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In nonlinear simulations the loading is, in general, applied in an incremental way. Path-following algorithms are used to trace the equilibrium path during the failure process. Standard displacement controlled solution strategies fail if snap-back phenomena occur. In this contribution, a path-following algorithm based on the dissipation of the inelastic energy is presented which allows for the simulation of snap-backs. Since the constraint is defined in terms of the internal energy, the algorithm is not restricted to continuum damage models. Furthermore, no a priori knowledge about the final damage distribution is required. The performance of the proposed algorithm is illustrated using nonlinear mesoscale simulations.
A fast solver method called the multigrid preconditioned conjugate gradient method is proposed for the mechanical analysis of heterogeneous materials on the mesoscale. Even small samples of a heterogeneous material such as concrete show a complex geometry of different phases. These materials can be modelled by projection onto a uniform, orthogonal grid of elements. As one major problem the possible resolution of the concrete specimen is generally restricted due to (a) computation times and even more critical (b) memory demand. Iterative solvers can be based on a local element-based formulation while orthogonal grids consist of geometrical identical elements. The element-based formulation is short and transparent, and therefore efficient in implementation. A variation of the material properties in elements or integration points is possible. The multigrid method is a fast iterative solver method, where ideally the computational effort only increases linear with problem size. This is an optimal property which is almost reached in the implementation presented here. In fact no other method is known which scales better than linear. Therefore the multigrid method gains in importance the larger the problem becomes. But for heterogeneous models with very large ratios of Young's moduli the multigrid method considerably slows down by a constant factor. Such large ratios occur in certain heterogeneous solids, as well as in the damage analysis of solids. As solution to this problem the multigrid preconditioned conjugate gradient method is proposed. A benchmark highlights the multigrid preconditioned conjugate gradient method as the method of choice for very large ratio's of Young's modulus. A proposed modified multigrid cycle shows good results, in the application as stand-alone solver or as preconditioner.
Experimental Validation of Dynamic Response of Small-Scale Metaconcrete Beams at Resonance Vibration
(2023)
Structures and their components experience substantially large vibration amplitudes at resonance, which can cause their failure. The scope of this study is the utilization of silicone-coated steel balls in concrete as damping aggregates to suppress the resonance vibration. The heavy steel cores oscillate with a frequency close to the resonance frequency of the structure. Due to the phase difference between the vibrations of the cores and the structure, the cores counteract the vibration of the structure. The core-coating inclusions are randomly distributed in concrete similar to standard aggregates. This mixture is referred to as metaconcrete. The main goal of this work is to validate the ability of the inclusions to suppress mechanical vibration through laboratory experiments. For this purpose, two small-scale metaconcrete beams were cast and tested. In a free vibration test, the metaconcrete beams exhibited a larger damping ratio compared to a similar beam cast from conventional concrete. The vibration amplitudes of the metaconcrete beams at resonance were measured with a frequency sweep test. In comparison with the conventional concrete beam, both metaconcrete beams demonstrated smaller vibration amplitudes. Both experiments verified an improvement in the dynamic response of the metaconcrete beams at resonance vibration.