From geometry to mechanics: a broken pipe
A profusion of shapes acquired from physical objects
With the considerable advance of automatic image-based capture in Computer Vision and Computer Graphics these latest years, it becomes now affordable to acquire quickly and precisely the full 3d geometry of many mechanical objects featuring intricate shapes such as cloth, skin, hair fibers, or trees and foliage. Acquisition technologies range from expensive structured light or laser scans to new low-price devices such as depth cameras, which are often sufficient for capturing a static pose precisely.
Yet, while more and more geometrical data get collected and shared among the communities, there is currently very little study about how to infer the underlying mechanical properties of the captured objects merely from their geometrical configurations. One can however suspect that the pure static shape of a physical object may already give some insights about the constitutive material of the object and the interplaying contacts: from the folding patterns of a tablecloth or a curtain, the human eye may perceive whether the fabric is made of rough cotton or silk, and identify zones of contacts.
One may then have the dream that feeding a well-designed physics-based simulator with such easy-available initial data could help predict the deformations or even the dynamics of the objects.
Material tests for measuring physical parameters
In parallel, contactless measurement methods, which reconstruct full-displacement fields based on camera capture and digital image correlation, have recently gained much interest in Experimental Mechanics. Indeed, unlike sensor-based capture, image-based capture does not interfere with the displacement field being measured. Combined with FEM-based inverse modeling, contactless measurement methods allow for a complete parameter identification of complex materials. They however request that a number of specific material tests (e.g. tensile and shear tests) be performed, which may often require some expensive material and time-costly measurement protocols, and sometimes may even be impracticable when objects are not directly manipulable. Moreover, although some recent developments in Computer Graphics have extended the range of studies from small to moderate 3D deformations and partly lightened the necessary amount of control in the experimental setup, such methods remain limited to the study of contact-free objects.
In contrast, leveraging geometric acquisitions of a minimum number of uncontrolled static poses would release the burden of material testing and provide a breakthrough in the non-invasive and fast measurement of many mechanical features including rest configuration, material parameters (e.g. mass, stiffness, internal damping), self-contacting forces and friction coefficients at contact.
Giving a physical meaning to mere geometric data would not only serve as an innovative parameter measurement method, but also as a powerful strategy to convert a purely descriptive approach into a generative one, able to predict an infinite number of new and rich dynamic scenarios.
The Gem Challenge: Interpreting Geometry as a Mechanical State
The key challenge of the Gem proposal is the automatic connection between the geometrical shape of physical objects and their underlying mechanical properties. More precisely, I intend to focus this study on complex deformable objects featuring detailed geometrical configurations. Typical objects of interest include slender deformable structures such as rods, plates and shells, all of them being widespread in our environment, from the macroscopic scale (e.g. tree branches and leaves, hair, cloth, skin, paper) to nanoscopic and molecular scales (e.g. carbon nanotubes, DNA). Such structures, which are prone to strongly nonlinear behaviors as well as to possibly prominent self-contacting causing knots, folds, complex surface patterns or even unstable structures such as plectonemes, exhibit very rich geometrical configurations.
My claim in this proposal, supported by some preliminary results I recently gained on hair fibers after years of research, is that these complex geometrical features reveal a lot about the underlying mechanical structures.
