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 The theory of elasticity is concerned with the mechanics of deformable media which, after the removal of the forces producing deformation, completely recover their original shape and give up all the work expended in the deformation. The first attempts to develop the theory of elasticity on the basis of the concept of a continuous medium, which enables one to ignore its molecular structure and describe macroscopic phenomena by the methods of mathematical analysis, date back to the first half of the eighteenth century. The fundamental contribution to the classical theory was made by R. Hooke, C. L. M. H. Navier, A. L. Cauchy, G. Lame, G. Green, B. P. E. Clapeyron. In 1678 Hooke established a law linearly con- necting stresses and strains. After Navier established the basic equations in 1821 and Cauchy developed the theory of stress and strain, of great importance in the development of elasticity theory were the investigations of B. de Saint Venant. In his classical work on the theory of torsion and bending Saint Venant gave the solution of the problems of torsion and bending of prismatic bars on the basis of the general equations of the theory of elasticity. In these investigations Saint Venant devised a semi-inverse method for the solution of elasticity problems, formulated the famous Saint Venant's principle, which enables one to obtain the solution of elasticity problems. Since then much effort has been made to develop the theory of elasticity and its applications, a number of general theorems have been proved, the general methods for the integration of differential equations of equilibrium and motion have been proposed, many special problems of fundamental interest have been solved. The development of new fields of engineering demands deeper and more extensive studies of the theory of elasticity. High velocities call for the formulation and solution of complex vibrational problems. Lightweight metallic structures draw particular attention to the question of elastic stability. The concentration of stress entails dangerous consequences, which cannot safely be ignored.

We present an elastic model of B-form DNA as a stack of thin, rigid plates or base pairs that are not permitted to deform. The symmetry of DNA and the constraint of plate rigidity limit the number of bulk elastic constants contributing to a macroscopic elasticity theory of DNA to four. We derive an effective twist-stretch energy in terms of the macroscopic stretch epsilon along and relative excess twist sigma about the DNA molecular axis. In addition to the bulk stretch and twist moduli found previously, we obtain a twist-stretch modulus with the following remarkable properties: 1) it vanishes when the radius of the helical curve following the geometric center of each plate is zero, 2) it vanishes with the elastic constant K_{23} that couples compression normal to the plates to a shear strain, if the plates are perpendicular to the molecular axis, and 3) it is nonzero if the plates are tilted relative to the molecular axis. This implies that a laminated helical structure carved out of an isotropic elastic medium will not twist in response to a stretching force, but an isotropic material will twist if it is bent into the shape of a helix.

We present an elastic model of B-form DNA as a stack of thin, rigid plates or base pairs that are not permitted to deform. The symmetry of DNA and the constraint of plate rigidity limit the number of bulk elastic constants contributing to a macroscopic elasticity theory of DNA to four. We derive an effective twist-stretch energy in terms of the macroscopic stretch epsilon along and relative excess twist sigma about the DNA molecular axis. In addition to the bulk stretch and twist moduli found previously, we obtain a twist-stretch modulus with the following remarkable properties: 1) it vanishes when the radius of the helical curve following the geometric center of each plate is zero, 2) it vanishes with the elastic constant K_{23} that couples compression normal to the plates to a shear strain, if the plates are perpendicular to the molecular axis, and 3) it is nonzero if the plates are tilted relative to the molecular axis. This implies that a laminated helical structure carved out of an isotropic elastic medium will not twist in response to a stretching force, but an isotropic material will twist if it is bent into the shape of a helix.

We present an elastic model of B-form DNA as a stack of thin, rigid plates or base pairs that are not permitted to deform. The symmetry of DNA and the constraint of plate rigidity limit the number of bulk elastic constants contributing to a macroscopic elasticity theory of DNA to four. We derive an effective twist-stretch energy in terms of the macroscopic stretch epsilon along and relative excess twist sigma about the DNA molecular axis. In addition to the bulk stretch and twist moduli found previously, we obtain a twist-stretch modulus with the following remarkable properties: 1) it vanishes when the radius of the helical curve following the geometric center of each plate is zero, 2) it vanishes with the elastic constant K_{23} that couples compression normal to the plates to a shear strain, if the plates are perpendicular to the molecular axis, and 3) it is nonzero if the plates are tilted relative to the molecular axis. This implies that a laminated helical structure carved out of an isotropic elastic medium will not twist in response to a stretching force, but an isotropic material will twist if it is bent into the shape of a helix.

