Homogenized Balance Equations for Nonlinear Poroelastic Composites

Within this work, we upscale the equations that describe pore-scale behaviour of nonlinear porous elastic composites, using asymptotic homogenization technique in order to derive macroscale effective governing equations. A hyperelastic composite can be thought as being comprised a matrix interacting with number subphases and percolated by fluid flowing pores (which is chosen Newtonian incompressible here). general model derived then specified for particular choice strain energy function, namely de Saint-Venant function. This leads system PDEs, which poroelastic type additional terms transformations account material. Our new porohyperelastic-type describes composites prescribing stress balance equations, conservation mass Darcy’s law. The coefficients these encode detailed microstructure material are found solving differential problems. reduces following limit cases (a) linear when deformation gradient approaches identity, (b) there no (c) poroelasticity only matrix–fluid interaction considered. applicable interactions between various solid phases occur at pore-scale, biological tissues such artery walls, myocardium, lungs liver.