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Progress in solid mechanics, vol. II
ROOK Progress in Solid Mechanics, Vol. I’ublishing Company, Amsterdam,
REVIEWS
II. Edited by I. N. SXKI~I~ON and R. HILL. 1961. xi + 331 pp., ’70s.
North-Holland
THE second volume of this series is somewhat shorter than the first (containing seven chapters as compared with eight), most of the contributions :tgGn being concerned with aspects of the Welcome innovations, howcrer, are an article dealing specitheories of elasticity and plasticity. fically with experimental methods and one on general continuum mechanics. Chapter 1 by J. IL ,\DICINS is entitled ’ Large Elastic Deformations, ’ and frotlr the considcrablc literature which has accunrulatcd in this field since 104X the author has made a Iiic,~ly-bRlancet1 sclcction of lopics. The first section is nu~inly dcvotrd to a discussion of the elastic strain cncrgy function and the restrictions which may bc imposed ~1,011 it by symmetry propertics and by internal geometrical constraints such as the condition of incompressibility. Exact solutions oj problems of finite elastic strain are then reviewed and the final sccticn is concerned with approuimate methods. Since the interests of the author are clearly reflected in this choice of material, one regrets the omission of a personal view of the directions in which future research might proceed. is content to set In Chapter 2, ’ Elastic \Varcs in Anisotropic Media,’ 1LI. J. 1’. MUS~I~AVE out the salient thcorctiral results with a nrinimun1 of analysis. ‘I’hc rcsulling, rather terse, trcalnlrnt of the basic Itrc,ory is Ihllowed by an account of wave l)ropagation in Inrdia having hcsa~onal and cubic symmetry and a brief discussion of surface waves. .J. 1). Esu~:r.u~‘s treatment of ’ l%stic Inclusions and Illhotlrogcrlciliri ’ in (‘haptcr 3 is lllrlch more discursive in style. The two problems considered are the transformation problcnl, which involves the solution of tbc equations of elasticity in a homogeneous medium containing an inclusion which has undergone a permanent change cf form rcprescnted, in the absence of the surrounding material, by a uniform strain ; and the inhomogencity problem in which it is required to find the disturbance of a uniform elastic field prcduccd by a region in which the elastic ronstants are different from those of the surrounding material. Complete solutions of these problems are presented for ellipsoidal inclusions and inhomogeneities, and the author concludes his most rcadablc survey by relating them to an astonishing variety of physical applications. In Chapter 4 on ’ Plastic Waves,’ J. U. CRAGGS has given a lucid account of another subject which has comparatively recently acquired an extensive literature, much of it concerned wit11 esprrimental studies. The author’s viewpoint, which is stated in forthright fashion in the introductory section, enables hinl to bring a degree of unity to this rather tliffusc material. The trratmcnt is notablr, howcvcr, for depth rather than breadth, the initial contention that, ‘ at tiw present time, thcrc is no conclusive experimental evidence of the existence of visco-elastic effects in metals at high rates of strain ’ being in marked contrast to the claim mado in another recent rcvicw article* that ‘ It is now well-established that the mrchanical behaviour of metals is often dependent upm ratr-of-strain.’ The latter sections of this chapter discuss waves of uniavial stress, plunc waves, spherical and cylindrical waves, flexural wa\-es in beams, waves in plates and shells and experimental methods. The title of Chapter 5, ‘ The Measurement of Dynamic Elastic Properties, by I<. \Y. HILLIEIL rather ronccals the fact that the author is concerned with viscoclastic as well as perfectly elastic behaviaur. The bulk of the article is devoted to a description of experimental mrthods based upon free or forced vibretions of a specinrcn (resonance methods) or upon the propagation of waves within it. The conclusion that ‘ at the present time it appears that cspcrirnental data is in advance of comprehensive theory ’ echoes the view express4 by (‘II.\GGRin the previous chapter anti thcsc two articles deserve the attention of those theoreticians who wish to work OIL ljarticular problems rather than general theories. In Chapter 6, ’ Discontinuity Relations in Mechanics of Solids,’ R. HILL discusses a subject which is at present being actively
