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Damage mechanics of rock
Published in Xie Heping, Fractals in Rock Mechanics, 2020
Microstructural observations of rock materials indicate that rock damage can be responsible for the strain-softening effect, so that the rock’s material laws are non-monotone in nature, and its superpotential functions are non-convex. Non-smooth deformation will often form in jointed or fractured rock masses, where the superpotential function is both non-convex and nondifferentiable. Displacements located in joints or fracture beds are jumpy mutable and multi-valued. Therefore, non-smooth mechanics could be the proper theory to describe the deformation of rock masses. With regard to previous exploration, unified descriptions of rock deformation are rigorously presented in terms of mathematics in this section. A new variational principle — hemivariational inequality is established. Finally, numerical examples achieved by approach algorithm are shown.
Experimental validation of numerical rockfall trajectory models
Published in António S. Cardoso, José L. Borges, Pedro A. Costa, António T. Gomes, José C. Marques, Castorina S. Vieira, Numerical Methods in Geotechnical Engineering IX, 2018
A. Caviezel, Y. Bühler, G. Lu, M. Christen, P. Bartelt
The RAMMS::ROCKFALL simulation tool is a numerical software package applying non-smooth mechanics coupled with hard contact laws to the rockfall problem. The tool has been developed at the WSL Institute for Snow and Avalanche Research SLF (Leine et al. 2014). Together with the modules for avalanche and debris flow simulations, the RAMMS software provides a unified software environment for integral hazard management of snow avalanches, debris flows and rockfalls (Christen and Bühler 2012). A detailed description of the non-smooth mechanics and numerical solution methods can be found in Leine et al. (2014). An interesting comparison of non-smooth mechanical approaches and discrete element type methods can be found in Lu et al. (2018).
Experimental validation of numerical rockfall trajectory models
Published in António S. Cardoso, José L. Borges, Pedro A. Costa, António T. Gomes, José C. Marques, Castorina S. Vieira, Numerical Methods in Geotechnical Engineering IX, 2018
A. Caviezel, Y. Bühler, G. Lu, M. ChristenTo, P. Bartelt
The RAMMS::ROCKFALL simulation tool is a numerical software package applying non-smooth mechanics coupled with hard contact laws to the rockfall problem. The tool has been developed at the WSL Institute for Snow and Avalanche Research SLF (Leine et al. 2014). Together with the modules for avalanche and debris flow simulations, the RAMMS software provides a unified software environment for integral hazard management of snow avalanches, debris flows and rockfalls (Christen and Bühler 2012). A detailed description of the non-smooth mechanics and numerical solution methods can be found in Leine et al. (2014). An interesting comparison of non-smooth mechanical approaches and discrete element type methods can be found in Lu et al. (2018).
A survey: dynamics of humanoid robots
Published in Advanced Robotics, 2020
Tomomichi Sugihara, Mitsuharu Morisawa
The above Equation (14) has equations and unknown variables; equations are missing to be solved. If the Coulomb friction is assumed, only the following conditions are accepted for : where is the outward unit normal vector of the terrain, and and are the static and kinetic friction coefficients at , respectively. The above conditions represent the unilaterality and the friction limit of contact forces. Penetration is not acceptable. Any of Equations (15), (16) and (17) includes three independent equalities. Hence, the total number of equations balances with the number of variables when combined with Equation (14). A difficulty is that it is hard to know which condition fits the state to be evolved over time in advance. This is a typical non-smooth mechanics [16] and has been mainly studied in the context of dynamics simulations [17–25].
Discrete element modelling of hot mix asphalt complex modulus using realistic aggregate shapes
Published in Road Materials and Pavement Design, 2022
Juan Carlos Quezada, Cyrille Chazallon
The CD method is a particle-based approach for the modelling of non-smooth mechanics in granular systems. The main difference between this approach and the distinct element method (Cundall, 1971, 1988; Cundall & Strack, 1979) or molecular dynamics (Brilliantov et al., 1996; Herrmann & Luding, 1998; Pöschel & Buchholtz, 1995; Radjaï& Dubois, 2011) lies in the formulation of the contact models as complementary relations between impulses and velocities at the particle-scale. Here, the unilateral contact interactions and Coulomb friction law guarantee the non-interpenetration between perfectly-rigid particles.