Abstract
A general method giving the perturbation due to the introduction of an inhomogeneity into any initial elastic field is discussed within the framework of plane linear elasticity. Then, the method is applied to obtain the full perturbative solution for the problem of an elliptic inhomogeneity in an infinite plane. Exact formulas for the special cases of void, rigid, and circular inhomogeneity are also worked out and discussed. The obtained results can noticeably simplify the analytic work needed to determine the elastic field in composite or cracked plates.
Riassunto
Nell'ambito della teoria dell'elasticità in mezzi piani e isotropi, si discute un metodo generale per ottenere la perturbazione dovuta all'introduzione di una disomogeneità in un qualsiasi campo elastico preesistente. Il metodo viene poi applicato al caso di una disomogeneità ellittica in un mezzo infinito. Inoltre, si ricavano e si discutono formule esatte che risolono i casi particolari di disomogeneità ellittica vuota oppure rigida, e di disomogeneità circolare. I risultati ottenuti possono semplificare notevolmente l'analisi delle deformazioni piane di lamine composite o con cricche interne.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J. D. Eshelby,Elastic inclusions and inhomogeneities, in: Progress in Solids Mechanics, (eds. I. N. Sneddon and R. Hills), North Holland, Amsterdam89, (1961)
K. Aderogba,An elastostatic circle therorem. Proc. Camb. Phil. Soc.73, 169 (1973).
N. I. Muskhelishvili,Some basic problems of the mathematical theory elasticity. Noordhoff, Leyden (1975)
D. I. Sherman,Nonhomogeneity in elasticity and plasticity. Pergamon, London,3, (1959).
R. D. List and J. P. O. Silberstein,Two-dimensional elastic inclusion problems. Proc. Camb. Phil. Soc.62, 303 (1966).
P. S. Theocaris and N. I. Ioakimidis,The inclusion problem in plane elasticity. Q. J. Mech. appl. Math. XXX, pt.4, 437 (1977).
N. J. Hardiman,Elliptic elastic inclusion in an infinite elastic plate. Q. J. Mech. appl. Math.7, 226 (1954).
R. D. Bhargava and H. C. Radhakrishna,Elliptic inclusion in a stressed matrix. Proc. Camb. Phil. Soc.59, pt. 4, 821 (1963).
A. C. Gangadharan and J. Dundurs,Edge dislocation near an interface crack in a two-phase material. Indian J. Technol.11, 410 (1973).
V. Vitek,Yielding from a crack with finite root-radius loaded in uniform tension. J. Mech. Phys. Sol.24, 67 (1976).
V. Vitek and J. P. Hirth,Line singularity fields in the presence of a crack of elliptical crosssection. Scr. Metall.11, 339 (1977).
R. R. Bhargava,A misfitting elastic inclusion in an infinite plane containing a crack. J. Elasticity7, 201 (1977).
P. S. Theocaris and N. I. Ioakimidis,The problem of interaction between a misfitting inclusion and a crack in an infinite elastic medium. J. Elasticity9, 97 (1979).
J. Orr and D. K. Brown,Elasto-plastic solution for a cylindrical inclusion in plane strain. Eng. Fract Mech.6, 261 (1974).
S. Itou,The effect of couple-stresses on stress concentration around a rigid circular inclusion in a strip under tension. Acta Mech.27, 261 (1977).
I. Mizushima and M. Hamada,Tensile and compressive stress problems for a rigid circular disk in an infinite plate. Bull. JSME21, 1325 (1978).
M. Hetenyi and J. Dundurs,The elastic plane with a circular insert, loaded by a tangentially directed force. Trans. ASME J. Appl. Mech.29, 362 (1962).
R. D. Bhargava and O. P. Kapoor,Circular inclusion in an infinite elastic medium with a circular hole. Proc. Camb. Phil. Soc.60, 675 (1964)
J. Dundurs and T. Mura,Interaction between an edge dislocation and a circular inclusion. J. Mech. Phys. Solids12, 177 (1964).
J. Dundurs and A. C. Gangadharan,Edge dislocation near an inclusion with a slipping interface. J. Mech. Phys. Solids17, 459 (1969).
R. D. List,A two-dimensional circular inclusion problem. Proc. Camb. Phil. Soc.65, 823 (1969).
J. H. Holbrook and W. D. Nix,Edge dislocation climb over non-deformable circular inclusion. Metall. Trans.5, 1033 (1974).
I. Mizushima and M. Kusano,Tensile and compressive stress problems for a circular disk in an infinite plate. Bull. JSME22, 1175 (1979).
L. Stagni,Circular misfitting inhomogeneity in a half-plane. Arch. Mech.32, 299 (1980).
L. Stagni and R. Lizzio,Edge dislocation trapping by a cylindrical inclusion near a traction-free surface. J. Appl. Phys. 52, 1104 (1981).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Stagni, L. On the elastic field perturbation by inhomogeneities in plane elasticity. Z. angew. Math. Phys. 33, 315–325 (1982). https://doi.org/10.1007/BF00944440
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00944440