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Shear band dynamics

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WHTW01 - Factorisation of matrix functions: New techniques and applications

When a ductile material is subject to severe strain, failure is preluded by the emergence of shear bands, which initially nucleate  in  a  small  area,  but  quickly  extend  rectilinearly  and  accumulate  damage,  until  they  degenerate  into  fractures.  Therefore, research on shear bands yields a fundamental understanding of the intimate rules of failure, so that it may be important in the design of new materials with superior mechanical performances.A shear band of finite length, formed inside a ductile material at a certain stage of a continued homogeneous strain, provides  a  dynamic  perturbation to an incident wave field, which strongly influences the dynamics of the material and affects  its  path  to  failure.  The  investigation  of  this  perturbation  is  presented  for  a  ductile  metal,  with  reference  to  the  incremental mechanics of a material obeying the J2–deformation theory of plasticity. The treatment originates from the derivation of integral representations relating the incremental mechanical fields at every point of the medium to the incremental  displacement  jump  across  the  shear  band  faces,  generated  by  an  impinging  wave.  The  boundary  integral  equations are numerically approached through a collocation technique, which keeps into account the singularity at the shear band tips and permits the analysis of an incident wave impinging a shear band. It is shown that the presence of the shear band induces a resonance, visible in the incremental displacement field and in the stress intensity factor at the shear band tips, which promotes shear band growth. Moreover, the waves scattered by the shear band are shown to generate a fine texture of vibrations, parallel to the shear band line and propagating at a long distance from it, but leaving a sort of conical shadow zone, which emanates from the tips of the shear band [1,2].
References
[1] Giarola, D., Capuani, D. Bigoni, D. (2018) The dynamics of a shear band. J. Mech. Phys. Solids, 112, 472-490.
[2] Giarola, D., Capuani, D. Bigoni, D. (2018) Dynamic interaction of multiple shear bands. Scientific Reports 8 16033

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