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Computational Mechanics at Ruhr University Bochum


Ruhr University Bochum
Computational Durability Mechanics
Günther Meschke

December 2015


The durability of civil engineering infrastructure made of porous materials is considerably affected by the accumulation of damage induced by time variant external loading in conjunction with physico‐chemical processes (e.g. freeze‐thaw action, chemical dissolution processes, chemical expansive reactions, reinforcement corrosion). These phenomena are, to a large extent, controlled by the transport of fluids and ions through the (cracked) porous structure, which is characterized by a large range of spatial scales from the nm to the m scale. Adequate computational models in durability mechanics need to account for the multiscale and multiphase character of these phenomena along with their mutual interactions, considering the large range of spatio‐temporal scales involved in the description of transport, physical and chemical processes as well as fracture. 


For the modeling of ion diffusion in porous materials with distributed microcracks, a multi‐level approach is adopted. Electrolyte diffusion models are formulated to describe ion transport in concentrated pore solutions. At the level of the multiphase porous material with its hierarchical pore structure, methods of continuum micromechanics are used to compute effective transport properties. A cascade scheme, based on the concept of self‐similarity, is proposed. In a subsequent level, incorporating the homogenized solution for the porous material, effects of distributed micro‐cracks, their orientation and density on the transport process are accounted for. The information from the micro‐scale is used as input for advection‐ diffusion‐reaction models at the macro‐scale. Phase change phenomena (freezing of pore water) are des‐ cribed by a thermo‐poromechanics model, in which cryo‐suction processes acting at lower scales are implicitly accounted for. For the modeling of macro‐ cracks in the context of multiphase materials, we are investigating various advanced discretization methods, including Embedded Crack methods, Extended Finite Element Methods (XFEM) and isogeometric analysis using adaptive T‐spline technologies.  


The cascade scheme predicts topological evolutions of connected pore channels in terms of volume fractions and the degree of self‐similarity. This intrinsic information on the tortuosity allows the prediction of the dependence of the macroscopic diffusivity on the porosity over almost the complete size range. Furthermore, the proposed homogenization scheme predicts percolation thresholds depending on long‐range and short‐range interphase interactions. The model shows that the microstructure topology highly affects ion transport at lower porosities. For micro‐cracked materials, the multi‐level model correctly predicts interactions between the pore structure and the micro‐crack geometry and distribution. With regards to crack modeling in multiphase porous materials, incorporation of locally enriched displacement and fluid pressure fields in a two‐phase XFEM model allows for the discretization independent resolution of crack propagation, considering, at the local scale of cracks, fluid flow within and orthogonal to the crack. Numerical predictions and observations with regard to freezing processes in porous materials include micro‐cryo‐suction driven deformations, latent‐heat‐ associated phase transitions and the mutual interactions between fluid flow and freezing processes.


Methods of micromechanics in conjunction with advanced poromechanics models and discretization techniques constitute a key step towards i) more re‐ liable predictions of long‐term deterioration and life time of structures subject to chemo‐physical action, ii) more efficient rehabilitation methods, and iii) a performance‐based design of engineered cementitious materials with improved durability properties. As specific modeling components, the cascade micromechanics scheme provides explicit formulas for pore‐space topology and micro‐crack dependent ion diffusion in porous materials; poromechanics models allow for the description of interactions between transport, phase change processes such as freezing, deformations and damage of porous materials. XFEM models enable predictions of fracture propagation and accelerated fluid transport in discrete fractures. They have recently been successfully applied to the analysis of hydraulic fracture. 

Selected Publications

1. G. Meschke, D. Leonhart, J. Timothy and M.M. Zhou,
Computational Mechanics of Multiphase Problems ‐
Modeling Strategies at Different Scales, Computer Assisted
Methods in Engineering Sciences
, 2011, in print.
2. J. Timothy and G. Meschke. Micromechanics model for
tortuosity and homogenized diffusion properties of porous
materials with distributed micro‐cracks. Proceedings in
Applied Mathematics and Mechanics
, 2011. in print.
3. M. Zhou and G. Meschke. A three‐phase finite element
model of water‐infiltrated porous materials subjected to
freezing. In M. Papadrakakis, E. Onate, and B. Schrefler,
(Eds.), Coupled Problems 2011.
4. G. Hofstetter and G. Meschke, Numerical Modeling of
Concrete Cracking
, Springer Wien‐New York, 2011
5. F. Stangenberg, R. Breitenbücher, O.T. Bruhns, D.
Hartmann, D. Kuhl, G. Meschke; Lifetime oriented
structural design concepts
, Springer Berlin, 2009
6. G. Meschke and P. Dumstorff. Energy‐based modeling of
cohesive and cohesionless cracks via X‐FEM. Computer
Methods in Applied Mechanics and Engineering
196:2338‐2357, 2007.
7. D. Kuhl, F. Bangert, and G. Meschke. Coupled chemo‐
mechanical deterioration of cementitious materials. Part
1: Modeling., Part 2: Numerical methods and

simulations. International Journal for Solids and
, 41:15‐67, 2004.

Core Competencies

  • Multi‐scale, multi‐phase models for porous materials;
  • Computational durability mechanics & life‐time oriented structural analysis;
  • Advanced discretization methods for fracture;
  • Computational modeling of fibre reinforced composites;
  • Computational biomechanics of soft biological tissues;

Günther Meschke

Current Research Team Members:
• Günther Meschke (PI)
• M. Gofman (Postdoctoral Fellow)
• Dirk Leonhart (Ph.D. Candidate)
• Melanie Kemper (Ph.D. Candidate)
• Meng‐Meng Zhou (Ph.D. Candidate)
• Jithender J. Timothy (Ph.D. Candidate)