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logo SMC logo SMC  NLIN logo SMC  NLIN  PROJ1 Multi-scale modeling of failure in quasi-brittle materials
Contact Thierry J. Massart

Peter Berke

Benoît Mercatoris

Keywords computational solid mechanics, quasi-brittle failure, coarse graining methodologies, multi-scale modeling homogenisation, shells, uncertainties
  • Prof. M.G.D. Geers, TU Eindhoven, the Netherlands
  • Dr. Ir. R.H.J. Peerlings, TU Eindhoven, the Netherlands
Scientific motivation To understand the failure behavior of materials and structures, computational methods offer an important complement to experimental investigations. In this spirit, multi-scale descriptions of failure avoid complex constitutive formulations and their identification by combining lower scale laws with coarse graining techniques.

A large variety of materials used in civil engineering exhibits a quasi-brittle behaviour. The understanding and the prediction of the cracking and the failure behaviour of these materials are of interest to ensure the structural safety of constructions. Damage is a phenomenon originating from the lowest scale of the heterogeneous microstructure of the materials, which by crossing all intermediate length scales, determines its macroscale behaviour. The microstructure of a material therefore plays a determinant role in the propagation of cracks during the evolution to structural failure. The study and the understanding of the quasi-brittle failure of such materials generally require the use of computational models.

Quasi-brittle materials Multi-scale modeling of shell failure for quasi-brittle materials

Due to their mesostructure and the quasi-brittle nature of their constituents, quasi-brittle periodic materials such as masonry present preferential damage orientations, strongly localised failure modes and damage-induced anisotropy. Furthermore, such structures are generally subjected to complex loading processes including both in-plane and out-of-plane loads which considerably influence the potential failure mechanisms.

Macrosopic models used in structural computations are based on phenomenological laws including a large set of parameters which need to be identified through costly experimental efforts. The mesoscopic models at the scale of constituents can be easier to identify, but become unaffordable in terms of computational cost for large structures. A multi-scale framework using computational homogenisation is therefore developed to extract the macroscopic constitutive material response from computations performed on the scale of the mesostructure. Damage localisation at the structural scale is treated by means of embedded strong discontinuities representing the collective behaviour of fine-scale cracks with an evolving orientation related to fine-scale damage evolutions. A criterion based on the homogenisation of a fine-scale model is used to detect automatically crack propagation in a shell description and determine its evolving orientation. An enhanced scale transition based on homogenisation-driven embedded discontinuities is used for both in-plane loaded and out-of-plane loaded structures as sketched in Figure 1.

NL 1 Fig1

Figure 1. Multi-scale computational scheme.

Such multiscale approaches for failure can be applied on masonry wall tests and verified against direct fine-scale computations in which all the constituents are discretised as illustrated in Figure 2.

NL 1 Fig2

Figure 2. Flexural failure of masonry wall - Comparison of direct fine-scale simulation and multi-scale approach.

Fracture of geomaterials Multi-scale adaptive modelling of quasi-brittle geomaterials using semi-discrete numerical approaches

The multi-scale methods developed hitherto for the treatment of quasi-brittle failure suffer from the drawbacks of a high degree of complexity and a high computational cost (low selectivity in the computation on the fine scale). This research project considers the development of a new approach, which would allow the efficient simulation of multi-scale quasi-brittle fracture. To overcome the mentioned drawbacks, the simultaneous treatment of damage on the scale of the microstructure and on the macroscale is proposed by coupling computational homogenization to a discrete form of macroscale equilibrium incorporating data of the microstructure. The proposed scheme would allow decreasing the complexity of the multi-scale computation, since the discrete data issued from the computation on the scale of the microstructure can be directly used to drive the macroscale computation. Moreover the discrete material representation on the macroscale also leads to an easier introduction of adaptivity in the computation.

Uncertainties Incorporation of uncertainties and multi-physical couplings in multi-scale computational approaches for geomaterials

The developments presented above are part of a more global research subject, the multi-scale representation of geomaterials, and result in computational tools with a large scope of potential applications. A first extension resides in coupling mechanical failure to other processes (moisture, thermal or chemical effects) in geomaterials. Developments are under way to incorporate failure effects in permeability of rocks and to model soil treatments (lime treatment – chemical couplings). A second field of investigation resides in incorporating the scattering of fine scale material parameters in upscaling of material properties.

  • F.R.S.-FNRS
Selected publications
  • [1] T.J. Massart, R.H.J. Peerlings, M.G.D. Geers, S. Gottcheiner, Mesoscopic modeling of failure in brick masonry acconting for three-dimensional effects, Engineering Fracture Mechanics, 72, 1238–1253, 2005.
  • [2] T.J. Massart, R.H.J. Peerlings, M.G.D. Geers, An enhanced multi-scale approach for masonry walls computations with localization of damage, International Journal for Numerical Methods in Engineering, 69(5), 1022-1059, 2007.
  • [3] B.C.N. Mercatoris, Ph. Bouillard, T.J. Massart, Multi-scale detection of failure in planar masonry thin shells using computational homogenisation, Engineering Fracture Mechanics, 76(4), 479-499, 2009.
  • [4] B.C.N. Mercatoris, T.J. Massart, A coupled two-scale computational scheme for the failure of periodic quasi-brittle thin shells, International Journal for Numerical Methods in Engineering, 85, 1177-1206, 2011.