We present an elastic model of B-form DNA as a stack of thin, rigid plates or base pairs that are not permitted to deform. The symmetry of DNA and the constraint of plate rigidity limit the number of bulk elastic constants contributing to a macroscopic elasticity theory of DNA to four. We derive an effective twist-stretch energy in terms of the macroscopic stretch epsilon along and relative excess twist sigma about the DNA molecular axis. In addition to the bulk stretch and twist moduli found previously, we obtain a twist-stretch modulus with the following remarkable properties: 1) it vanishes when the radius of the helical curve following the geometric center of each plate is zero, 2) it vanishes with the elastic constant K_{23} that couples compression normal to the plates to a shear strain, if the plates are perpendicular to the molecular axis, and 3) it is nonzero if the plates are tilted relative to the molecular axis. This implies that a laminated helical structure carved out of an isotropic elastic medium will not twist in response to a stretching force, but an isotropic material will twist if it is bent into the shape of a helix.

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Journal of Research of the National Bureau of Standards

Bibliography: p. 30-32

"Elements of a Mathematical Theory of Elasticity. [Abstract]" is an article from Proceedings of the Royal Society of London, Volume 8 . View more articles from Proceedings of the Royal Society of London . View this article on JSTOR . View this article's JSTOR metadata . You may also retrieve all of this items metadata in JSON at the following URL: https://archive.org/metadata/jstor-111297

Randomly crosslinked macromolecules undergo a liquid-to-amorphous solid phase transition at a critical crosslink concentration. This transition has two main signatures: the random localization of a fraction of the monomers and the emergence of a nonzero static shear modulus. In this article, a semi-microscopic statistical mechanical theory of the elastic properties of the amorphous solid state is developed. This theory takes into account both quenched disorder and thermal fluctuations, and allows for the direct computation of the free energy change of the sample due to a given macroscopic shear strain. This leads to an unambiguous determination of the static shear modulus. At the level of mean field theory, it is found (i) that the shear modulus grows continuously from zero at the transition, and does so with the classical exponent, i.e., with the third power of the excess crosslink density and, quite surprisingly, (ii) that near the transition the external stresses do not spoil the spherical symmetry of the localization clouds of the particles.

Design Methodolgy

Book Source: Digital Library of India Item 2015.171095 dc.contributor.author: Isaac Todhunter, D.sc., F.r.s., Karl Pearson, M.a. dc.contributor.other: Carnegie Mellon University dc.date.accessioned: 2015-07-07T02:45:41Z dc.date.available: 2015-07-07T02:45:41Z dc.date.digitalpublicationdate: 0000-00-00 dc.date.citation: 1886 dc.identifier.barcode: 1990040049835 dc.identifier.origpath: /data/upload/0049/840 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/171095 dc.description.scanningcentre: SASTRA University, Thanjavur dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 952 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher.digitalrepublisher: S.krishnan dc.publisher: Cambride At The University Press dc.rights: Out_of_copyright dc.title: A History Of Theory Of Elasticity And The Strength Of Materials Volume I

Book Source: Digital Library of India Item 2015.177455 dc.date.accessioned: 2015-07-07T05:19:40Z dc.date.available: 2015-07-07T05:19:40Z dc.date.digitalpublicationdate: 0000-00-00 dc.date.citation: 1946 dc.identifier.barcode: 99999990013552 dc.identifier.origpath: /data/upload/0013/557 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/177455 dc.description.scanningcentre: IIAp, Bangalore dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 389 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher.digitalrepublisher: Iiap dc.publisher: Mcgraw Hill Book Co dc.rights: Out_of_copyright dc.source.library: Indian Institute Of Astrophysics dc.title: Mathematical Theory Of Elasticity

Book Source: Digital Library of India Item 2015.177455 dc.date.accessioned: 2015-07-07T05:19:40Z dc.date.available: 2015-07-07T05:19:40Z dc.date.digitalpublicationdate: 0000-00-00 dc.date.citation: 1946 dc.identifier.barcode: 99999990013552 dc.identifier.origpath: /data/upload/0013/557 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/177455 dc.description.scanningcentre: IIAp, Bangalore dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 389 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher.digitalrepublisher: Iiap dc.publisher: Mcgraw Hill Book Co dc.rights: Out_of_copyright dc.source.library: Indian Institute Of Astrophysics dc.title: Mathematical Theory Of Elasticity

Source: Digital Library of India Scanning Centre: Allama Iqbal Library, University of Kashmir Source Library: Allama Iqbal Library University Of Kashmir Date Accessioned: 9/29/2015 16:51 The Digital Library of India was a project under the auspices of the Government of India.

