Related papers: A few notes about viscoplastic rheologies
Existence and uniqueness of solutions is shown for a class of viscoelastic flows in porous media with particular attention to problems with nonsmooth porosities. The considered models are formulated in terms of the time-dependent nonlinear…
Relativistic fluid hydrodynamics, organized as an effective field theory in the velocity gradients, has zero radius of convergence due to the presence of non-hydrodynamic excitations. Likewise, the theory of elasticity of brittle solids,…
Viscoelastic rate-type fluid models constitute a fundamental framework for the mathematical description of complex materials exhibiting coupled elastic and viscous effects, with a wide range of applications in engineering, biomaterials, and…
The velocity and friction properties of laminar pipe flow of a viscoelastic solution are bounded by the corresponding values for two Newtonian fluids, namely, the solvent and a fluid with a viscosity identical to the total viscosity of the…
Lubrication flows appear in many applications in engineering, biophysics, and in nature. Separation of surfaces and minimisation of friction and wear is achieved when the lubrication fluid builds up a lift force. In this paper we analyse…
As inelastic structures are ubiquitous in many engineering fields, a central task in computational mechanics is to develop accurate, robust and efficient tools for their analysis. Motivated by the poor performances exhibited by standard…
We study convex integration solutions in the context of the modelling of shape-memory alloys. The purpose of the article is two-fold, treating both rigidity and flexibility properties: Firstly, we relate the maximal regularity of convex…
The rheological characterisation of complex fluids is mostly performed under simple shear flow in rotational rheometers. Their modern commercial versions are extremely sensitive instruments which are able to provide very accurate…
Viscoelastic materials have non-negative relaxation spectra. This property implies that viscoelastic response functions satisfy certain necessary and sufficient conditions. It is shown that these conditions can be expressed in terms of each…
A brief review is presented of the scaling of complex fluids, polymers and polyelectrolytes in solution and in confined geometry, in thermodynamical, structural and rheology properties using equilibrium and nonequilibrium dissipative…
The development of a coherent conceptual basis for the treatment of non-linear microscopic phenomena, such as, hydrodynamic interaction, finite extensibility, excluded volume and internal viscosity, in molecular theories of dilute polymer…
Heterogeneities in the cell membrane due to coexisting lipid phases have been conjectured to play a major functional role in cell signaling and membrane trafficking. Thereby the material properties of multiphase systems, such as the line…
We review the construction and analysis of numerical methods for strongly nonlinear PDEs, with an emphasis on convex and nonconvex fully nonlinear equations and the convergence to viscosity solutions. We begin by describing a fundamental…
Metamaterials are composite structures whose properties arise from a mesoscale organization of their constituents. Provided this organization occurs on scales smaller than the characteristic lengths associated with their response, it is…
We formulate a quasistatic nonlinear model for nonsimple viscoelastic materials at a finite-strain setting in the Kelvin's-Voigt's rheology where the viscosity stress tensor complies with the principle of time-continuous frame-indifference.…
In this paper, we investigate some micromechanical aspects of elasto-plasticity in heterogeneous geomaterials. The aim is to upscale the elasto-plastic behavior for a representative volume of the material which is indeed a very challenging…
A fundamental assumption in our understanding of material rheology is that when microscopic deformations are reversible, the material responds elastically to external loads. Plasticity, i.e. dissipative and irreversible macroscopic changes…
Tailoring microscopic details to tune bulk rheology is a key paradigm in soft matter physics, yet the vast parameter space associated with constituent interactions precludes a fully systematic approach. To address this, we have designed a…
We consider a multiscale approach based on immersed methods for the efficient computational modeling of tissues composed of an elastic matrix (in two or three-dimensions) and a thin vascular structure (treated as a co-dimension two…
Surface-subsurface flow models for hydrological applications solve a coupled multiphysics problem. This usually consists of some form of the Richards and shallow water equations. A typical setup couples these two nonlinear partial…