The installation, named 44, is made up of more than 300 coral-shaped aluminium forms suspended from the ceiling by a series of thin cables.
Each of the 300 pieces was formed by pouring molten aluminium into a large canister filled with rock-like resin shapes.
Low voltage electricity is transmitted through the metal castings, allowing circular bulbs to be suspended between them without using cables.
"The exploration of materials is at the heart of Arbel's practice," said the Barbican. "By delving into their chemical, physical or mechanical properties, he discovers forms that are appropriate to the materials' intrinsic qualities."
"He fuses engineering and scientific disciplines with aesthetic ideals, pushing the boundaries of material research and endeavour even further."
Towards the top of the ceiling, the pieces in the installation are spread out. But as they approach the ground, the wires become more narrow before appearing to descend into a metal vessel.
"As the sculpture descends into the space and expands, it punctuates the spaces of the Barbican foyer, engaging with notions of weightlessness and mass," said Bocci.
Arbel established Bocci in 2005 on the outskirts of Vancouver. The company is best known for its 28 Series pendant light, which it has used to create a variety of installations, including a giant colourful chandelier at London's V&A museum.
The 44 installation was unveiled to coincide with this year's London Design Festival, and will remain in-situ until 18 April 2017.