We investigate the dependence of the mechanical and hydraulic properties of poroelastic materials on the interstitial volume fraction (porosity) of the fluid flowing through their pores and compressibility of their elastic (matrix) phase. The mechanical behavior of the matrix is assumed of linear elastic type and we conduct a three-dimensional microstructural analysis by means of the asymptotic homogenization technique exploiting the length scale separation between the pores (pore-scale or microscale) and the average tissue size (the macroscale). The coefficients of the model are therefore obtained by suitable averages which involve the solutions of periodic cell problems at the pore-scale. The latter are solved numerically by finite elements in a cubic cell by assuming a cross-shaped interconnected cylindrical structure which results in a cubic symmetric stiffness tensor on the macroscale. Therefore, the macroscale response of the material is fully characterized by six parameters, namely the elastic Young's and shear moduli, Poisson's ratio, the hydraulic conductivity, and the poroelastic parameters, i.e. Biot's modulus and Biot's coefficient. We present our findings in terms of a parametric analysis conducted by varying the porosity as well as the Poisson's ratio of the matrix. Our novel three-dimensional results, which are presented in the context of tumor modeling, serve as a robust first step to (a) quantify the macroscale response of poroelastic materials on the basis of their underlying microstructure, (b) relate the compressibility of the tissue, which can be used to distinguish between benign tumor and cancer, to its microstructural properties (such as porosity), and (c) reveal a nontrivial dependency of Biot's modulus on porosity and compressibility of the matrix, which can pave the way to the optimal design of artificial constructs in terms of fluid volume available for transport of mass and solutes. Figure 1. The microstructure, shown on the left, is assumed to be periodic. An example macroscale domain, where pore-scale details are smoothed out, is shown on the right.

Predictive analysis of poroelastic materials typically require expensive and time-consuming multiscale and multiphysics approaches, which demand either several simplifications or costly experimental tests for model parameter identification.This problem motivates us to develop a more efficient approach to address complex problems with an acceptable computational cost. In particular, we employ artificial neural network (ANN) for reliable and fast computation of poroelastic model parameters. Based on the strong-form governing equations for the poroelastic problem derived from asymptotic homogenisation, the weighted residuals formulation of the cell problem is obtained. Approximate solution of the resulting linear variational boundary value problem is achieved by means of the finite element method. The advantages and downsides of macroscale properties identification via asymptotic homogenisation and the application of ANN to overcome parameter characterisation challenges caused by the costly solution of cell problems are presented. Numerical examples, in this study, include spatially dependent porosity and solid matrix Poisson ratio for a generic model problem, application in tumour modelling, and utilisation in soil mechanics context which demonstrate the feasibility of the presented framework. Keywords Artificial neural network • Multiscale and multiphysics problems • Poroelastic media • Material characterisation • Data-driven computational mechanics B Hamidreza Dehghani

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The knowledge I learned during this period will benefit the rest of my life. Lots of support and help have been given by family, colleagues, and friends during these years. I would like to express my sincere gratitude to all of them. First of all, I would like to thank my supervisor, Prof. Jose Merodio, for his strong and kind support, giving me the opportunity of working in a group with a great and friendly environment, and for sharing his knowledge and experience with me. I would also like to thank my colleague and my good friend Dr. Raimondo Penta, for guiding me into the entrance of the multiscale analysis, his generous support in many aspects, and hosting me in Glasgow. I am very grateful to have had the chance to work in the welcoming and professional atmosphere of the University of Glasgow, provided by the staff of School of Mathematics and Statistics, especially, Prof. Raymond Ogden who helped me to continue collaboration with Dr. Raimondo Penta. A sincere thank you is given to Dr. Javier Rodríguez for his helpful advice about Abaqus. Special thanks to Prof. Andreas Menzel who gave me the chance to work in the very friendly and professional environment of the Division of Mechanics at the Technical University of Dortmund and vii viii also to start a fruitful collaboration with him and his Ph.D. student, Isabelle Guschke.Finally, my heartfelt thanks to my family for their everlasting love and support. My wife, Fateme, no words in the world can express my thankfulness for your endless love.My Ph.D. journey finally came to an end. However, "This is not the end. It is not even the beginning of the end. But it is, perhaps, the end of the beginning." (Winston Churchill, 1942

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