explored
and which, in the author’s
view, is likely to become
1 S,E
BOOK J(Kv~I,.\vs
of i~wrea.siu,g itnpo~lancc. Results originally due to tIAD.malrl) on the l)ossibk values taken ou a surface 2 by tllc dcrivati\w of a I‘unction tlefincd in a ncigt~bourllood ol’ z‘ are rca-st;ltctl, arid sucwssivcly extrndctl to huwtions tlcliucd on both sides of 2 which arc continuous but ma)- have discontiuuorls tlerivnti\-cs on 2, and to such functions which are thcnrsclves discontinuous ou 2. Iiirlenlalic relations for jumps in tillrc-tlerivati\-es wlwn Z is :I moving surface arc tlren tlrri\,ctt. ‘I’llc final thrre sections arc devoted to apl)lications ol’ the analysis to the study 01’ possible tliscontinuities in stress-ralr, to the treatment of diwontinuities in perfectly elastic solids subject to infinitesimal strain, and to rigid/plastic solids. This clcgant, but closrly-arguctl, accouul of a dillicrdt su~~,jcc1. will bc found to repa,y careful rr-rrading. Tlw linal ch:q)tcr, ’ The Stability of l!kstic-l’lastir Structures ’ by RI. II. IIoniw, is conccrnctl \vitll t tw rcspousc to apl~licd loading of structures crllibiting etastic/perfcctly plastic behaviour. Sections on gcncral principles and analytic tectmiqucs arc hollowed by a critique of existing calculations, particular attention king paid to the estimatiou of tllc loads nreded to bring about failure. ‘I’llrougllout thr artirk tllr rcwlcr’s at tcmtion is carct’ully dramn to points of tile thcoq at wtlicll furttwr research i5 rccluircd. ‘l‘hv :ilt ictcs in this \-olu~~w rwch :I high standard or cspo~ition , ant1 slwcialists in tnoht branollcs of solitl nlcchanics as wail iis those brginnirrg rescawh in this field \vitl find nrllrh to gllidc and illullrinatc tllcir work. 1’. CHal,wIc%
REVIEWS
II. Edited by I. N. SXKI~I~ON and R. HILL. 1961. xi + 331 pp., ’70s.
North-Holland
THE second volume of this series is somewhat shorter than the first (containing seven chapters as compared with eight), most of the contributions :tgGn being concerned with aspects of the Welcome innovations, howcrer, are an article dealing specitheories of elasticity and plasticity. fically with experimental methods and one on general continuum mechanics. Chapter 1 by J. IL ,\DICINS is entitled ’ Large Elastic Deformations, ’ and frotlr the considcrablc literature which has accunrulatcd in this field since 104X the author has made a Iiic,~ly-bRlancet1 sclcction of lopics. The first section is nu~inly dcvotrd to a discussion of the elastic strain cncrgy function and the restrictions which may bc imposed ~1,011 it by symmetry propertics and by internal geometrical constraints such as the condition of incompressibility. Exact solutions oj problems of finite elastic strain are then reviewed and the final sccticn is concerned with approuimate methods. Since the interests of the author are clearly reflected in this choice of material, one regrets the omission of a personal view of the directions in which future research might proceed. is content to set In Chapter 2, ’ Elastic \Varcs in Anisotropic Media,’ 1LI. J. 1’. MUS~I~AVE out the salient thcorctiral results with a nrinimun1 of analysis. ‘I’hc rcsulling, rather terse, trcalnlrnt of the basic Itrc,ory is Ihllowed by an account of wave l)ropagation in Inrdia having hcsa~onal and cubic symmetry and a brief discussion of surface waves. .J. 1). Esu~:r.u~‘s treatment of ’ l%stic Inclusions and Illhotlrogcrlciliri ’ in (‘haptcr 3 is lllrlch more discursive in style. The two problems considered are the transformation problcnl, which involves the solution of tbc equations of elasticity in a homogeneous medium containing an inclusion which has undergone a permanent change cf form rcprescnted, in the