Recent progresses in nanotechnology have clearly shown that the incorporation of nanomaterials within concrete elements leads to a sensible increase in strength and toughness, especially if used in combination with randomly distributed short fiber reinforcements, as for ultra high-performance fiber-reinforced concrete (UHPFRC). Current damage models often are not able to accurately predict the development of diffuse micro/macro-crack patterns which are typical for such concrete structures. In this work, a diffuse cohesive interface approach is proposed to predict the structural response of UHPFRC structures enhanced with embedded nanomaterials. According to this approach, all the internal mesh boundaries are regarded as potential crack segments, modeled as cohesive interfaces equipped with a mixed-mode traction-separation law suitably calibrated to account for the toughening effect of nano-reinforcements. The proposed fracture model has been firstly validated by comparing the failure simulation results of UHPFRC specimens containing different fractions of graphite nanoplatelets with the available experimental data. Subsequently, such a model, combined with an embedded truss model to simulate the concrete/steel rebars interaction, has been used for predicting the load-carrying capacity of steel bar-reinforced UHPFRC elements enhanced with nanoplatelets. The numerical outcomes have shown the reliability of the proposed model, also highlighting the role of the nano-reinforcement in the crack width control.

In this article we study the homogenization of an optimal control problem for a parabolic equation in a domain with highly oscillating boundary. We identify the limit problem, which is an optimal control problem for the homogenized equation and with a different cost functional.

The ability to manipulate concrete-based and composite materials at the nanoscale represents an innovative approach to improving their mechanical properties and designing high-performance building structures. In this context, a numerical investigation of the reinforcing effect of nano-modified epoxy resin on the structural response of fiber-reinforced polymer (FRP)-plated reinforced concrete (RC) components has been proposed. In detail, an integrated model, based on a cohesive crack approach, is employed in combination with a bond–slip model to perform a failure analysis of strengthened structures. In particular, the proposed model consists of cohesive elements located on the physical interface between concrete and FRP systems equipped with an appropriate bond–slip law able to describe the reinforcing effect induced by the incorporation of nanomaterials in the bonding epoxy resin. Preliminary analyses, performed on reinforced concrete prisms, highlight an increment of 28% in the bond strength between concrete and the FRP system, offered by the nanomaterials embedded in the adhesive layer with respect to the standard one. Moreover, the numerically predicted structural response of a nano-modified FRP-plated beam shows an increment of around 5.5% in the failure load and a reduction in the slip between concrete and the FRP plate of around 76%, with respect to the reinforced beam without nanomaterial incorporation. Finally, the good agreement with experimental results, taken from the literature, highlights the excellent capability of the proposed model to simulate the mechanical behavior of such types of reinforced structures, emphasizing the beneficial effects of the nano-enhanced epoxy resin on the bond strength between concrete and FRP systems.

The present work investigates the crack-induced degradation of the dynamic characteristics in plain concrete elements subjected to mixed-mode fracture conditions. Specifically, a discrete fracture model, based on an inter-element cohesive approach, has been improved and implemented into a 2D finite element framework to evaluate the progressive variation of the static and dynamic properties as the damage level increases. The obtained numerical results highlight the effectiveness of the proposed model in determining the load-carrying capacity and the degradation of natural vibration frequencies during damage propagation, demonstrating its applicability in the framework of structural health monitoring.

We study the asymptotic behavior of the solution of the Laplace equation in a domain perforated along the boundary. Assuming that the boundary microstructure is random, we construct the limit problem and prove the homogenization theorem. Moreover we apply those results to some spectral problems.