smart technologies for safety engineering

Adaptive Impact Absorption 205
5.6.2 Energy Absorption by the Prismatic Thin-Walled Structure
One of the most important issues of the energy-absorbing structure’s properties are their
technical and economical efficiencies. Technical efficiency of the impact energy absorber,
in the case of lightweight means of transport applications, can be measured as a ratio of its
maximal energy-absorption capability to the gross mass of the absorber. The defined indicator is
known as the SEA (J/kg), the specific energy absorption parameter. The significant economical
efficiency index can be formulated as the quotient of the protective structure cost to its SEA.
One of the best known SEA performance energy-absorbing processes is the axial crushing of
the thin-walled tube. Its huge advantage is the fact that all internal forces generated during the
process of crushing are self-balanced; hence tubes do not need any external supports to provide
stable and progressive deformation. Such profiles can be used in many engineering objects as
structural members, where the most popular examples are the automotive crash zones.
The first scientific studies devoted to the problem of crash behavior focused on a simple
process of crushing of the thin-walled circular tube, being loaded along the direction of
its axis of symmetry. During experimental studies, two characteristic deformation patterns
were observed: axisymmetric, called the ‘concertina’ mode and nonaxis-symmetric mode
known as the ‘diamond’ pattern. An approximate theoretical formula, describing the concertina
folding mode, was derived and published by Alexander in 1960 [40] and modified
later by several scientists for better accuracy. The mentioned family of analytical solutions
was based on the rigid–perfectly plastic material model. Following the experimental observations,
Alexander proposed the kinematics of the axisymmetric deformation pattern with
stationary plastic hinges, contributing to bending dissipation combined with the contribution
of the circumferential stretching of a shell (cf. Figure (5.50). The described approach, with
later modifications introducing a more complex description of the folding pattern, gave the
answer to important parameters of the quasi-static crushing process: the average crushing force
Pm and the length of the plastic folding wave 2H. Alexander’s theory has given a base to the
general macroelements method developed by Abramowicz and Wierzbicki [41] in the last two
decades of the twentieth century.
The macroelement method is applicable to more complex structures and deformation forms,
allowing axial, bending and torsional responses of assemblies of macroelements to be solved.
Crushing of the profile, with the prismatic thin-walled cross-section, can be discretized into a
set of super-folding elements (SFE). For a simple rectangular tube, three basic folding patterns
were isolated: symmetric, asymmetric and inverted modes. The asymmetric mode has the
Figure 5.50 Alexander’s model of concertina mode crushing of a round thin walled tube [40]