A Numerical Comparison of Ionic Multi-Species Diffusion with and without Sorption Hysteresis for Cement-Based Materials

Creep and relaxation of cement paste caused by stress‐induced dissolution of hydrated solid components

“…Although the total moles of each solid that tend to dissolve/form under an applied load can be calculated in the updated GEMS, the actual moles of solids that can really dissolve/form between 2 neighboring time steps are strictly limited by the dissolution kinetic rules of every solid phase. One thing to note is due to the small size of the analyzed composite (100 3 μm 3 ), it took solutes much less than one time step to diffuse throughout the microstructure such that diffusion was not considered as a limiting constraint on the dissolution kinetics. If a much larger volume with nonhomogenous distribution of phases were considered then diffusion might be a limiting constraint on dissolution.…”

A multi-species reactive transport model based on ion-solid phase interaction for saturated cement-based materials

“…A modified Newton-Raphson iteration scheme is used to improve the FEM solution of the non-linear governing equations for the employed single time-stepping scheme. The modified iteration scheme reduces computational time compared to the complete scheme while minimizing the residual of the problem [9,62]. The weak forms of the local differential equations, i.e., Eq.…”

“…In a modified Newton-Raphson method, the iteration scheme is established between Eq. (A.13) and a modified Taylor expansion without considering the higherorder terms for minimizing the residual of the problem [9,60,62]. The improved result a n+1 i is determined in each iteration as,…”

Optimal control of a population dynamics model with hysteresis

“…[1]). During the last three decades, hysteresis operators have been extensively applied in modeling, analysis, and control of a variety of irreversible nonlinear phenomena in applied sciences including phase transitions [2][3][4][5][6][7], porous media flow [8][9][10][11][12], thermostat models [13][14][15][16][17], concrete carbonation [18][19][20][21][22] and many others. In the same vein, system (1.1)-(1.5) (without the control u) was introduced in [23] (see, also, [24,25]) to model the evolution of populations in the vegetation-preypredator framework when diffusive effects in the dynamics of three species are taken into account and the food density for the prey exhibits hysteretic character.…”