Non-local theories and stochastic mechanics: Two convergent directions for structural modelling?

Many Civil Engineering structures are made of non-homogeneous materials such as concrete, masonry and composites, and understanding their response to different loading regimes is crucial to assess performance under ordinary and extreme events.

Nowadays computer simulations of structures and materials have seen a rapid expansion as a result of the progress in computing technology. However, many issues are still unsolved, including the accurate modelling of man-made materials. One may choose to include every single detail into the analysis, but for large structures this approach is time consuming and requires sophisticated computer capabilities. An efficient alternative is to replace the complex material with an equivalent continuum. This is done in the everyday engineering practice when classical elasticity models are adopted for finite element analyses, delivering accurate solutions to many practical problems in a reasonable time. However, classical elasticity may overlook many important phenomena caused by the underlying microstructure. Stress wave propagation in heterogeneous materials due to dynamic/impact loading is one of such phenomena.

This is of significant concern because many of the experimental techniques used in structural health monitoring, damage detection and seismic wave analysis require deep understanding and reliable models of wave propagation in heterogeneous structures. A key challenge for the research community is to develop new analytical and numerical models that bring microstructure information into the structural scale model.

This issue can be successfully tackled by enriched continua, which enjoy non-local behaviour, i.e. they include also a microstructural length scale parameters to account for the influence of stress and strain at neighbouring points. Moreover, as mechanical properties of such materials and structures show great variability, engineers are challenged by problems where also uncertainties play a crucial role. This suggests stochastic methods as the theoretical framework where uncertainties in material and geometric properties can be successfully treated to improve reliability and safety and prevent catastrophic structural failure. In analogy to the non-local theories, random materials are described by some functions related to the "length scale" of the distribution of the heterogeneities.

Motivated by the observation that non-local theory and stochastic mechanics are alternative strategies to tackle multiscale problems involving heterogeneity and uncertainties, this project aims to shed new light on questions such: How does stochastic description of material properties interact with non-local continuum models for dynamic problems? Would one or the other modelling philosophy work better for some engineering problems? Can we establish a relationship between the two strategies and then take advantage of the tools used exclusively for one or the other?

This project will seek answers to these questions by investigating the dynamics of concrete beams, selected as a case study because concrete has an inherent randomness due to the irregular arrangement of the constituents and it is possible to capture its microstructure with a digital camera. This is important because the research will also develop a new approach for the identification of the length scale parameters by using digital images of the microstructure, and a sensitivity study of the model's parameters will be conducted in a full stochastic mechanics setting.

Diagnostic tools based on wave propagation in natural and man-made structures and materials are used in many fields of engineering for material characterisation or detection of components failure. We can mention the aerospace industry where ultrasounds are used for detecting damage in ultra-light composites, or bio-medical inspections for the characterisation of bone strength. Wave signals are also commonly employed in non-destructive techniques to detect early damage in civil engineering structures, for example bridges, power plants or dams, whose failure may cause loss of money and lives. Furthermore, the analysis of wave propagation in soils due to earthquakes or impacts provides fundamental information for designing a more resilient built environment. Structural failures have a tremendous impact on society: the collapse of buildings, infrastructures or strategic facilities unfortunately often results in loss of lives, but certainly in a huge financial disruption. This is a fundamental driver behind the increasing use of computational simulation as an advanced prediction and design tool to complement expensive (and not always achievable) experimental tests.

Computational mechanics is a major component in engineering design and manufacturing. Many technological achievements have been possible thanks to detailed computer simulations. While computational mechanics had a profound impact on the growth of major established industries such as aerospace, chemical and high-tech electronics, recently also the construction industry has relied on simulation software to design complex systems and as a tool to complement and validate experiments.

The proposed research suggests a new computational technique for modelling engineering structures which is based on mathematical modelling and will put forward a new point of view for the interpretation of the results of the experiments. In the PI's vision, a modelling strategy based on the tools of probabilistic analysis combined with advanced continuum theories allows reliability assessment whilst preserving ease of implementation. The target audience for the proposed advances are national and international researchers in the field of structural mechanics but there are also strong links with other communities, like materials, aerospace and chemistry. The use of the proposed approach has the potential for profound impact when assessing the performance of new and existing structures under severe loading conditions. If implemented in engineering practice, it is expected that the new multi-scale strategy will reduce the cost of design.

It is well known that probabilistic methods and reliability assessment are already established tools for engineering design of many strategic constructions and mechanical components, but a systematic use in everyday Civil Engineering practice is still not common even though it would result in more economic design and construction cycle. Considering all the mentioned motivations and aiming to impact also the construction industry, concrete has been selected as the subject of investigation. Many projects use such material and there is an increased urgency for the widespread adoption of structural health monitoring. Not only will the current infrastructure network benefit from a new multiscale reliability assessment, but also designers of new systems may benefit from the predictive capabilities of new simulation tools. As follow-on activities, the PI will utilise the excellent links with industry of the School of Civil and Building Engineering to disseminate the results of the project by organising a workshop at Loughborough University in collaboration with other academics working to advance structural design. A possible route for knowledge exchange in structural engineering design practice can be the dissemination of the outcome of the project through the IStrucE or ICE journals which are read by structural engineers working across UK design practice.