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. Author manuscript; available in PMC: 2013 Oct 1.

Published in final edited form as: Int J Non Linear Mech. 2011 Jul 23;47(8):938–949. doi: 10.1016/j.ijnonlinmec.2011.07.006

Kinematics of finite growth. Illustration of covariant spatial metric g, deformation tensors C and C^e, stress tensors S, P, P^e and τ, and mappings F = F^e · F^g and F^−t = F^{e −t} · F^{g −t} between tangent spaces T and cotangent spaces T ^* in the material configuration, the intermediate configuration, and the spatial configuration [27, 48].

Inline graphic — Kinematics of finite growth. Illustration of covariant spatial metric g, deformation tensors C and C^e, stress tensors S, P, P^e and τ, and mappings F = F^e · F^g and F^−t = F^{e −t} · F^{g −t} between tangent spaces T and cotangent spaces T ^* in the material configuration, the intermediate configuration, and the spatial configuration [27, 48].