Constitutive modeling of clay is an important research in geotechnical engineering. It is difficult to use precise mathematical expressions to approximate stress-strain relationship of clay. Artificial neural network (ANN) and support vector machine (SVM) have been successfully used in constitutive modeling of clay. However, generalization ability of ANN has some limitations, and application of...

Solution of the diffusion equation is usually performed with the finite element discretization for the spatial elliptic part of the equation and the time dependency is integrated via some difference scheme, often the trapezoidal rule (Crank-Nicolson) or the unconditionally stable semi-implicit two-step algorithm of Lees. A common procedure is to use Picard’s iteration with the trapezoidal rule....

Electro-active solids are solids that are either infused with electrorheological fluids or embedded with electrically conducting particles, the body as a whole however conducting negligible current. In this paper, we provide a mathematical framework, within the context of continuum mechanics, for the study of electro-active solids. The theory assumes that the body can be considered as a continu...

The paper is devoted to homogenization of two-phase incompressible viscoelastic flows with disordered microstructure. We study two cases. In the first case, both phases are modeled as Kelvin-Voight viscoelastic materials. In the second case, one phase is a Kelvin-Voight material, and the other is a viscous Newtonian fluid. The microscale system contains the conservation of mass and balance of m...

Ideal memristor is a resistor with a memory, which adds dynamics to its behavior. The most usual characteristics describing this dynamics are the constitutive relation (i.e. the relation between flux and charge), or Parameter-vs-state map (PSM), mostly represented by the memristance-to-charge dependence. One of the so far unheeded tools for memristor description is its differential equation (DE...

4 constitutive equation for unstimulated muscle based on nonlinear elastic and linear damping elements is proposed. This equation is solved in closed form to predict creep and stress relaxation in passive muscle and. if combined with an active contractile element in a three-element model. initial response to a sudden change in length or force during an isometric twitch. A stress relaxation expe...

Recent research by Xing [Phys. Rev. Lett. 98, 075502 (2007)] has provided an expression for the Helmholtz free energy related to phonon fluctuations in polymer networks. We extend this result by constructing the corresponding nonlinear constitutive equation, usable for entirely general, volume conserving deformation fields. Constitutive equations for the sliplink model and the tube model are de...

[1] A generalized constitutive equation for bubbly liquids is presented which successfully reproduces the expected viscosity response for both steady flows with varying capillary number Ca (a measure of the bubble deformation) and unsteady flows with varying dynamic capillary number Cd (a measure of the steadiness of the flow) previously given in separate studies. The constitutive equation is g...

We solve exactly and describe in detail a simplified scalar model for the low frequency shear rheology of foams, emulsions, slurries, etc. @P. Sollich, F. Lequeux, P. Hébraud, and M. E. Cates, Phys. Rev. Lett. 78, 2020 ~1997!#. The model attributes similarities in the rheology of such ‘‘soft glassy materials’’ to the shared features of structural disorder and metastability. By focusing on the d...

Structures made of transforming materials exhibit a striking capacity to hysteretically recover significant deformation with a controllable amount of energy absorbed in the process. The unusual properties of these materials are due to the fact that large deformations and inelastic behavior are accomplished by coordinated migration of mobile phase or domain boundaries. Intensive research in rece...