We derive, by means of Gamma-convergence, the equations of homogenized bending rod starting from $3D$ nonlinear elasticity equations. The main assumption is that the energy behaves like h^2 (after dividing by the order h^2 of vanishing volume) where h is the thickness of the body. We do not presuppose any kind of periodicity and work in the general framework. The result shows that, on a subsequence, we always obtain the equations of bending-torsion rod and identifies, in an abstract formulation, the limiting quadratic form connected with that model. This is a generalization from periodic to non-periodic homogenization of bending-torsion rod theory already present in the literature.

We consider vectorial variational problems in nonlinear elasticity of the form $I[u]=\int W(Du)dx$, where $W$ is continuous on matrices with positive determinant and diverges to infinity long sequences of matrices whose determinant is positive and tends to zero. We show that, under suitable growth assumptions, the functional $\int W^{qc}(Du)dx$ is an upper bound on the relaxation of $I$, and coincides with the relaxation if the quasiconvex envelope $W^{qc}$ of $W$ is polyconvex and has $p$-growth from below with $p\ge n$. This includes several physically relevant examples. We also show how a constraint of incompressibility can be incorporated in our results.

This paper is in the public domain in USA. Metadata comes from the CrossRef API, see full record in the source URL below.

This paper is in the public domain in USA. Metadata comes from the CrossRef API, see full record in the source URL below.

134 p. 24 cm

14

Elements of a Mathematical Theory of Elasticity. Thomson, W Proceedings of the Royal Society of London (1854-1905). 1856-01-01. 8:85–87

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Elements of a Mathematical Theory of Elasticity. Thomson, W Philosophical Transactions of the Royal Society of London (1776-1886). 1856-01-01. 146:481–498

Elements of a Mathematical Theory of Elasticity. Thomson, W Philosophical Transactions of the Royal Society of London (1776-1886). 1856-01-01. 146:481–498

Journal of Research of the National Bureau of Standards

Journal of Research of the National Bureau of Standards

Journal of Research of the National Bureau of Standards

Journal of Research of the National Bureau of Standards

This paper is in the public domain in USA. Metadata comes from the CrossRef API, see full record in the source URL below.

This paper is in the public domain in USA. Metadata comes from the CrossRef API, see full record in the source URL below.

This paper is in the public domain in USA. Metadata comes from the CrossRef API, see full record in the source URL below.

The second edition of the book includes nine chapters covering six topics: (1) general concepts and equations; (2) the simplest problems; (3) the elastic equilibrium of a body bounded by a cylindrical surface in which the stresses do not vary along the generators (generalized plane strain, generalized torsion, plane problem, pure torsion Chaps. 3 to 6); (4) the equilibrium of an anisotropic cantilever; (5) the torsion of bodies of revolution, and (6) the axially symmetric deformation of bodies of revolution. At the end of the book we have appended a list of refer­ ences containing the titles of works used directly in the text,

The second edition of the book includes nine chapters covering six topics: (1) general concepts and equations; (2) the simplest problems; (3) the elastic equilibrium of a body bounded by a cylindrical surface in which the stresses do not vary along the generators (generalized plane strain, generalized torsion, plane problem, pure torsion Chaps. 3 to 6); (4) the equilibrium of an anisotropic cantilever; (5) the torsion of bodies of revolution, and (6) the axially symmetric deformation of bodies of revolution. At the end of the book we have appended a list of refer­ ences containing the titles of works used directly in the text,

The second edition of the book includes nine chapters covering six topics: (1) general concepts and equations; (2) the simplest problems; (3) the elastic equilibrium of a body bounded by a cylindrical surface in which the stresses do not vary along the generators (generalized plane strain, generalized torsion, plane problem, pure torsion Chaps. 3 to 6); (4) the equilibrium of an anisotropic cantilever; (5) the torsion of bodies of revolution, and (6) the axially symmetric deformation of bodies of revolution. At the end of the book we have appended a list of refer­ ences containing the titles of works used directly in the text,

