[图书][B] Preconditioning and the conjugate gradient method in the context of solving PDEs

J Málek, Z Strakoš - 2014 - SIAM
Our times can be characterized by, among many other attributes, the seemingly increasing
speed of everything. Within science, it has led to the publication explosion, which reflects the …

A novel approach to the description of constitutive relations

KR Rajagopal, G Saccomandi - Frontiers in Materials, 2016 - frontiersin.org
Recent advances in the development of implicit constitutive relations to describe the
response of both solids and fluids have greatly increased the repertoire of the modeler in his …

Derivation of the variants of the Burgers model using a thermodynamic approach and appealing to the concept of evolving natural configurations

J Málek, KR Rajagopal, K Tůma - Fluids, 2018 - mdpi.com
Viscoelastic rate-type fluid models involving the stress and frame-indifferent time derivatives
of second order, like those in Burgers' model, are used to describe the complicated …

Infinitesimal and infinite numbers in applied mathematics

A Bryzgalov, K Islami, P Giordano - Nonlinear Dynamics, 2024 - Springer
The need to describe abrupt changes or response of nonlinear systems to impulsive stimuli
is ubiquitous in applications. Also the informal use of infinitesimal and infinite quantities is …

Time periodic pulse electroosmotic flow of Jeffrey fluids in a circular microchannel under the depletion effect

D Li, K Li - Journal of Mechanical Science and Technology, 2022 - Springer
We used the Laplace transform method to investigate the time periodic pulse electroosmotic
flow (EOF) of linear viscoelastic fluids through a circular microchannel driven by pulse …

A new class of quasi-linear models for describing the nonlinear viscoelastic response of materials

A Muliana, KR Rajagopal, AS Wineman - Acta Mechanica, 2013 - Springer
In this short note, we develop a new class of “quasi-linear” viscoelastic models wherein the
linearized strain is expressed in terms of a nonlinear measure of the stress. The class of …

An implicit thermomechanical theory based on a Gibbs potential formulation for describing the response of thermoviscoelastic solids

KR Rajagopal, AR Srinivasa - International Journal of Engineering Science, 2013 - Elsevier
The aim of this paper is to develop an implicit constitutive for the thermoviscoelastic behavior
of polymers, based on a thermomechanical framework. The core idea is to assume that the …

On the response of physical systems governed by non-linear ordinary differential equations to step input

V Průša, KR Rajagopal - International Journal of Non-Linear Mechanics, 2016 - Elsevier
The response of physical systems governed by linear ordinary differential equations to step
input is traditionally investigated using the classical theory of distributions. The response of …

Modelling the nonlinear viscoelastic response of asphalt binders

SPA Narayan, DN Little… - International Journal of …, 2016 - Taylor & Francis
In a recent article, Narayan et al.[Narayan, SPA, et al., 2012b. Nonlinear viscoelastic
response of asphalt binders: experimental study of relaxation of torque and normal force in …

Colombeau algebra as a mathematical tool for investigating step load and step deformation of systems of nonlinear springs and dashpots

V Průša, M Řehoř, K Tůma - Zeitschrift für angewandte Mathematik und …, 2017 - Springer
The response of mechanical systems composed of springs and dashpots to a step input is of
eminent interest in the applications. If the system is formed by linear elements, then its …