13 pp 127– (1997) · Zbl 0878.73055 |

[4] | Jirásek, Embedded crack model. Part II: combination with smeared cracks, International Journal for Numerical Methods in Engineering 50 pp 1291– (2001) · Zbl 1013.74068 |

[5] | Simone, From continuous to discontinuous failure in a gradient-enhanced continuum damage model, Computer Methods in Applied Mechanics and Engineering 192 (41-42) pp 4581– (2003) |

[6] | Wells, A new method for modelling cohesive cracks using finite elements, International Journal of Numerical Methods in Engineering 50 (12) pp 2667– (2001) · Zbl 1013.74074 |

[7] | Dugdale, Yielding of steel sheets containing slits, Journal of the Mechanics and Physics of Solids 8 (2) pp 100– (1960) |

[8] | Barenblatt, The mathematical theory of equilibrium cracks in brittle fracture, Advances in Applied Mechanics 7 pp 55– (1962) |

[9] | Hillerborg, Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements, Cement and Concrete Research 6 (6) pp 773– (1976) |

[10] | Moonen, A continuous-discontinuous approach to simulate fracture processes in quasi-brittle materials, Philosophical Magazine 88 (28-29) pp 3281– (2008) |

[11] | Wu, A site-scale model for fluid and heat flow in the unsaturated zone of Yucca Mountain, Nevada, Journal of Contaminant Hydrology 38 (1-3) pp 185– (1999) |

[12] | Pruess K Oldenburg C Moridis G TOUGH2 User’s Guide, Version 2.0 1999 |

[13] | Vandersteen, A network approach to derive unsaturated hydraulic properties of a roughwalled fracture, Transport in Porous Media 50 (3) pp 197– (2003) |

[14] | Carmeliet, Three-dimensional liquid transport in concrete cracks, International Journal for Numerical and Analytical Methods in Geomechanics 28 (7-8) pp 671– (2004) · Zbl 1112.74486 |

[15] | Segura, Coupled HM analysis using zero-thickness interface elements with double nodes. Part I: Theoretical model, International Journal for Numerical and Analytical Methods in Geomechanics 32 (18) pp 2083– (2008) · Zbl 1273.74546 |

[16] | Roels, A coupled discrete-continuum approach to simulate moisture effects on damage processes in porous materials, Computer Methods in Applied Mechanics and Engineering 195 (52) pp 7139– (2006) · Zbl 1331.76118 |

[17] | de Borst, Discrete vs smeared crack models for concrete fracture: bridging the gap, International Journal for Numerical and Analytical Methods in Geomechanics 28 (7-8) pp 583– (2004) · Zbl 1086.74044 |

[18] | Réthoré, A two-scale model for fluid flow in an unsaturated porous medium with cohesive cracks, Computational Mechanics 42 (2) pp 227– (2008) · Zbl 1154.76053 |

[19] | Réthoré, A two-scale approach for fluid flow in fractured porous media, International Journal for Numerical Methods in Engineering 71 (7) pp 780– (2007) |

[20] | Fagerström, A thermo-mechanical cohesive zone formulation for ductile fracture, Journal of the Mechanics and Physics of Solids 56 (10) pp 3037– (2008) · Zbl 1183.74245 |

[21] | Moonen P Continuous-discontinuous modelling of hygrothermal damage processes in porous media 2009 |

[22] | Coussy, Mechanics of Porous Continua (1995) |

[23] | Janssen, Conservative modelling of the moisture and heat transfer in building components under atmospheric excitation, International Journal of Heat and Mass Transfer 50 (5-6) pp 1128– (2007) · Zbl 1124.80332 |

[24] | Melenk, The partition of unity finite element method: basic theory and applications, Computer Methods in Applied Mechanics and Engineering 39 (1-4) pp 289– (1996) · Zbl 0881.65099 |

[25] | Duarte, Generalized finite element methods for three-dimensional structural mechanics problems, Computers and Structures 77 (2) pp 215– (2000) |

[26] | Duarte, H-p clouds-an h-p meshless method, Numerical Methods for Partial Differential Equations 12 (6) pp 673– (1996) · Zbl 0869.65069 |

[27] | Moës, A finite element method for crack growth without remeshing, International Journal for Numerical Methods in Engineering 46 (1) pp 131– (1999) · Zbl 0955.74066 |

[28] | Durner, Hydraulic conductivity estimation for soils with heterogenous pore structure, Water Resources Research 30 pp 211– (1994) |

[29] | Mualem, A new model for predicting the hydraulic conductivity of unsaturated porous media, Water Resources Research 12 pp 513– (1976) |

[30] | Kumaran MK 1996 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.