Abstract
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.
Highlights
A poroelastic medium consists of a solid porous material interacting with fluid percolating its pores
We have presented a computational framework using Artificial Intelligence (AI) to identify the macroscale parameters of poroelastic media in an efficient approach
We have trained the network by a dataset of known values which is acquired by solving numerous cell problems of asymptotic homogenisation in 3D
Summary
A poroelastic medium consists of a solid porous material (solid matrix) interacting with fluid percolating its pores. We aim at bypassing the process of macroscale properties identification derived from asymptotic homogenisation by providing an ANN that efficiently computes the coefficients of the macroscale system of PDEs without solving the cell problems. First, we need to create a sufficiently rich dataset mapping (microscale properties) as the input to the model coefficients at the macroscale (as the output data), which is constructed by solving a certain number of the cell problems derived from asymptotic homogenisation via DNS This dataset should cover a wide range of Poisson ratios and porosities so that the machine-learnt model be applicable in a wide range of scenarios of interest reducing the risk of extrapolation.
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