zbMATH — the first resource for mathematics

Poroelastic model parameter identification using artificial neural networks: on the effects of heterogeneous porosity and solid matrix Poisson ratio. (English) Zbl 07262508
Summary: 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.
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74S99 Numerical and other methods in solid mechanics
Adam; FEniCS; PyTorch
Full Text: DOI
[1] Maurice, AB, General theory of three-dimensional consolidation, J Appl Phys, 12, 155-164 (1941)
[2] Pride, SR; Gangi, AF; Morgan, FD, Deriving the equations of motion for porous isotropic media, J Acoust Soc Am, 92, 6, 3278-3290 (1992)
[3] Pride, SR; Berryman, JG, Connecting theory to experiment in poroelasticity, J Mech Phys Solids, 46, 4, 719-747 (1998) · Zbl 0973.74024
[4] James, GB, Comparison of upscaling methods in poroelasticity and its generalizations, J Eng Mech, 131, 9, 928-936 (2005)
[5] Dehghani, H.; Penta, R.; Merodio, J., The role of porosity and solid matrix compressibility on the mechanical behavior of poroelastic tissues, Mater Res Exp, 6, 3, 035404 (2019)
[6] Penta, R.; Gerisch, A., Investigation of the potential of asymptotic homogenization for elastic composites via a three-dimensional computational study, Comput Vis Sci, 17, 01 (2016)
[7] Hori, M.; Nemat-Nasser, S., On two micromechanics theories for determining micro-macro relations in heterogeneous solid, Mech Mater, 31, 667-682 (1999)
[8] Burridge, R.; Keller, JB, Poroelasticity equations derived from microstructure, J Acoust Soc Am, 70, 4, 1140-1146 (1981) · Zbl 0519.73038
[9] Penta, R.; Ambrosi, D.; Shipley, RJ, Effective governing equations for poroelastic growing media, Q J Mech Appl Math, 67, 1, 69-91 (2014) · Zbl 1346.74159
[10] Dehghani H (2019) Mechanical modeling of poroelastic and residually stressed hyperelastic materials and its application to biological tissues. Ph.D. dissertation, Universidad politécnica de Madrid
[11] Dehghani H, Noll I, Penta R, Menzel A, Merodio J (2020) The role of microscale solid matrix compressibility on the mechanical behaviour of poroelastic materials. Eur J Mech A/Solids, p 103996 · Zbl 07212924
[12] Bock, FE; Aydin, RC; Cyron, CJ; Huber, N.; Kalidindi, SR; Klusemann, B., A review of the application of machine learning and data mining approaches in continuum materials mechanics, Front Mater, 6, 110 (2019)
[13] Cherkassky, V.; Mulier, FM, Learning from data: concepts, theory, and methods (2007), New York: Wiley-IEEE Press, New York · Zbl 1130.62002
[14] Ramprasad, R.; Batra, R.; Pilania, G.; Mannodi-Kanakkithodi, A.; Kim, C., Machine learning in materials informatics: recent applications and prospects, npj Comput Mater, 3, 1, 54 (2017)
[15] Rosenblatt, F., The perceptron: a probabilistic model for information storage and organization in the brain, Psychol Rev, 65, 386 (1958)
[16] Oishi, A.; Yagawa, G., Computational mechanics enhanced by deep learning, Comput Methods Appl Mech Eng, 327, 09 (2017)
[17] Kirchdoerfer, T.; Ortiz, M., Data-driven computational mechanics, Comput Methods Appl Mech Eng, 304, 81-101 (2016) · Zbl 1425.74503
[18] Teichert, G.; Garikipati, K., Machine learning materials physics: Surrogate optimization and multi-fidelity algorithms predict precipitate morphology in an alternative to phase field dynamics, Comput Methods Appl Mech Eng, 344, 10 (2018)
[19] Zdunek, A.; Rachowicz, W., A mixed finite element formulation for compressible finite hyperelasticity with two fibre family reinforcement, Comput Methods Appl Mech Eng, 345, 11 (2018)
[20] Stainier, L.; Leygue, A.; Ortiz, M., Model-free data-driven methods in mechanics: material data identification and solvers, Comput Mech, 64, 2, 381-393 (2019) · Zbl 07095670
