In this report, computable global bounds on errors due to the use of various mathematical models of physical phenomena are derived. The procedure involves identifying a so-called fine model among a class of models of certain events and then using that model as a datum with respect to which coarser models can be compared. The error inherent in a coarse model, compared to the fine datum, can be bounded by residual functionals unambiguously defined by solutions of the coarse model. Whenever there exist hierarchical classes of models in which levels of sophistication of various coarse models can be defined, an adaptive modeling strategy can be implemented to control modeling error. In the present work, the class of models is within those embodied in nonlinear continuum mechanics.

For decades, one of the most critical considerations of civil engineers has been the construction of structures that can sufficiently resist earthquakes. However, in many parts of the globe, ancient and contemporary buildings were constructed without regard for engineering; thus, there is a rising necessity to adapt existing structures to avoid accidents and preserve historical artefacts. There are various techniques for retrofitting a masonry structure, including foundation isolations, the use of Fibre-Reinforced Plastics (FRPs), shotcrete, etc. One innovative technique is the use of Shape Memory Alloys (SMAs), which improve structures by exhibiting high strength, good re-centring capabilities, self-repair, etc. One recent disastrous earthquake that happened in the city of Bam, Iran, (with a large proportion of masonry buildings) in 2003, with over 45,000 casualties, is analysed to discover the primary causes of the structural failure of buildings and its ancient citadel. It is followed by introducing the basic properties of SMAs and their applications in retrofitting masonry buildings. The outcomes of preceding implementations of SMAs in retrofitting of masonry buildings are then employed to present two comprehensive schemes as well as an implementation algorithm for strengthening masonry structures using SMA-based devices.

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Every year, structural flaws or breakdowns cause thousands of people to be harmed and cost billions of dollars owing to the limitations of design methods and materials to withstand extreme earthquakes. Since earthquakes have a significant effect on sustainability factors, there is a contradiction between these constraints and the growing need for more sustainable structures. There has been a significant attempt to circumvent these constraints by developing various techniques and materials. One of these viable possibilities is the application of smart structures and materials such as shape memory and piezoelectric materials. Many scholars have examined the use of these materials and their structural characteristics up to this point, but the relationship between sustainability considerations and the deployment of smart materials has received little attention. Therefore, through a review of previous experimental, numerical, and conceptual studies, this paper attempts to draw a more significant relationship between smart materials and structural sustainability. First, the significant impact of seismic events on structural sustainability and its major aspects are described. It is then followed by an overview of the fundamentals of smart material’s behaviour and properties. Finally, after a comprehensive review of the most recent applications of smart materials in structures, the influence of their deployment on sustainability issues is discussed. The findings of this study are intended to assist researchers in properly addressing sustainability considerations in any research and implementation of smart materials by establishing a more explicit relationship between these two concepts.

Concrete is the most widely used construction material nowadays. We are concerned with the computational modelling and laboratory testing of high-performance concrete (HPC). The idea of HPC is to enhance the functionality and sustainability of normal concrete, especially by its greater ductility as well as higher compressive, tensile, and flexural strengths. In this paper, the influence of three types (linear displacement, uniform traction, and periodic) of boundary conditions used in numerical homogenization on the calculated values of HPC properties is determined and compared with experimental data. We take into account the softening behavior of HPC due to the development of damage (micro-cracks), which finally leads to failure. The results of numerical simulations of the HPC samples were obtained by using the Abaqus package that we supplemented with our in-house finite element method (FEM) computer programs written in Python and the homogenization toolbox Homtools. This has allowed us to better account for the nonlinear response of concrete. In studying the microstructure of HPC, we considered a two-dimensional representative volume element using the finite element method. Because of the random character of the arrangement of concrete’s components, we utilized a stochastic method to generate the representative volume element (RVE) structure. Different constitutive models were used for the components of HPC: quartz sand—linear elastic, steel fibers—ideal elastic-plastic, and cement matrix—concrete damage plasticity. The numerical results obtained are compared with our own experimental data and those from the literature, and a good agreement can be observed.