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Material geometry. (English) Zbl 1454.74006

Summary: Walter Noll’s trailblazing constitutive theory of material defects in smoothly uniform bodies is recast in the language of Lie groupoids and their associated Lie algebroids. From this vantage point the theory is extended to non-uniform bodies by introducing the notion of singular material distributions and the physically cognate idea of graded uniformity and homogeneity.

MSC:

74A20 Theory of constitutive functions in solid mechanics
53Z05 Applications of differential geometry to physics
22A22 Topological groupoids (including differentiable and Lie groupoids)
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References:

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