The Influence of Spatially Varying Boundary Conditions Based on Material Heterogeneity

Authors

  • Evan John Ricketts School of Engineering, Cardiff University, Cardiff, CF24 3AA, UK
  • Peter John Cleall School of Engineering, Cardiff University, Cardiff, CF24 3AA, UK
  • Anthony Jefferson School of Engineering, Cardiff University, Cardiff, CF24 3AA, UK
  • Pierre Kerfriden Centre de Matériaux, Mines Paris /PSL University, Evry, France
  • Paul Lyons LUSAS, Surrey, UK

DOI:

https://doi.org/10.13052/ejcm2642-2085.3331

Keywords:

Heterogeneous boundary conditions, finite element methods, unsaturated soils, random field, spatial variability

Abstract

When conducting numerical analyses, boundary conditions are generally applied homogeneously, neglecting the inherent heterogeneity of the material being represented. Whilst the heterogeneity is often considered within the medium, its influence on the response at the boundary should also be accounted for. In this study, A novel approach to applying heterogeneous boundary conditions in the simulation of physical systems is presented, particularly focusing on moisture transport in unsaturated soils. The proposed method divides the surface into blocks or “macro-elements” and scales the boundary conditions based on the variation of material properties within these blocks. The principle of using overlapping kernel functions allows local effects to be considered, impacting neighbouring regions. To demonstrate the efficacy of the approach, a set of analyses were conducted that considered infiltration into a body of unsaturated soil, with various configurations of material properties and boundary conditions. The numerical simulations indicate that the application of scaled boundary conditions leads to a more natural and realistic response in the system. The applied method is independent on the numerical techniques employed in the simulation process, making it adaptable to existing computational codes, offering flexibility in capturing complex behaviours, and providing insights into how heterogeneity influences the system’s overall response.

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Author Biographies

Evan John Ricketts, School of Engineering, Cardiff University, Cardiff, CF24 3AA, UK

Evan John Ricketts Lecturer in numerical methods at the School of Engineering, Cardiff University. His research journey began with numerical investigations of unsaturated flow in heterogeneous soils. This has since evolved to include areas of geotechnical engineering, machine learning and generative AI, and materials research, such as the simulation of heterogeneous materials through Gaussian random fields, multi-scale simulations, and approaches to discrete random field generation.

Peter John Cleall, School of Engineering, Cardiff University, Cardiff, CF24 3AA, UK

Peter John Cleall Professor of Geo-environmental Engineering, School of Engineering, Cardiff University. His research activities initially focused on the area of coupled flow and deformation behaviour in soils and have developed to encompass a number of areas in the subject of geoenvironmental and geotechnical engineering including ground energy, thermal fluxes and inter-seasonal heat storage, in-situ resource recovery from geological repositories and behaviour of modified soils. Work in these areas, supported by RCUK and industrial funding has developed a number of specific analytical and numerical models alongside an improved understanding of fundamental processes.

Anthony Jefferson, School of Engineering, Cardiff University, Cardiff, CF24 3AA, UK

Anthony Jefferson studied at Swansea and Cardiff universities and obtained PhD from Cardiff. He spent 10 years with a firm of consulting engineers before joining Cardiff University in 1994. He undertakes research on the computational modelling of cementitious and self-healing materials, and the development of new construction material systems. His chair is sponsored by the software company LUSAS.

Pierre Kerfriden, Centre de Matériaux, Mines Paris /PSL University, Evry, France

Pierre Kerfriden their scientific interests lie in the field of advanced numerical methods for the simulation of complex physical phenomena described by partial differential equations. Applications range from the prediction of fracture in composite materials to the control of micromanufacturing processes. Their research focuses on the development of multiscale numerical solvers and automated, data-driven complexity reduction methods.

Paul Lyons, LUSAS, Surrey, UK

Paul Lyons is the founder and managing director of the international engineering software company LUSAS. He founded LUSAS in 1982 and has led the company throughout its history. He has a PhD from Imperial College and has been a visiting professor at Imperial College and Cardiff University.

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Published

2024-07-15

How to Cite

Ricketts, E. J., Cleall, P. J., Jefferson, A., Kerfriden, P., & Lyons, P. (2024). The Influence of Spatially Varying Boundary Conditions Based on Material Heterogeneity. European Journal of Computational Mechanics, 33(03), 199–226. https://doi.org/10.13052/ejcm2642-2085.3331

Issue

2024: Vol 33 Iss 3

Section

UKACM 2023