This is an account of the nonlinear theory of thin shells from the standpoint of finite elasticity, together with a brief summary of some related recent researches on the subject. The development of the basic theory, as well as a discussion of constitutive equations for elastic shells, are presented via a direct approach on the basis of a continuum model known as a Cosserat surface rather than from the three-dimensional equations of nonlinear elasticity. (Author)

The elastic response is studied of a single flexible chain grafted on a rigid plane and an ensemble of non-interacting tethered chains. It is demonstrated that the entropic theory of rubber elasticity leads to conclusions that disagree with experimental data. A modification of the conventional approach is proposed, where the end-to-end distribution function (treated as the governing parameter) is replaced by the average energy of a chain. It is revealed that this refinement ensures an adequate description of the mechanical behavior of flexible chains. Results of numerical simulation are compared with observations on uniaxial compression of a layer of grafted chains, and an acceptable agreement is shown between the model predictions and the experimental data. Based on the analysis of combined compression and shear, a novel micro-mechanism is proposed for the reduction of friction of polymer melts at rigid walls.

We present a field formulation for defects that draws from the classical representation of the cores as force dipoles. We write these dipoles as singular distributions. Exploiting the key insight that the variational setting is the only appropriate one for the theory of distributions, we arrive at universally applicable weak forms for defects in nonlinear elasticity. Remarkably, the standard, Galerkin finite element method yields numerical solutions for the elastic fields of defects that, when parameterized suitably, match very well with classical, linearized elasticity solutions. The true potential of our approach, however, lies in its easy extension to generate solutions to elastic fields of defects in the regime of nonlinear elasticity, and even more notably for Toupin's theory of gradient elasticity at finite strains(Arch. Rat. Mech. Anal., 11, 385, 1962). In computing these solutions we adopt recent numerical work on an isogeometric analytic framework that enabled the first three-dimensional solutions to general boundary value problems of Toupin's theory (Rudraraju et al. Comp. Meth. App. Mech. Engr., 278, 705, 2014). We first present exhaustive solutions to point defects, edge and screw dislocations, and a study on the energetics of interacting dislocations. Then, to demonstrate the generality and potential of our treatment, we apply it to other complex dislocation configurations, including loops and low-angle grain boundaries.

We show existence of solutions for the equations of static atomistic nonlinear elasticity theory on a bounded domain with prescribed boundary values. We also show their convergence to the solutions of continuum nonlinear elasticity theory, with energy density given by the Cauchy-Born rule, as the interatomic distances tend to zero. These results hold for small data close to a stable lattice for general finite range interaction potentials. We also discuss the notion of stability in detail.

https://gioumeh.com/product/theory-of-elasticity-and-thermal-solution/ ----------------------------------------------------------   Authors:  M. Reza Eslami, Richard B. Hetnarski, Józef Ignaczak   Published:  Springer 2013   Edition:  1st   Pages:   786   Type:  pdf   Size:   11MB Sample:   Solution sample file   Download After Payment

