A Generalized Backward Euler algorithm for the numerical integration of an isotropic hardening elastoplastic model for mechanical and chemical degradation of bonded geomaterials

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A constitutive model for bonded geomaterials subject to mechanical and/or chemical degradation (2003, methodology): “The response of the model to the different loading programs has been obtained by numerical integration adopting an explicit adaptive Runge–Kutta–Fehlberg scheme of third order, implemented in MATLAB, as in Reference [26].”
On the numerical integration of three-invariant elastoplastic constitutive models (2003, methodology): “This algorithm, advocated and used in [19], provides an alternative approach for determining the principal values and principal directions of a symmetric second-order tensor.”
A stable mesh-independent approach for numerical modelling of structured soils at large strains (2019, methodology): “The elastic response is characterized by means of an hyperelastic model incorporating a tensile range (Houlsby, 1985; Tamagnini et al., 2002), which in this work it is formulated in terms of the Hencky strain and the Kirchhoff stress tensor.”
Return mapping for nonsmooth and multiscale elastoplasticity (2009, methodology): “Implicit return mappings rely heavily on Newton–Raphson schemes to iteratively arrive at a solution [12,28,29].”