Multiplicative Decomposition-Embedded Logarithmic Strain-Based Statements for Viscoelasticity in Glaciological Applications

This paper formulates a thermodynamically consistent finite-strain Maxwell-Glen model for glaciological applications in a Lagrangian setting. A multiplicative decomposition of the deformation gradient separates the elastic and viscous mappings, while a trace-free material velocity gradient describes isochoric creep. The elastic state is represented by a logarithmic strain, and its associated material stress drives a temperature-dependent Glen law. Under the isotropic constitutive assumptions, commutation reduces the multiplicative metric update to an additive elastic-viscous corrector. The exponential map is evaluated by a Cayley-Hamilton reduction for generally nonsymmetric arguments, and a consistent linearisation supplies the material tangent. Homogeneous simple shear verifies agreement with spatial Glen flow under non-coaxial deformation. A self-weighted plane-strain column confirms preservation of the incremental viscous Jacobian to the solver tolerance. For a floating shelf, depth-dependent viscous resistance reverses the shelf-edge bending relative to uniform viscosity.