Book•
The non-linear field theories of mechanics
01 Jan 1992-
TL;DR: A theory aiming to describe their mechanical behavior must take heed of their deformability and represent the definite principles it obeys as mentioned in this paper, which is not the case in modern physics, since it concerns solely the small particles of matter.
Abstract: Matter is commonly found in the form of materials. Analytical mechanics turned its back upon this fact, creating the centrally useful but abstract concepts of the mass point and the rigid body, in which matter manifests itself only through its inertia, independent of its constitution; “modern” physics likewise turns its back, since it concerns solely the small particles of matter, declining to face the problem of how a specimen made up of such particles will behave in the typical circumstances in which we meet it. Materials, however, continue to furnish the masses of matter we see and use from day to day: air, water, earth, flesh, wood, stone, steel, concrete, glass, rubber, ... All are deformable. A theory aiming to describe their mechanical behavior must take heed of their deformability and represent the definite principles it obeys.
Citations
More filters
TL;DR: In this paper, a mathematical framework is developed to study the mechanical behavior of material surfaces, and the tensorial nature of surface stress is established using the force and moment balance laws using a linear theory with non-vanishing residual stress.
Abstract: A mathematical framework is developed to study the mechanical behavior of material surfaces. The tensorial nature of surface stress is established using the force and moment balance laws. Bodies whose boundaries are material surfaces are discussed and the relation between surface and body stress examined. Elastic surfaces are defined and a linear theory with non-vanishing residual stress derived. The free-surface problem is posed within the linear theory and uniqueness of solution demonstrated. Predictions of the linear theory are noted and compared with the corresponding classical results. A note on frame-indifference and symmetry for material surfaces is appended.
2,641 citations
TL;DR: The basic explicit finite element and finite difference methods that are currently used to solve transient, large deformation problems in solid mechanics are reviewed.
Abstract: Explicit finite element and finite difference methods are used to solve a wide variety of transient problems in industry and academia. Unfortunately, explicit methods are rarely discussed in detail in finite element text books. This paper reviews the basic explicit finite element and finite difference methods that are currently used to solve transient, large deformation problems in solid mechanics. A special emphasis has been placed on documenting methods that have not been previously published in journals.
1,218 citations
Cites background from "The non-linear field theories of me..."
...The material time derivative of the stress is not objective [28], i....
[...]
TL;DR: In this paper, a unified framework for Ginzburg-Landau and Cahn-Hilliard type equations was developed using a balance law for microforces in conjunction with constitutive equations consistent with a mechanical version of the second law.
892 citations
Book•
01 May 1996
TL;DR: In this article, a concise treatment of the theory of nonlinear evolutionary partial differential equations is provided, and a rigorous analysis of non-Newtonian fluids is provided for applications in physics, biology, and mechanical engineering.
Abstract: This book provides a concise treatment of the theory of nonlinear evolutionary partial differential equations. It provides a rigorous analysis of non-Newtonian fluids, and outlines its results for applications in physics, biology, and mechanical engineering
795 citations
TL;DR: This short treatise presents a concise history of the study of solid tumour growth, illustrating the development of mathematical approaches from the early decades of the twentieth century to the present time, showing the crucial relationship between experimental and theoretical approaches.
710 citations
References
More filters
TL;DR: The mating of Brazilian and Guatemalan flies is, therefore, selective rather than random; however, the particular type of selectivity here observed does not constitute a barrier to gene exchange.
6,273 citations
TL;DR: In this article, Murnaghan's theory of finite strain is developed for a medium of cubic symmetry subjected to finite hydrostatic compression, plus an arbitrary homogeneous infinitesimal strain.
Abstract: Murnaghan's theory of finite strain is developed for a medium of cubic symmetry subjected to finite hydrostatic compression, plus an arbitrary homogeneous infinitesimal strain. The free energy is developed for cubic symmetry to include terms of the third order in the strain components. The effect of pressure upon the second-order elastic constants is found and compared with experiment, with particular reference to the compressibility; the pressure-volume relation in several approximations is compared with the measurements to 100,000 kg/${\mathrm{cm}}^{2}$. The simplest approximation is shown to give a satisfactory account of most of the experimental data. The results are also compared with some of the calculations based on Born's lattice theory.
4,834 citations
3,323 citations
TL;DR: In this paper, it was deduced that the general strain energy function, W, has the form W=G4 ∑ i=13(λi−1λi)2+H 4 ∑ t=13 (λi2−1 ε)2 + H 4, where the λi's are the principal stretches, G is the modulus of rigidity, and H is a new elastic constant not found in previous theories.
Abstract: It is postulated that (A) the material is isotropic, (B) the volume change and hysteresis are negligible, and (C) the shear is proportional to the traction in simple shear in a plane previously deformed, if at all, only by uniform dilatation or contraction. It is deduced that the general strain‐energy function, W, has the form W=G4 ∑ i=13(λi−1λi)2+H4 ∑ t=13(λi2−1λi2), where the λi's are the principal stretches (1+principal extension), G is the modulus of rigidity, and H is a new elastic constant not found in previous theories. The differences between the principal stresses are σi[minus]σi=λi∂ W/∂λi[minus]λi∂ W/∂λi.Calculated forces agree closely with experimental data on soft rubber from 400 percent elongation to 50 percent compression.
2,775 citations
TL;DR: HAL as discussed by the authors is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not, which may come from teaching and research institutions in France or abroad, or from public or private research centers.
Abstract: HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Elastic materials with couple-stresses R. Toupin
2,574 citations