357 p. 22 cm

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Approved For Release 2008/12/04: CIA-RDP80T00246AO03400020001-1 Next 3 Page(s) In Document Denied Iq Approved For Release 2008/12/04: CIA-RDP80T00246AO03400020001-1 Approved For Release 2008/12/04: CIA-RDP80T00246AO03400020001-1 I+,Nele Vii. C. 1. Paron -Bro. re t: ON" $A NN"fii or. 1i-19i7 ASUPRA IPOTEZEI SEL;TIU\IL011 PLANE: IN HEZISTE11TA MATERIALELOR PETR. P. TEODORESCU 1. Una din cele mai importante ipoteze care so fac in Rezistenta materialelor, ipoteza care caracterizeaza aceasta disciplinA fats de celelalte discipline din cadrul Mecanicii corpurilor continue deformabile, este ipo- teza sectiunilor plane. Aeeasta ipoteza are diferite aspecte dupa cum ne referim la o bara. (grinds) sau la o plae (plans sau curbs). In cele ce urmeazii not ne vom referi numai.la o barn dreapta supusa la o solicitare simply : i:ntindere sau compresiune simply, forfecare simply, Incovoiere simply sau rasuciro simply. Rezultatele ramin valabile, prin suprapunerea efectelor, ~i in cazul unor solicitari compuse, cum sint de pilda : intinderea sau compresiunea excen- trica; ele lint valabile $i in cazul Incovoierii oblice (care este tot o solici- tare simply, obtinuta prin compunerea a dons incovoieri simple In dourii.le (s') ?i puni.nd couditia ca origina 0 sA nu se depla- seze r}i ca elementele plane in jurul Pi sA nu se roteascA, pentru ca iseciiiunea din capAtul din stinga sA r#minA SncastratA, gAsim pentru deplasAri urmA- toarele expresii M u _ EI- xy. _ M t+ m (x2 + u ( y2 - z2)], 2EI Al u? ,,- ? Et y~. :f. VOnI cAuta s:i vedem ,?e ... iltti:mpbi (?+i diferite ele-rn me ale harei dupA (leforrnatie. Perttr?u aeeasta ol)ner%" Jill ;aAnl,,i ,I.?f?rniatie. luinetnl deg i!u _:1f~ (a'J ?/i =i1 astl'+ I fla it r I~il,ra nLedI harei :u~ iILait,t, ,I, ,i, t?inj;I(it y 0: u. (~) 1)up-t deformatie. ecuatiile pararn1?triee ale filu?ei ineilii ,iefor?mate vor fi (parametrsll este v.iriabila x) f 2 HI :Lee.t,;la ue aratA vii fibra medie defor-natA este cupritt,s:i in planul x0y, deci este o curbA platiA. Eliminind pe x intre primele loud eeua~ii, constatAm cA aceastA curbA este o parabolA - rezultat diferit de oel Pe care ni-1 dA Rezistenta materialelor, care afirmit cA aceastA curhA este un are de eere. Este drept insA ea in cazul inicilor deformatii, care se presupun in Teoria liuiar.i a elasticitatii, arrsil de parabolic este aproximaI fourte birte de areal de. sere. 0 sectiune Plana, itormalii 1,e fibra medic itutinte de defoi?nsatie. are ecuatia t:i Approved For Release 2008/12/04: CIA-RDP80T00246AO03400020001-1 Approved For Release 2008/12/04: CIA-RDP80T00246AO03400020001-1 Dupadeformatie,aceasts sectiunenu mai rsmIne plan.; forma aupra- fetii este dats de ecuatiile parametrice xt - X0 M 1 - y El l1 r Al unde y ili z lint parametrii variabili. Aceasta este o suprafata de gradul 4, care intersecteaza planul xOy ' dupa o parabola. Remarcam ca ea devine un plan dacs Et = 0, deci daps se neglijeazs influenta contractiei transversale. Acest lucru nu are ins. nicio influents asupra distributi.ei eforturilor unitare. Daes luam o sectiune transversalil, cu contur dreptunghiular, este interesant de vazut ce se intimpla dupa deformatie. Lat urile + b .t1 2E/ tl a?n 2 F! E~ + Y_ b2 1 (8') h I l , if If

