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This study explores the role that the microstructure plays in determining the macroscopic static response of porous elastic continua and exposes the occurrence of position-dependent nonlocal effects that are strictly correlated to the…
A geometrical interpretation of the $G$-structures associated to elastic material bodies is given. In addition, characterizations of their integrability are obtained. Since the lack of integrability is a geometrical measure of the lack of…
This paper investigates the homogenization, dimension reduction, and linearization of a composite plate subjected to external loading within the framework of non-linear elasticity problem. The total elastic energy of the problem is of order…
As an effective method to deliver external materials into biological cells, microinjection has been widely applied in the biomedical field. However, the cognition of cell mechanical property is still inadequate, which greatly limits the…
We consider a strongly heterogeneous medium saturated by an incompressible viscous fluid as it appears in geomechanical modeling. This poroelasticity problem suffers from rapidly oscillating material parameters, which calls for a thorough…
We use an elastic model to explore faceting of solid-wall vesicles with elastic heterogeneities. We show that faceting occurs in regions where the vesicle wall is softer, such as areas of reduced wall thicknesses or concentrated in…
We introduce a class of continuum mechanical models aimed at describing the behaviour of viscoelastic fluids by incorporating concepts originated in the theory of solid plasticity. Within this class, even a simple model with constant…
The paper presents a new type of weakly nonlinear two-scale model of controllable periodic porous piezoelectric structures saturated by Newtonian fluids. The flow is propelled by peristaltic deformation of microchannels which is induced due…
In this article, we study a thermodynamically consistent thermo-visco-elastic model describing the balance of internal energy in a heat-conducting inelastic body. In the considered problem, the temperature dependence appears in both the…
The immersed boundary method is a mathematical formulation and numerical method for solving fluid-structure interaction problems. For many biological problems, such as models that include the cell membrane, the immersed structure is a…
We prove the existence of martingale solutions to a stochastic fluid-structure interaction problem involving a viscous, incompressible fluid flow, modeled by the Navier-Stokes equations, through a deformable elastic tube modeled by…
Using a well defined soft model glass in the framework of Molecular Dynamics simulations, the inherent structures are probed by means of a recently developed deformation protocol that aims to capture the Dynamical Heterogeneities (DH), as…
Motivated by elastography that utilizes tissue mechanical properties as biomarkers for liver disease, with the eventual objective of quantitatively linking histopathology and bulk mechanical properties, we develop a micromechanical modeling…
In this paper an asymptotic homogenization method for the analysis of composite materials with periodic microstructure in presence of thermodiffusion is described. Appropriate down-scaling relations correlating the microscopic fields to the…
The Peskin problem models the dynamics of a closed elastic filament immersed in an incompressible fluid. In this paper, we consider the case when the inner and outer viscosities are possibly different. This viscosity contrast adds further…
There is a growing mechanics literature concerning the macroscopic properties of mechanism-based mechanical metamaterials. This amounts mathematically to a homogenization problem involving nonlinear elasticity. A key goal is to identify the…
Elastic microphase separation refers to equilibrium patterns that form by phase separation in elastic gels. Recent experiments revealed a continuous phase transition from the homogeneous phase to a regularly patterned phase, whose period…
In non-linear incompatible elasticity, the configurations are maps from a non-Euclidean body manifold into the ambient Euclidean space, $\mathbb{R}^k$. We prove the $\Gamma$-convergence of elastic energies for configurations of a converging…
We study a phenomenological electropermeabilization model in a periodic medium representing biological tissue. Starting from a cell-level model describing the electric potential and the degree of porosity, we perform dimension analysis to…
We investigate the well-posedness and solution regularity of an evolution equation with non-positive type variable-exponent memory, which describes multiscale viscoelasticity in materials with memory. The perturbation method is applied for…