Related papers: A texture tensor to quantify deformations: the exa…
The consolidation of suspended particulate matter under external forces such as pressure or gravity is of widespread interest. In this work, we derive a constitutive relation to describe the deformation of a {\it two-dimensional} strongly…
Randomly textured polycrystalline materials of constituents with highly anisotropic nature of grains can be considered globally isotropic. In order to determine the isotropic properties, like elasticity or conductivity, we propose a theory…
The problem of surface effects at a fluid boundary created by the force field of finite value is investigated. A classical simple fluid with a locally introduced field imitating a permeable solid is considered. The cases of micro- and…
Amorphous solids such as coffee foam, toothpaste or mayonnaise display a transient creep flow when a stress $\Sigma$ is suddenly imposed. The associated strain rate is commonly found to decay in time as $\dot{\gamma} \sim t^{-\nu}$,…
Solid interfaces have intrinsic elasticity. However, in most experiments, this is obscured by bulk stresses. Through microscopic observations of the contact-line geometry of a partially wetting droplet on an anisotropically stretched…
We formulate and apply a continuum model that incorporates elasticity, yield stress, plasticity and viscous drag. It is motivated by the two-dimensional foam rheology experiments of Debregeas et al. [G. Debregeas, H. Tabuteau, and J.-M. di…
Real-world solids, such as rocks, soft tissues, and engineering materials, are often under some form of stress. Most real materials are also, to some degree, anisotropic due to their microstructure, a characteristic often called the…
Ordinarily, the stress tensor that one derives for a Madelung fluid is not regarded as being coupled to a strain tensor, which is consistent with the fluid hypothesis. However, based upon earlier work regarding the geometric nature of the…
A general procedure to investigate the elastic response and calculate the elastic constants of stressed and unstressed materials through continuum field modeling, particularly the phase field crystal (PFC) models, is presented. It is found…
A finite simple shear deformation of an elastic solid induces unequal normal stresses. This nonlinear phenomenon, known as the Poynting effect, is governed by a universal relation between shear strain and first normal stresses difference,…
We suggest a scalar model for deformation and flow of an amorphous material such as a foam or an emulsion. To describe elastic, plastic and viscous behaviours, we use three scalar variables: elastic deformation, plastic deformation rate and…
In continuum mechanics, stress concept plays an essential role. For complicated materials, different stress concepts are used with ambiguity or different understanding. Geometrically, a material element is expressed by a closed region with…
In this paper, we study the fully developed gravity-driven flow of granular materials between two inclined planes. We assume that the granular materials can be represented by a modified form of the second-grade fluid where the viscosity…
The 2D flow of a foam confined in a Hele-Shaw cell through a contraction is investigated. Its rheological features are quantified using image analysis, with measurements of the elastic stress, rate of plasticity, and velocity. The behavior…
Finite plasticity theories are still a subject of controversy and lively discussions. Among the approaches to finite elastoplasticity two became especially popular. The first, implemented in the commercial finite element codes, is based on…
Built on the tenets of rational thermodynamics, this article proposes a theory of strain gradient thermo-visco-plasticity for isotropic polycrystalline materials under high strain rates. The effect of micro-inertia, which arises due to…
Fluid deformation and strain history are central to wide range of fluid mechanical phenomena ranging from fluid mixing and particle transport to stress development in complex fluids and the formation of Lagrangian coherent structures…
We investigate the two-dimensional flow of a liquid foam around circular obstacles by measuring all the local fields necessary to describe this flow: velocity, pressure, bubble deformations and rearrangements. We show how our experimental…
This work is concerned with the purely dissipative version of a well-established model of rate-independent strain-gradient plasticity. In the conventional theory of plasticity the approach to determining plastic flow is local, and based on…
A constitutive relation between stress and strain relative to a reference state is the basic assumption of elasticity theory. However, in living matter, force generation is governed by motor molecule activity, which does not depend on…