[21] Liu, Z.; Ct, Wu; Koishi, M., A deep material network for multiscale topology learning and accelerated nonlinear modeling of heterogeneous materials, Comput Methods Appl Mech Eng, 345, 1138-1168 (2018) · Zbl 1440.74340
[22] Zhang, S.; Yin, S., Determination of in situ stresses and elastic parameters from hydraulic fracturing tests by geomechanics modeling and soft computing, J Petrol Sci Eng, 124, 09 (2014)
[23] Su, F.; Larsson, F.; Runesson, K., Computational homogenization of coupled consolidation problems in micro-heterogeneous porous media, Int J Numer Meth Eng, 88, 11, 1198-1218 (2011) · Zbl 1242.74088
[24] Yang, H.; Tang, S.; Liu, W., Derivation of heterogeneous material laws via data-driven principal component expansions, Comput Mech, 64, 05 (2019)
[25] Liu, Z.; Ct, Wu, Exploring the 3d architectures of deep material network in data-driven multiscale mechanics, J Mech Phys Solids, 127, 03 (2019)
[26] Lähivaara, T.; Kärkkäinen, L.; Huttunen, JMJ; Hesthaven, JS, Deep convolutional neural networks for estimating porous material parameters with ultrasound tomography, J Acoust Soc Am, 143, 2, 1148-1158 (2018)
[27] Vasilyeva M, Tyrylgin A (2018) Machine learning for accelerating effective property prediction for poroelasticity problem in stochastic media. 10
[28] Hochreiter, S.; Schmidhuber, J., Long short-term memory, Neural Comput, 9, 8, 1735-1780 (1997)
[29] Alnæs M, Blechta J, Hake J, Johansson A, Kehlet B, Logg A, Richardson C, Ring J, Rognes M, Wells G (2015) The fenics project version 1.5. 3, 01
[30] Penta, R.; Gerisch, A., The asymptotic homogenization elasticity tensor properties for composites with material discontinuities, Continuum Mech Thermodyn, 29, 08 (2016)
[31] Taber, LA, Biomechanics of growth, remodeling, and morphogenesis, Appl Mech Rev, 48, 8, 487-545 (1995)
[32] Schmidhuber, J., Deep learning in neural networks: an overview, Neural Netw, 61, 85-117 (2015)
[33] Parisi G, Kemker R, Part J, Kanan C, Wermter S (2018) Continual lifelong learning with neural networks: a review. Neural Netw 02
[34] Itakura F, Saito S (1968) Analysis synthesis telephony based upon the maximum likelihood method. In The 6th international congress on acoustics, pp 280-292
[35] Kingma D, Ba J (2014) Adam: a method for stochastic optimization., vol 12
[36] Paszke A, Gross S, Chintala S, Chanan G, Yang E, DeVito Z, Lin Z, Desmaison A, Antiga L, Lerer A (2017) Automatic differentiation in pytorch
[37] Nabovati, A.; Hinebaugh, J.; Bazylak, A.; Amon, C., Effect of porosity heterogeneity on the permeability and tortuosity of gas diffusion layers in polymer electrolyte membrane fuel cells, J Power Sour, 248, 83-90 (2014)
[38] Nield, DA; Bejan, A., Convection in porous media (2017), Berlin: Springer, Berlin · Zbl 1375.76004
[39] Lee, K.; Sills, GC, The consolidation of a soil stratum, including self-weight effects and large strains, Int J Numer Anal Meth Geomech, 5, 4, 405-428 (1981) · Zbl 0476.73085
[40] Prabhakaran, R.; Pater, H.; Shaoul, J., Pore pressure effects on fracture net pressure and hydraulic fracture containment: insights from an empirical and simulation approach, J Petrol Sci Eng, 157, 07 (2017)
[41] Cuss, R.; Harrington, J., An experimental study of the potential for fault reactivation during changes in gas and pore-water pressure, Int J Greenhouse Gas Control, 53, 41-55 (2016)
[42] Wu, M.; Frieboes, H.; Chaplain, M.; Mcdougall, S.; Cristini, V.; Lowengrub, J., The effect of interstitial pressure on therapeutic agent transport: coupling with the tumor blood and lymphatic vascular systems, J Theoret Biol, 355, 194-207 (2014)
[43] Rofstad, E.; Galappathi, K.; Mathiesen, B., Tumor interstitial fluid pressure-a link between tumor hypoxia, microvascular density, and lymph node metastasis, Neoplasia, 16, 586-594 (2014)
