Poroelasticity derived via asymptotic homogenization - Mathematical modelling and numerical simulations. State of the art, further perspectives, and extension to poroelastic composites.

Raimondo Penta (University of Glasgow)

Monday 20th May 11:40-12:20 Lecture Theatre 116

Abstract

The mechanical behavior of a solid elastic structure interplaying with fluid percolating its pores can be studied via the Theory of Poroelasticity. There exists a large variety of scenarios of interest that can be treated by means of a poroelastic modeling approach, including soil mechanics, (bio) artificial constructs and biological tissues, such as bone, organs, healthy and malignant (tumorous) cell aggregates. Here, we (a) revisit the equations of poroelasticity derived via asymptotic homogenization [I], (b) focus on recent applications of the theory [II, V], and (c) we discuss recent advances on the subject which are relevant for linear and nonlinear poroelastic composites [III, IV]. These latter are materials where the average distance between the various constituents of the matrix is comparable with the porescale. Poroelasticity derived from the microstructure can be used to meaningful insights concerning more appropriate experimental protocols which are commonly applied to the study of brain tumours, such as poroelastography [V].

References:

[I] Burridge, Robert, and Joseph B. Keller. Poroelasticity equations derived from microstructure; The Journal of the Acoustical Society of America 70.4 (1981): 1140- 1146.

[II] Dehghani, H., R. Penta, and J. Merodio. The role of porosity and solid matrix compressibility on the mechanical behavior of poroelastic tissues; Materials Research Express 6.3 (2018): 035404.

[III] Miller, Laura, and Raimondo Penta. ”Effective balance equations for poroelastic composites.” Continuum Mechanics and Thermodynamics (2020): 1-25.

[IV] Miller, Laura, and Raimondo Penta. ”Homogenized Balance Equations for Nonlinear Poroelastic Composites.” Applied Sciences 11.14 (2021): 6611.

[V] 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. European Journal of Mechanics-A/Solids, 83, 103996

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