absence of the surrounding material, by a uniform strain ; and the inhomogencity problem in which it is required to find the disturbance of a uniform elastic field prcduccd by a region in which the elastic ronstants are different from those of the surrounding material. Complete solutions of these problems are presented for ellipsoidal inclusions and inhomogeneities, and the author concludes his most rcadablc survey by relating them to an astonishing variety of physical applications. In Chapter 4 on ’ Plastic Waves,’ J. U. CRAGGS has given a lucid account of another subject which has comparatively recently acquired an extensive literature, much of it concerned wit11 esprrimental studies. The author’s viewpoint, which is stated in forthright fashion in the introductory section, enables hinl to bring a degree of unity to this rather tliffusc material. The trratmcnt is notablr, howcvcr, for depth rather than breadth, the initial contention that, ‘ at tiw present time, thcrc is no conclusive experimental evidence of the existence of visco-elastic effects in metals at high rates of strain ’ being in marked contrast to the claim mado in another recent rcvicw article* that ‘ It is now well-established that the mrchanical behaviour of metals is often dependent upm ratr-of-strain.’ The latter sections of this chapter discuss waves of uniavial stress, plunc waves, spherical and cylindrical waves, flexural wa\-es in beams, waves in plates and shells and experimental methods. The title of Chapter 5, ‘ The Measurement of Dynamic Elastic Properties, by I<. \Y. HILLIEIL rather ronccals the fact that the author is concerned with viscoclastic as well as perfectly elastic behaviaur. The bulk of the article is devoted to a description of experimental mrthods based upon free or forced vibretions of a specinrcn (resonance methods) or upon the propagation of waves within it. The conclusion that ‘ at the present time it appears that cspcrirnental data is in advance of comprehensive theory ’ echoes the view express4 by (‘II.\GGRin the previous chapter anti thcsc two articles deserve the attention of those theoreticians who wish to work OIL ljarticular problems rather than general theories. In Chapter 6, ’ Discontinuity Relations in Mechanics of Solids,’ R. HILL discusses a subject which is at present being actively
explored
and which, in the author’s
view, is likely to become
1 S,E
BOOK J(Kv~I,.\vs
of i~wrea.siu,g itnpo~lancc. Results originally due to tIAD.malrl) on the l)ossibk values taken ou a surface 2 by tllc dcrivati\w of a I‘unction tlefincd in a ncigt~bourllood ol’ z‘ are rca-st;ltctl, arid sucwssivcly extrndctl to huwtions tlcliucd on both sides of 2 which arc continuous but ma)- have discontiuuorls tlerivnti\-cs on 2, and to such functions which are thcnrsclves discontinuous ou 2. Iiirlenlalic relations for jumps in tillrc-tlerivati\-es wlwn Z is :I moving surface arc tlren tlrri\,ctt. ‘I’llc final thrre sections arc devoted to apl)lications ol’ the analysis to the study 01’ possible tliscontinuities in stress-ralr, to the treatment of diwontinuities in perfectly elastic solids subject to infinitesimal strain, and to rigid/plastic solids. This clcgant, but closrly-arguctl, accouul of a dillicrdt su~~,jcc1. will bc found to repa,y careful rr-rrading. Tlw linal ch:q)tcr, ’ The Stability of l!kstic-l’lastir Structures ’ by RI. II. IIoniw, is conccrnctl \vitll t tw rcspousc to apl~licd loading of structures crllibiting etastic/perfcctly plastic behaviour. Sections on gcncral principles and analytic tectmiqucs arc hollowed by a critique of existing calculations, particular attention king paid to the estimatiou of tllc loads nreded to bring about failure. ‘I’llrougllout thr artirk tllr rcwlcr’s at tcmtion is carct’ully dramn to points of tile thcoq at wtlicll furttwr research i5 rccluircd. ‘l‘hv :ilt ictcs in this \-olu~~w rwch :I high standard or cspo~ition , ant1 slwcialists in tnoht branollcs of solitl nlcchanics as wail iis those brginnirrg rescawh in this field \vitl find nrllrh to gllidc and illullrinatc tllcir work. 1’. CHal,wIc%