## a theory of an elastic-plastic continuum with special

### Continuum mechanics

Alternative Titles: c-number theory, classical field theory, continuum physics, mechanics of deformable media Figure 1: The position vector x and the velocity vector v of a material point, the body force f dV acting on an element dV of volume, and the surface force T dS acting on an element dS of surface in a Cartesian coordinate system 1, 2, 3 (see text).

### Thermodynamical Modeling of Elastic

The change in elastic moduli due to damage development and the initial and the subsequent damage surface expressed in stress space are described well by the proposed theory. Finally, experimental verification of the existence of a damage potential and the corresponding normality law is performed.

### A UNIFIED APPROACH TO FINITE DEFORMATION ELASTOPLASTIC ANALYSIS BASED ON THE USE OF HYPERELASTIC

226 J.C. Simo, M. Om'z, Finite deformation elastoplastic analysis 2.2. Multiplicative theory Relative to the intermediate configuration, Table 2, the al plastic state is characterized by the Lagrangian strain ten_sors 3 = f( - G) and EP

### A continuum theory of amorphous solids undergoing large

gradient F into elastic and plastic parts, Fe and Fp ([9], [10]). An important feature of our theory is the assump-tion that the (Helmholtz) free energy depends on Fp, an assumption that leads directly to a backstress in the under-lying owrule. Further, akeyfeature

### Elastic Buckling Strength of Buried Flexible Culverts

based on the elastic continuum model is then described that permits rational predictions of culvert buckling strength. Finally, a number of example problems are considered, to demon strate how the elastic continuum theory differs from existing design rules.

### The Continuum Stored Energy for Constitutive Modeling

In order to better understand finite elastic-plastic deformations of polymers, c 1, c 2, and c 3 terms in the continuum constitutive model are individually depicted for both LDPE and iPP ductile polymers. The true stress-stretch component curves for both

### A Theory of Crack Growth in Viscoelastic Media

it contains as a special case the classical theory of fracture for elastic and elastic-perfectly plastic media when the plastic zone size is small relative to crack length. We shall not attempt to review or even list the many experimental and theoretical papers which

### FINITE ELEMENT ANALYSIS OF A CONTINUUM UNDERGOING LARGE ELASTIC

CHAPTER 3 : ELASTIC-PLASTIC PROBLEMS 27 3.1 Basic Concepts of Plasticity 27 3.1.1 Yield Criterion 27 3.1.2 Flow rule 30 3.1.3 Hardening Rule 3 2 3.1.4 Prandtl-Reuss Equations 32 3.2 The Elastic-Plastic Matrix 33 3.2.1 Special Forms of the II

### Continuum Mechanics

in such a set of lecture notes. Personal taste has led me to include a few special (but still well-known) topics. Examples of these include sections on the statistical mechanical theory of polymer chains and the lattice theory of crystalline solids in the discussion

### Thermodynamics of Elastic‐Plastic Materials as a Theory

2003/11/18Rate‐independent plasticity is studied as a limiting case of the present theory. We illustrate the theory with a special case: a one‐dimensional, homogeneous, cyclic deformation of a rate‐independent elastic‐plastic body which exhibits a Bauschinger effect.

### Wave propagation in elastic–plastic material with voids:

2020/2/3The propagation of unidirectional plane waves has been explored in an infinite elastic–plastic material with voids, and it has been found that there exist four basic waves consisting of three coupled elastic–plastic waves and a lone transverse wave.

### Continuum Mechanics

Mechanics of Elastic Solids In this chapter, we apply the general equations of continuum mechanics to elastic solids . As a philosophical preamble, it is interesting to contrast the challenges associated with modeling solids to the fluid mechanics problems discussed in the preceding chapter.

