A poroplastic model of structural reorganisation in porous media of biomechanical interest

Abstract

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 study of growth and remodeling in isotropic tissues, based on the Anand‐Aslan‐Chester theory of strain‐gradient plasticity

“…In some works devoted to the theoretical foundations of volumetric growth, emphasis is put on the necessity of defining variables that, together with the descriptors of the tissue's standard mechanical state, are capable of catching its structural transformations. In Epstein and Maugin, this is done by having recourse to the theory of uniformity, and introducing the concepts of “archetype” and “transplant operator.” On the other hand, in several other contexts, the Bilby‐Kröner‐Lee multiplicative decomposition of the deformation gradient tensor is adopted, along with its generalizations, in order to frame remodeling in terms of “plastic‐like distortions.” We use this terminology in order to underline that, in the presence of remodeling, the structural transformations of the tissues considered in this work recall the plastic distortions of nonliving, elasto‐plastic materials. Sometimes, we use the adjectives “plastic” and “remodeling” interchangeably: we take this liberty when a physical quantity, historically conceived for the theory of plasticity, has to be re‐interpreted in compliance with the physical context of the present work.…”

Finite element modeling of finite deformable, biphasic biological tissues with transversely isotropic statistically distributed fibers: toward a practical solution

“…Moreover, it would be interesting to adapt the practical solution method presented in this work to the cases of remodeling and growth [58,59]. This should be done to investigate the influence of these phenomena on the material response of biological tissues (cf., e.g., [60], where the response was studied in the isotropic case, with the aid of the computational algorithm outlined in [61]).…”

Elastoplastic analysis of pressure‐sensitive materials by an effective three‐dimensional mixed finite element

“…Another application field concerns the research trend on generalized continua and their applications such as, for example, reported in for gradient models; in for second gradient models; in for multi‐constituent materials, in for some hints on non‐local problems, in for pantographic structure and in for an asymptotic approach.…”

“…Another application field concerns the research trend on generalized continua and their applications such as, for example, reported in [21,36,65] for gradient models; in [29] for second gradient models; in [41,48] for multi-constituent materials, www.zamm-journal.org Fig. 7 Meshes m1, m2, and m3 used in the analysis of the corner wall test and the relative displacement fields at the end of the loading phases.…”