Strain gradient based criterion for the onset of quasi-brittle failure for two-phase composites such as concrete.

SCK•CEN Mentor

Seetharam Suresh,, +32 (0)14 33 32 08

Expert group

Engineered and Geosystems Analysis


General context:

There is an ongoing collaboration between SCK-CEN and UAntwerp on thermo-hydro-mechanical behaviour of concrete at higher temperatures. In this context, there is a specific interest to pursue innovative work in the field of continuum damage mechanics of concrete, given its importance in nuclear engineering applications such as nuclear containment buildings, nuclear waste disposal, etc.

Scientific context:

Concrete is a highly heterogeneous material. Interpreting its micro-structure as stiff particles randomly distributed in a soft matrix, is a common first idealization.  Deformation behaviour of concrete is usually described by classical continuum theories which rely eventually on the  representative volume element (RVE) concept. The latter fails, if length characteristics of phenomena to be modelled are close to micro-structural length properties, like, for instance, the mean particle distance.  Examples are strong gradients in applied traction loads, damage and fracture processes, etc.

As long as a continuum approach is still preferred to describe these kind of phenomena, generalized continuum theories, such as strain gradient theories, have to be used. Although a theoretical framework is already available, a number of problems are still unresolved, which prevents the usage of corresponding concepts for practical design purposes.



The objective of this thesis is to develop a scheme similar to the RVE concept to determine parameters required by strain gradient elasticity and to derive a criterion for the onset of quasi-brittle failure based on the strain energy density in the context of strain gradient elasticity.


In a first step, virtual random composites with given particle fraction and correlation length are generated. Micro-mechanical simulations are performed, considering a given volume, the size of which is determined by the correlation length of the material. Volume elements are exposed to generalized displacement boundary conditions together with constraints imposed on fluctuation strains.

The parameters of the generalized elasticity tensor obtained by these simulations are compared with the results obtained by Drugan and Willis for two-phase composites. A methodology, how to obtain these parameters based on a volume element approach will be derived.

Afterwards, the micro-mechanical simulations are enhanced by a heuristic continuum damage model,  which ensures objectivity with respect to the spatial discretization used in simulations.  A  criterion for the onset of quasi-brittle failure based on the strain energy density in the context of strain gradient elasticity is derived. The latter will depend on elasticity constants for particles and matrix, particle fraction, correlation length, mean particle size or distance, applied mean strains and spatial gradients of the latter.

The minimum diploma level of the candidate needs to be

Professional bachelor