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Rheological Principles
Published in B. R. Gupta, Rheology Applied in Polymer Processing, 2023
Stress is simply a constraining force or influence. It is defined as the intensity of surface force acting on the system”[1, 2] that is, the forces on a member caused by loads: consisting of torsion or twisting, compression or pushing, tension or pulling, and shear or cutting. In continuum mechanics stress is a physical quantity that expresses the internal forces that the neighbouring particles of a continuous material exert on each other.
Theory of Strain
Published in Prasun Kumar Nayak, Mijanur Rahaman Seikh, Continuum Mechanics, 2022
Prasun Kumar Nayak, Mijanur Rahaman Seikh
Continuum mechanics, a scientific discipline, is a branch of mechanics that deals with the analysis of the kinematics and the mechanical behavior of substances (materials modeled as a continuous mass rather than as discrete particles) under the influence of external agents that make changes in the state of medium. These changes may appear in the form of contact forces, such as chemical, electrical, mechanical or any other type of disturbances.
An Introductory Guide to Solid Mechanics
Published in Jiro Nagatomi, Eno Essien Ebong, Mechanobiology Handbook, 2018
Continuum mechanics is arguably the most mature field of engineering science. Its parallel course work in physics is more often called Newtonian mechanics. Both assume that all events occur at speeds considerably less than the speed of light, i.e., no relativity. It has also been for many years the core subject in applied mathematics, sometimes under the title of rational mechanics. Continuum mechanics is the mathematical theory associated with the mechanical behavior of both solids and fluids, as they are subjected to forces or displacements considered on a macroscopic scale. At the finest scale, matter is discontinuous, composed of molecules, atoms, and smaller particles with significant space between them. Most engineering applications, however, deal with matter on a much larger, most often observable scale. At these scales, the concern is with the average response of the collection of the bits and pieces of matter rather than a detailed description of individual particles. While the mathematics of continuum mechanics often considers limits that approach a value at a single point in space, the point is still assumed to have the properties of the bulk material. Continuum mechanics can be further divided into kinematics, which is the study of motion, displacement, velocity, and acceleration, without a specific consideration of the forces required to affect the motion, and mechanics of materials, which is the study of the forces and variables that relate to them, forces per unit area, or per unit volume that can be linked to the energy of deformation as well as displacements and the gradients of displacement, which describe deformation. The most significant difference between solid and fluid mechanics is the idea of a reference state. In solids, even those that can exhibit large deformation, descriptions are with respect to a defined reference state, i.e., position, place, or shape of the material. In contrast, it is extremely difficult to define an original material-based shape for a fluid; fluids assume the shape of their external containers. Thus, the emphasis in fluid mechanics is on tracking what is observed with respect to a global, rather than material, position, i.e., what is the speed of the fluid past a specific point.
Compression–shear coupling rheological constitutive model of the deep-sea sediment
Published in Marine Georesources & Geotechnology, 2018
Feng Xu, Qiu-Hua Rao, Jie Zhang, Wenbo Ma
Endochronic theory based on second law of thermodynamics (Valanis 1978; Chen et al. 2003; Zhang and Xiong 2008) is adopted to establish the two-dimensional rheological model by reconstructing intrinsic time. Within the scope of continuum mechanics theory, it is assumed that (1) the material is homogeneous, continuous, and isotropic, (2) the deformation of material is small, and (3) the deformation process is under isothermal and adiabatic state.
The use of contravariant tensor invariants to model damage in anisotropic soft tissues
Published in Mechanics of Advanced Materials and Structures, 2022
Arthesh Basak, Rajagopal Amirtham, Umesh Basappa
Continuum Mechanics is a branch of mechanics that assumes the body as a continuum and not a collection of discrete particles. In continuum mechanics two different body configurations are considered (a) Lagrangian/undeformed/material configuration and (b) Eulerian/deformed/spatial configuration.
Determination of carbon nanotubes size-dependent parameters: molecular dynamics simulation and nonlocal strain gradient continuum shell model
Published in Mechanics Based Design of Structures and Machines, 2021
Khashayar Ghorbani, Ali Rajabpour, Majid Ghadiri
In the study of micro/nanoscale structures, in addition to experimental methods, molecular dynamics (MD) simulation, as a virtual laboratory and mathematical modeling based on the continuum mechanics, are also known as extensive and efficient methods in this regard. The classical continuum mechanics consider material as a continuum with an infinite number of material particles and are based on constitutive relations which assume that the stress at a specific point is a function of strain at that point. This assumption leads to neglecting the influences of long-range interatomic and intermolecular cohesive forces on the static and dynamic behavior of sub-micron structures. Hence, to use the continuum mechanics in the study of such structures, some complementary theories are presented along with this method. These theories, which are known as size-dependent theories, by applying the small-scale effects and introducing the size-dependent parameters (which are the material properties), support the classical continuum mechanics methods. Two main theories of this kind are the nonlocal (NL) (Eringen and Edelen 1972; Eringen 1983) and gradient elasticity theories (Toupin 1962; Koiter 1964; Mindlin 1964; Mindlin 1965; Aifantis 1992). In the NL theory, stress at a point is not only a function of the strain at that point but also is a function of strains at all points in the structure through an attenuation function (Eringen 1983). Within this theory, the long-range effects of cohesive forces between atoms or molecules are included in the continuum mechanics by an NL parameter (Lim, Zhang, and Reddy 2015). The NL parameter contains information including the lattice spacing. This theory can only be used to capture the stiffness softening effect which is accompanied by an increase in the NL parameter (Li and Hu 2015), while the stiffness enhancement effect observed from experiential studies (Lam et al. 2003) cannot be determined by the NL theory and classical continuum mechanics. The stiffness enhancement effect is considered by the gradient elasticity theories in which micro/nanoscale materials are presumed to be consisting of atoms with higher-order deformation mechanism and cannot be modeled as collections of points. This assumption is provided by the further higher-order strain gradient (SG) terms that contain the material length scale (MLS) parameter (Li and Hu 2016).