The computation of the exponential and logarithmic mappings and their first and second linearizations

By Michael Ortiz, Raúl A. Radovitzky, E. A. Repetto. 2001

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Towards variational constitutive updates for non-associative plasticity models at finite strain: models based on a volumetric-deviatoric split (2009, unknown): “[35,36].”
Variationally consistent modeling of finite strain plasticity theory with non-linear kinematic hardening (2010, unknown): “[47,48].”
On the implementation of rate-independent standard dissipative solids at finite strain – Variational constitutive updates (2010, unknown): “[49, 50].”
Geometry of Logarithmic Strain Measures in Solid Mechanics (2015, methodology): “This property is, however, not unique to geodesic (or logarithmic) strain measures; for example, the Frobenius norm ‖Ẽ1/2(U)‖ = 12‖U − U−1‖ = 12‖V − V −1‖ of the Bažant approximation Ẽ1/2 = 1 2 (U − U−1), cf. (1.4) and [17], which can be considered a “quasilogarithmic” strain measure, fulfils the”
Three‐dimensional adaptive meshing by subdivision and edge‐collapse in finite‐deformation dynamic–plasticity problems with application to adiabatic shear banding (2002, methodology): “Simple explicit formulae for the evaluation of these objects may be found elsewhere [ 37 ].”
Closed‐form matrix exponential and its application in finite‐strain plasticity (2014, methodology): “The corresponding method of evaluation of the derivative involves differentiation and summation of the terms in the series [13, 14], but this turns out to be numerically inefficient.”