Approved For Release 2008/12/04: CIA-RDP80T00246AO03400020001-1 Next 3 Page(s) In Document Denied Iq Approved For Release 2008/12/04: CIA-RDP80T00246AO03400020001-1 Approved For Release 2008/12/04: CIA-RDP80T00246AO03400020001-1 I+,Nele Vii. C. 1. Paron -Bro. re t: ON" $A NN"fii or. 1i-19i7 ASUPRA IPOTEZEI SEL;TIU\IL011 PLANE: IN HEZISTE11TA MATERIALELOR PETR. P. TEODORESCU 1. Una din cele mai importante ipoteze care so fac in Rezistenta materialelor, ipoteza care caracterizeaza aceasta disciplinA fats de celelalte discipline din cadrul Mecanicii corpurilor continue deformabile, este ipo- teza sectiunilor plane. Aeeasta ipoteza are diferite aspecte dupa cum ne referim la o bara. (grinds) sau la o plae (plans sau curbs). In cele ce urmeazii not ne vom referi numai.la o barn dreapta supusa la o solicitare simply : i:ntindere sau compresiune simply, forfecare simply, Incovoiere simply sau rasuciro simply. Rezultatele ramin valabile, prin suprapunerea efectelor, ~i in cazul unor solicitari compuse, cum sint de pilda : intinderea sau compresiunea excen- trica; ele lint valabile $i in cazul Incovoierii oblice (care este tot o solici- tare simply, obtinuta prin compunerea a dons incovoieri simple In dourii.le (s') ?i puni.nd couditia ca origina 0 sA nu se depla- seze r}i ca elementele plane in jurul Pi sA nu se roteascA, pentru ca iseciiiunea din capAtul din stinga sA r#minA SncastratA, gAsim pentru deplasAri urmA- toarele expresii M u _ EI- xy. _ M t+ m (x2 + u ( y2 - z2)], 2EI Al u? ,,- ? Et y~. :f. VOnI cAuta s:i vedem ,?e ... iltti:mpbi (?+i diferite ele-rn me ale harei dupA (leforrnatie. Perttr?u aeeasta ol)ner%" Jill ;aAnl,,i ,I.?f?rniatie. luinetnl deg i!u _:1f~ (a'J ?/i =i1 astl'+ I fla it r I~il,ra nLedI harei :u~ iILait,t, ,I, ,i, t?inj;I(it y 0: u. (~) 1)up-t deformatie. ecuatiile pararn1?triee ale filu?ei ineilii ,iefor?mate vor fi (parametrsll este v.iriabila x) f 2 HI :Lee.t,;la ue aratA vii fibra medie defor-natA este cupritt,s:i in planul x0y, deci este o curbA platiA. Eliminind pe x intre primele loud eeua~ii, constatAm cA aceastA curbA este o parabolA - rezultat diferit de oel Pe care ni-1 dA Rezistenta materialelor, care afirmit cA aceastA curhA este un are de eere. Este drept insA ea in cazul inicilor deformatii, care se presupun in Teoria liuiar.i a elasticitatii, arrsil de parabolic este aproximaI fourte birte de areal de. sere. 0 sectiune Plana, itormalii 1,e fibra medic itutinte de defoi?nsatie. are ecuatia t:i Approved For Release 2008/12/04: CIA-RDP80T00246AO03400020001-1 Approved For Release 2008/12/04: CIA-RDP80T00246AO03400020001-1 Dupadeformatie,aceasts sectiunenu mai rsmIne plan.; forma aupra- fetii este dats de ecuatiile parametrice xt - X0 M 1 - y El l1 r Al unde y ili z lint parametrii variabili. Aceasta este o suprafata de gradul 4, care intersecteaza planul xOy ' dupa o parabola. Remarcam ca ea devine un plan dacs Et = 0, deci daps se neglijeazs influenta contractiei transversale. Acest lucru nu are ins. nicio influents asupra distributi.ei eforturilor unitare. Daes luam o sectiune transversalil, cu contur dreptunghiular, este interesant de vazut ce se intimpla dupa deformatie. Lat urile + b .t1 2E/ tl a?n 2 F! E~ + Y_ b2 1 (8') h I l , if If

Source: Digital Library of India Scanning Centre: C-DAC, Noida Source Library: Central Library, Bits- Pilani Date Accessioned: 7/10/2015 22:17 The Digital Library of India was a project under the auspices of the Government of India.

Source: Digital Library of India Scanning Centre: C-DAC, Noida Source Library: Central Library, Bits- Pilani Date Accessioned: 7/10/2015 22:17 The Digital Library of India was a project under the auspices of the Government of India.

Strain energy density is calculated for a network of flexible chains with weak excluded-volume interactions (whose energy is small compared with thermal energy). Constitutive equations are developed for an incompressible network of chains with segment interactions at finite deformations. These relations are applied to the study of uniaxial and equi-biaxial tension (compression), where the stress--strain diagrams are analyzed numerically. It is demonstrated that intra-chain interactions (i) cause an increase in the Young's modulus of the network and (ii) induce the growth of stresses (compared to an appropriate network of Gaussian chains), which becomes substantial at relatively large elongation ratios. The effect of excluded-volume interactions on the elastic response strongly depends on the deformation mode, in particular, it is more pronounced at equi-biaxial tension than at uniaxial elongation.

Although fully elastic when static, granular media become transiently elastic when being slowly sheared -- during which both the elastic energy and stress relax. Starting from this observation, we cogently derive the framework for granular hydrodynamics, a set of differential equations consistent with general principles of physics, especially reversible and irreversible thermodynamics. In addition, an expression for the granular elastic energy is reviewed and further discussed.

Although fully elastic when static, granular media become transiently elastic when being slowly sheared -- during which both the elastic energy and stress relax. Starting from this observation, we cogently derive the framework for granular hydrodynamics, a set of differential equations consistent with general principles of physics, especially reversible and irreversible thermodynamics. In addition, an expression for the granular elastic energy is reviewed and further discussed.