[44] Bae, K.; Park, Y., Targeted drug delivery to tumors: myths, realityand possibility, J Controll Release Off J Controlled Release Soc, 153, 198-205 (2011)
[45] Karagianni, A.; Karoutzos, G.; Ktena, S.; Vagenas, N.; Vlachopoulos, I.; Sabatakakis, N.; Koukis, G., Elastic properties of rocks, Bull Geol Soc Greece, 43, 1165 (2017)
[46] Rudnicki, J.; Rice, J., Effective normal stress alteration due to pore pressure changes induced by dynamic slip propagation on a plane between dissimilar materials, J Geophys Res, 111, 10 (2006)
[47] Sefidgar, M.; Soltani, M.; Raahemifar, K.; Bazmara, H.; Nayinian, S.; Bazargan, M., Effect of tumor shape, size, and tissue transport properties on drug delivery to solid tumors, J Biol Eng, 8, 12 (2014)
[48] Islam, MdT; Righetti, R., Estimation of mechanical parameters in cancers by empirical orthogonal function analysis of poroelastography data, Comput Biol Med, 111, 103343 (2019)
[49] Malandrino, A.; Mak, M.; Kamm, R.; Moeendarbary, E., Complex mechanics of the heterogeneous extracellular matrix in cancer, Extreme Mech Lett, 21, 02 (2018)
[50] Hartono, D.; Liu, Y.; Tan, P.; Then, X.; Yung, L.; Lim, K., On-chip measurements of cell compressibility via acoustic radiation, Lab on a Chip, 11, 4072-80 (2011)
[51] Li, J.; Lowengrub, J., The effects of cell compressibility, motility and contact inhibition on the growth of tumor cell clusters using the cellular potts model, J Theor Biol, 343, 11 (2013)
[52] Jurvelin, JS; Buschmann, MD; Hunziker, EB, Optical and mechanical determination of poisson’s ratio of adult bovine humeral articular cartilage, J Biomech, 30, 3, 235-241 (1997)
[53] Fung, YC, Connecting incremental shear modulus and poisson’s ratio of lung tissue with morphology and rheology of microstructure, Biorheology, 26, 2, 279-289 (1989)
[54] Tilleman, T.; Tilleman, M.; Neumann, MHA, The elastic properties of cancerous skin: Poisson’s ratio and young’s modulus, Israel Med Assoc J IMAJ, 6, 753-755 (2004)
[55] Bakas, S.; Akbari, H.; Sotiras, A.; Bilello, M.; Rozycki, M.; Kirby, JS; Freymann, JB; Farahani, K.; Davatzikos, C., Advancing the cancer genome atlas glioma mri collections with expert segmentation labels and radiomic features, Sci Data, 4, 1, 170117 (2017)
[56] Gallaher, JA; Brown, JS; Anderson, ARA, The impact of proliferation-migration tradeoffs on phenotypic evolution in cancer, Sci Rep, 9, 1, 2425 (2019)
[57] Jain, R.; Martin, J.; Stylianopoulos, T., The role of mechanical forces in tumor growth and therapy, Ann Rev Biomed Eng, 16, 321-46 (2014)
[58] Penta, R.; Miller, L.; Grillo, A.; Ramírez-Torres, A.; Mascheroni, P.; Rodríguez-Ramos, R., Porosity and diffusion in biological tissues. Recent advances and further perspectives, 311-356 (2019), Cham: Springer, Cham · Zbl 1443.74238
[59] Loret, B.; Simões, F., Biomechanical aspects of soft tissues (2016), New York: CRC Press, New York
[60] Basser, PJ, Interstitial pressure, volume, and flow during infusion into brain tissue, Microvasc Res, 44, 2, 143-165 (1992)
[61] Zilian, A.; Dinkler, D.; Vehre, A., Projection-based reduction of fluid-structure interaction systems using monolithic space-time modes, Comput Methods Appl Mech Eng, 198, 47-48, 3795-3805 (2009) · Zbl 1230.74208
[62] Ravi S, Zilian A (2016) Numerical modeling of flow-driven piezoelectric energy harvesting devices. In: Computational methods for solids and fluids. Computational methods in applied sciences; vol 41, pp 399-426. Springer, Berlin
[63] Legay, A.; Zilian, A.; Janssen, C., A rheological interface model and its space-time finite element formulation for fluid-structure interaction, Int J Numer Meth Eng, 86, 6, 667-687 (2011) · Zbl 1235.74295
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.