We present a poroplastic model of structural reorganisation in a binary mixture comprising a solid and a fluid phase. The solid phase is the macroscopic representation of a deformable porous medium, which exemplifies the matrix of a biological system (consisting e.g. of cells, extracellular matrix, collagen fibres). The fluid occupies the interstices of the porous medium and is allowed to move throughout it. The system reorganises its internal structure in response to mechanical stimuli. Such structural reorganisation, referred to as remodelling, is described in terms of "plastic" distortions, whose evolution is assumed to obey a phenomenological flow rule driven by stress. We study the influence of remodelling on the mechanical and hydraulic behaviour of the system, showing how the plastic distortions modulate the flow pattern of the fluid, and the distributions of pressure and stress inside it. To accomplish this task, we solve a highly nonlinear set of model equations by elaborating a previously developed numerical procedure, which is implemented in a non-commercial finite element solver.

A computational algorithm for solving anelastic problems in finite deformations is introduced. The presented procedure, termed the Generalised Plasticity Algorithm (GPA) hereafter, takes inspiration from the Return Mapping Algorithm (RMA), which is typically employed to solve the Karush–Kuhn–Tucker (KKT) system arising in finite elastoplasticity, but aims to modify and extend the RMA to the case of more general flow rules and strain energy density functions as well as to non-classical formulations of elastoplasticity, in which the plastic variables are not treated as internal variables. To assess its reliability, the GPA is tested in two different contexts. First, it is used for solving two classical problems (a shear-compression test and the necking of a circular bar). In both cases, the GPA is compared with the RMA in terms of structural set-up, computational effort and flexibility, and its convergence is evaluated by solving several benchmarks. Some restrictions of the classical form of the RMA are pointed out, and it is shown how these can be overcome by adopting the proposed algorithm. Second, the GPA is applied to characterise the mechanical response of a biological tissue that undergoes large deformations and remodelling of its internal structure.

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