### Nonlinear Elasticity, Plasticity, and Viscoelasticity

given attention. This eld is very broad and special books are devoted to various types of nonlinearities (e.g. plasticity, viscoelasticity, and non-Newtonian ma-terials). The objective of this chapter is to brie y discuss nonlinear elastic and elastic{plastic material

### CHAP 4 FEA for Elastoplastic Problems

CHAP 4 FEA for Elastoplastic Problems Nam-Ho Kim Introduction • Elastic material: a strain energy is differentiated by strain to obtain stress – History-independent, potential exists, reversible, no permanent deformation • Elatoplastic material: – Permanent

### A large strain anisotropic elastoplastic continuum theory for

A large strain anisotropic elastoplastic continuum theory for nonlinear kinematic hardening and texture evolution Francisco Javier Montans3'*, Jose Maria Benitez3, Miguel Angel Caminerob a Escuela Tecnica Superior de Ingenieros Aeronauticos, Universidad Politecnica de Madrid, Pza.

### A finite elastic

1973/9/1A mechanical theory of a finite elastic-plastic material is presented as a special type of the more general simple material with memory. Thus, the concepts of invariance used in the theory of simple materials are applied to the special case to derive explicit forms for the various constitutive equations. The theory and the interpretation differ from previous theories byGreen andNaghdi and

### A continuum theory of a plastic

A continuum model is proposed for describing the plastic-elastic behaviour of a composite material consisting of a plastic-elastic matrix reinforced by strong elastic fibres. The composite is transversely isotropic about the fibre direction, the local axis of transverse isotropy being

### On the stability of elastic–plastic systems with hardening

of stability given in [11] is adapted to the continuum case. The structure of the article is the following. In Section 2, the mathematical formulations for dynamic and quasi-static elastic–plastic systems with hardening are presented. Using the theory of maximal

### A treatise on the mathematical theory of elasticity

analytical problems presented by elastic theory. The theory leads in every special case to a system of partial differential equations, and the solution of these subject to conditions given at certain bounding surfaces is required. The general problem is that of

### Modeling elastic and plastic deformations in

A continuum field theory approach is presented for modeling elastic and plastic deformation, free surfaces, and multiple crystal orientations in nonequilibrium processing phenomena. Many basic properties of the model are calculated analytically, and numerical

### [PDF] Theory Of Plasticity

2012/12/2Continuum Theory of Plasticity Book Description : The only modern, up-to-date introduction to plasticity Despite phenomenal progress in plasticity research over the past fifty years, introductory books on plasticity have changed very little. To meet the need for an

### Materials

In [2,3,4], elastic and elastic/plastic spherical vessels subjected to various loading conditions are considered. Thermo-elastic simply supported and clamped circular plates are studied in [ 5 ]. Many analytic and semi-analytic solutions are available for FGM discs and cylinders assuming that material properties vary in the radial direction but are independent of the circumferential and axial

### Cosserat elasticity; micropolar elasticity

2010/2/5A more general continuum theory such as Cosserat elasticity (micropolar continuum theory) or nonlocal elasticity, may be of use in predicting non-classical strain distributions. In this study, size effects in the mechanical rigidity of foams are examined experimentally.

### Plasticity (physics)

An idealized uniaxial stress-strain curve showing elastic and plastic deformation regimes for the deformation theory of plasticity There are several mathematical descriptions of plasticity. [9] One is deformation theory (see e.g. Hooke's law ) where the Cauchy stress tensor (of order d-1 in d dimensions) is a function of the strain tensor.

### Continuum mechanics

Continuum mechanics is a branch of mechanics that deals with the mechanical behavior of materials modeled as a continuous mass rather than as discrete particles.The French mathematician Augustin-Louis Cauchy was the first to formulate such models in the 19th century.

### Materials

In [2,3,4], elastic and elastic/plastic spherical vessels subjected to various loading conditions are considered. Thermo-elastic simply supported and clamped circular plates are studied in [ 5 ]. Many analytic and semi-analytic solutions are available for FGM discs and cylinders assuming that material properties vary in the radial direction but are independent of the circumferential and axial

### A general theory of an elastic

1965/1/1A general theory of an elastic-plastic continuum A. E. Green 1,2 P. M. Naghdi 1,2 Archive for Rational Mechanics and Analysis volume 18, pages 251 – 281 (1965)Cite this article 1304 Accesses 644 Citations Metrics details This is a preview of subscription