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Abstract Axial compression of aluminium spherical shells of R/t values ranging from 25 to 43 was per-formed under central loading. Quasi-static tests were conducted on an INSTRON machine (model 1197) of 50T capacity. Spherical shells were tested to identify their modes of collapse and to study the associated energy absorption capacity. In experiments all the spherical shells were found to collapse due to formation of an axisymmetric inward dimple associated with a rolling plastic hinge. A Finite Element computational model of development of the axisymmetric mode of collapse is also presented. Experimental and computed results of the deformed shapes and their corresponding load–compression and energy–compression curves were presented and compared to validate the computational model. The computed variations of the different strains and stresses were also studied. On the basis of the computational results mechanics of the development of the axisymmetric inward dimple mode of collapse has been presented, analysed and discussed.Keywords Hemispherical shells · Rolling plastic hinge · Energy absorption · FORGE2List of symbolsR mean radius of the spherical shellL span of the spherical shellZ depth of the spherical shellt average thickness of the spherical shellrp radius of the rolling or travelling plastic hingeh total axial compression of the spherical shell at any stage of compressionP load on the spherical shell at any stage of compressionMp plastic moment per unit length˜ Sij deviatoric stress tensorK material cnsistency˙ ¯ ε effective strain ratem strain rate sensitivity index 21675
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K constant term
1 Introduction
Thin walled structural shell elements such as cylindrical shells, conical shells and domes are commonly used
as energy absorbing elements in crashworthiness applications. Study of their collapse behaviour has received
considerable attention of the researchers in the last four decades [1–10]. Experimental and analytical studies
on these structural elements have been carried out under both quasi-static and dynamic loadings in axial and
lateral directions. Johnson and Reid reviewed the modes of collapse of various thin-walled shells and their
corresponding load–compression curves [1].
Large deformation of a rigid plastic hemispherical shell compressed between two rigid parallel plates was
studied by performing experiments and proposing analytical models obtained from their experimental finding
by few researchers [2–7] in the past. Among these, only De Oliveira and Wierzbicki [4] have studied the
deformation of the spherical shell under concentrated point load as well as between rigid plates as a part of
their studies on the crushing analysis of rotationally symmetric plastic shells. They proposed equation (1) to
predict the load deformation relationship for spherical shell under central point load through their analysis.
In their analysis they assumed formation of the two rolling plastic hinge in the current deforming region at
a spacing of “b”. Load deformation behaviour in this analysis was shown to be independent of the radius of
spherical shell.
where β is the angle subtended by chord length “b”, h is compression, P is the collapse load, Mp is the plastic
moment per unit length, t is the thickness of shell, R is the mean radius of the shell.
Recently finite element method has been employed [9,10] to analyse the axisymmetric concertina mode
of collapse developed in axial compression of moderately thick metal tubes. However available literature is
scarce regarding the study of development of axisymmetric mode of collapse occurs in the axial compression
of hemispherical domes.
In the present work an attempt has been made to study the axial compression of aluminium hemispherical
shells under quasi-static loading. Hemispherical shells resting on flat plate are compressed with axial central