Related papers: Testing Hooke-like isotropic hyper-/hypo-elastic m…
In a previous paper \cite{Itskov-MoSM} we presented a hyperelastic isotropic material model whose stress-strain response is nonlinear even at infinitesimal deformations and cannot thus be linearized. As a result values of Poisson's ratio…
A question of some fundamental importance is whether a given assembly of frictional granules (say sand or powder) will exhibit stress autocorrelations with long-range anisotropic decay as determined by the elastic Green's function. In…
A stress equilibration procedure for hyperelastic material models is proposed andanalyzed in this paper. Based on the displacement-pressure approximation computed with a stable finite element pair, it constructs, in a vertex-patch-wise…
For a given material, \emph{controllable deformations} are those deformations that can be maintained in the absence of body forces and by applying only boundary tractions. For a given class of materials, \emph{universal deformations} are…
A robust $hp$-adaptive finite element framework is presented for the investigation of static cracks in materials characterized by complex, pointwise density variations. Within such heterogeneous media, the equilibrium equation governed by…
We introduce models for viscoelastic materials, both solids and fluids, based on logarithmic stresses to capture the elastic contribution to the material response. The matrix logarithm allows to link the measures of strain, that naturally…
In this work, we study the deformation behavior of thin films of various soft glassy materials that are simultaneously subjected to two creep flow fields, rotational shear flow by applying torque and elongational flow by applying normal…
If the constitutive law linking the second Piola-Kirchhoff stress tensor and the right Cauchy-Green strain tensor derives from a potential, then the Cauchy stress tensor and the logarithm of the left Cauchy-Green strain tensor are linked by…
Cauchy-elastic solids include hyper-elasticity and a subset of elastic materials for which the stress does not follow from a scalar strain potential. More in general, hypo-elastic materials are only defined incrementally and comprise…
Hydrogels of semiflexible biopolymers such as collagen have been shown to contract axially under shear strain, in contrast to the axial dilation observed for most elastic materials. Recent work has shown that this behavior can be understood…
Crack-tip fields within a transversely isotropic strain-limiting elastic body are investigated under the influence of piecewise linear slope boundary loads. The mechanical response is characterized via a nonlinear constitutive framework…
This paper presents a finite element model for the analysis of crack-tip fields in a transversely isotropic strain-limiting elastic body. A nonlinear constitutive relationship between stress and linearized strain characterizes the material…
We find the strain energy function for isotropic incompressible solids exhibiting a linear relationship between shear stress and amount of shear, and between torque and amount of twist, when subject to large simple shear or torsion…
Metals are important structural materials for transport and the built environment. Low carbon steels can fail through strain localisation due to the role of interstitial solute atoms (such as carbon and nitrogen) interacting with mobile…
We study a fully discrete finite element approximation of a model for unsteady flows of rate-type viscoelastic fluids with stress diffusion in two and three dimensions. The model consists of the incompressible Navier--Stokes equation for…
In the framework of a deep geological radioactive waste disposal in France, the hydromechanical properties of the designated host rock, the Callovo-Oxfordian claystone (COx), are investigated in laboratory tests. Experiments presented in…
Materials under complex loading develop large strains and often transition via an elastic instability, as observed in both simple and complex systems. Here, we present Si I under large strain in terms of Lagrangian strain by an…
The theory of quasi-linear viscoelasticity (QLV) is modified and developed for transversely isotropic (TI) materials under finite deformation. For the first time, distinct relaxation responses are incorporated into an integral formulation…
We study the nonlinear elastic response of a two-dimensional material to a localized boundary force, with the particular goal of understanding the differences observed between isotropic granular materials and those with hexagonal…
Stochastic homogeneous hyperelastic solids are characterised by strain-energy densities where the parameters are random variables defined by probability density functions. These models allow for the propagation of uncertainties from input…