In this paper, a complete picture of the different plastic failure modes that can be predicted by the strain gradient plasticity model proposed in Del Piero et al. (J. Mech. Mater. Struct. 8:109-151, 2013) is drawn. The evolution problem of the elasto-plastic strain is formulated in Del Piero et al. (J. Mech. Mater. Struct. 8:109-151, 2013) as an incremental minimization problem acting on an energy functional which includes a local plastic term and a non-local gradient contribution.

To evaluate changes in the Soil Organic Carbon (SOC) index, one of the key indicators of land degradation neutrality, soil carbon modeling is of primary importance. In litera-ture, the analysis has been focused on the stability characterization of soil carbon steady states and in the calculation of the resilience of the stable equilibria. Neither stability nor resilience, however, provide any information about transient dynamics, and models with highly resilient equilibria can exhibit dramatic transient responses to perturbations.

During melting under gravity in the presence of a horizontal thermal gradient, buoyancy-driven convection in the liquid phase affects significantly the evolution of the liquid-solid interface. Due to the obvious engineering interest in understanding and controlling melting processes, fluid dynamicists and applied mathematicians have spent many efforts to model and simulate them numerically. Their endeavors concentrated in the twenty-five years period between the publication of the paper by Brent, Voller & Reid (1988) and that by Mansutti & Bucchignani (2011).

Recent literature confirms the crucial influence of non-viscous deformations together with temperature impact on glacier and rock glacier flow numerical simulation. Along this line, supported by the successful test on a one-dimensional set-up developed by two of the author, we propose the numerical solution of a two-dimensional rock-glacier flow model based on an ice constitutive law of second grade differential type .