Related papers: A few notes about viscoplastic rheologies
We develop topological methods for characterizing the relationship between polymer chain entanglement and bulk viscoelastic responses. We introduce generalized Linking Number and Writhe characteristics that are applicable to open linear…
In this article, we introduce the concept of energy-variational solutions for a large class of systems of nonlinear evolutionary partial differential equations. Under certain convexity assumptions, the existence of such solutions can be…
Rheological responses are the most relevant features to describe soft matter. So far, such constitutive relations are still not well understood in terms of small scale properties, although this knowledge would help the design of synthetic…
In the mathematical modelling of sediment compaction and porous media flow, the rheological behaviour of sediments is typically modelled in terms of a nonlinear relationship between effective pressure $p_e$ and porosity $\phi$, that is…
This is a survey on the geometry of warped products, without, or essentially with only soft, calculation. Somewhere in the paper, the goal was to give a synthetic account since existing approaches are rather analytic. Somewhere else, we…
We harness the power of Bayesian emulation techniques, designed to aid the analysis of complex computer models, to examine the structure of complex Bayesian analyses themselves. These techniques facilitate robust Bayesian analyses and/or…
In this work, a consistent viscoplasticity formulation is derived from thermodynamical principles and employing the concept of continuum elastic corrector rate. The proposed model is developed based on the principle of maximum viscoplastic…
We present a theoretical framework for the linear and nonlinear visco-elastic properties of reversibly crosslinked networks of semiflexible polymers. In contrast to affine models where network strain couples to the polymer end-to-end…
A mechanical interaction of compressible viscoelastic fluids with viscoelastic solids in Kelvin-Voigt rheology using the concept of higher-order (so-called 2nd-grade multipolar) viscosity is investigated in a quasistatic variant. The…
We study a model for the deformation of a visco-elasto-plastic material that is nearly incompressible. It originates from geophysics, is given in the Eulerian description and combines a Kelvin-Voigt rheology in the spherical part with a…
Given an assembly of viscoelastic spheres with certain material properties, we raise the question how the macroscopic properties of the assembly will change if all lengths of the system, i.e. radii, container size etc., are scaled by a…
Mesoscale simulations of woven composites using parameterized analytical geometries offer a way to connect constituent material properties and their geometric arrangement to effective composite properties and performance. However, the…
We consider {\it small solutions} of a vibrating system with smooth non-linearities for which we provide an approximate solution by using a double scale analysis; a rigorous proof of convergence of a double scale expansion is included; for…
Rheological properties of a material often require to be probed under extensional deformation. Examples include fibrous materials such as spider-silk, high-molecular weight polymer melts, and the contractile response of living cells. Such…
This work introduces a mathematical approach to analysing the polymer dynamics in turbulent viscoelastic flows that uses a new geometric decomposition of the conformation tensor, along with associated scalar measures of the polymer…
A new model of metal viscoplasticity, which takes combined isotropic, kinematic, and distortional hardening into account, is presented. The basic modeling assumptions are illustrated using a new two-dimensional rheological analogy. This…
Various spatial-gradient extensions of standard viscoelastic rheologies of the Kelvin-Voigt, Maxwell's, and Jeffreys' types are analyzed in linear one-dimensional situations as far as the propagation of waves and their dispersion and…
The thermodynamical model of visco-elastic deformable solids at finite strains is formulated in a fully Eulerian way in rates. Also effects of thermal expansion or buoyancy due to evolving mass density in a gravity field are covered. The…
Maxwell models for viscoelastic flows are famous for their potential to unify elastic motions of solids with viscous motions of liquids in the continuum mechanics perspective. But the usual Maxwell models allow one to define well motions…
We propose a unified approach to the formal long-wave reduction of several fluid models for thin-layer incompressible homogeneous flows driven by a constant external force like gravity. The procedure is based on a mathematical coherence…