Related papers: A mathematical justification for nonlinear constit…
We develop a continuum theory for equilibrium elasticity of a network of crosslinked semiflexible filaments, spanning the full range between flexible entropy-driven chains to stiff athermal rods. We choose the 3-chain constitutive model…
Constitutive equations of unsaturated soils are often derived in a thermodynamically consistent framework through the use a unique 'effective' interstitial pressure. This later is naturally chosen as the space averaged interstitial…
An expression is derived for the strain energy of a polymer chain under an arbitrary three-dimensional deformation with finite strains. For a Gaussian chain, this expression is reduced to the conventional Moony--Rivlin constitutive law,…
A nonlinear small-strain elastic theory is constructed from a systematic expansion in Biot strains, truncated at quadratic order. The primary motivation is the desire for a clean separation between stretching and bending energies for…
In this paper, we study phase transitions in a slender circular cylinder composed of a compressible hyperelastic material with a non-convex strain energy function. We aim to construct the asymptotic solutions based on an axisymmetrical…
The theory of evolving natural configurations is an effective technique to model dissipative processes. In this paper, we use this theory to revisit nonlinear constitutive models of viscoelastic solids. Particularly, a Maxwell and a…
It is recalled that stress-strain incremental modelling is a common feature of most theoretical description of the mechanical behaviour of granular material. An other commonly accepted characteristics of the mechanical behaviour of granular…
Using mode-coupling theory, we derive a constitutive equation for the nonlinear rheology of dense colloidal suspensions under arbitrary time-dependent homogeneous flow. Generalizing previous results for simple shear, this allows the full…
This paper is devoted to describe the asymptotic behavior of a structure made by a thin plate and a thin rod in the framework of nonlinear elasticity. We scale the applied forces in such a way that the level of the total elastic energy…
We discuss the decomposition of the tensorial relaxation function for isotropic and transversely isotropic Modified Quasi-Linear Viscoelastic models. We show how to formulate the constitutive equation by using a convenient decomposition of…
A new, extended nonlinear framework of the ordinary real analysis incorporating a novel concept of {\em duality structure} and its applications into various nonlinear dynamical problems is presented. The duality structure is an asymptotic…
We introduce templates for exponential asymptotic expansions that, in contrast to matched asymptotic approaches, enable the simultaneous satisfaction of both boundary values in classes of linear and nonlinear equations that are singularly…
We propose a physics and chemistry-based constitutive framework to predict the stress responses of thermo-chemically aged elastomers and capture their brittle failure using the phase-field approach. High-temperature aging in the presence of…
Surface growth is a crucial component of many natural and artificial processes from cell proliferation to additive manufacturing. In elastic systems surface growth is usually accompanied by the development of geometrical incompatibility…
We prove new results on the asymptotic behavior of the nonlinear integrate-and-fire neuron model. Among them, we give a criterion for the linearized stability or instability of equilibria, without restriction on the connectivity parameter,…
Constitutive modelling of the stress-strain response of rubbery polymers is described, with an emphasis on the limits to linearity for both neat and filled rubber (the latter due to the Payne effect). Deviations from the Boltzmann…
We consider the problem of least squares parameter estimation from single-trajectory data for discrete-time, unstable, closed-loop nonlinear stochastic systems, with linearly parameterised uncertainty. Assuming a region of the state space…
The modeling of the elastic properties of disordered or nanoscale solids requires the foundations of the theory of elasticity to be revisited, as one explores scales at which this theory may no longer hold. The only cases for which…
In this study, we consider a linearized compressible flow structure interaction PDE model for which the interaction interface is under the effect of material derivative term. While the linearization takes place around a constant pressure…
The stress-gradient theory has a third order tensor as kinematic degree of freedom, which is work-conjugate to the stress gradient. This tensor was called micro-displacements just for dimensional reasons. Consequently, this theory requires…