Algorithm for simulating fracture processes in concrete by lattice modeling

To simulate fracture behaviors in concrete more realistically, a theoretical analysis on the potential question in the quasi-static method is presented, then a novel algorithm is proposed which takes into account the inertia effect due to unstable crack propagation and meanwhile requests much lower computational efforts than purely dynamic method. The inertia effect due to load increasing becomes less important and can be ignored with the loading rate decreasing, but the inertia effect due to unstable crack propagation remains considerable no matter how low the loading rate is. Therefore, results may become questionable if a fracture process including unstable cracking is simulated by the quasi-static procedure excluding completely inertia effects. However, it requires much higher computational effort to simulate experiments with not very high loading rates by the dynamic method. In this investigation which can be taken as a natural continuation, the potential question of quasi-static method is analyzed based on the dynamic equations of motion. One solution to this question is the new algorithm mentioned above. Numerical examples are provided by the generalized beam (GB) lattice model to show both fracture processes under different loading rates and capability of the new algorithm.

A simple method to simulate shrinkage-induced cracking in cement-based composites by lattice-type modeling

A new numerical procedure is proposed to investigate cracking behaviors induced by mismatch between the matrix phase and aggregates due to matrix shrinkage in cement-based composites. This kind of failure processes is simplified in this investigation as a purely spontaneous mechanical problem, therefore, one main difficulty during simulating the phenomenon lies that no explicit external load serves as the drive to propel development of this physical process. As a result, it is different from classical mechanical problems and seems hard to be solved by using directly the classical finite element method (FEM), a typical kind of "load -> medium -> response" procedures. As a solution, the actual mismatch deformation field is decomposed into two virtual fields, both of which can be obtained by the classical FEM. Then the actual response is obtained by adding together the two virtual displacement fields based on the principle of superposition. Then, critical elements are detected successively by the event-by-event technique. The micro-structure of composites is implemented by employing the generalized beam (GB) lattice model. Numerical examples are given to show the effectiveness of the method, and detailed discussions are conducted on influences of material properties.

Numerical investigation of crack growth in concrete subjected to compression by the generalized beam lattice model

The beam lattice-type models, such as the Euler-Bernoulli (or Timoshenko) beam lattice and the generalized beam (GB) lattice, have been proved very effective in simulating failure processes in concrete and rock due to its simplicity and easy implementation. However, these existing lattice models only take into account tensile failures, so it may be not applicable to simulation of failure behaviors under compressive states. The main aim in this paper is to incorporate Mohr-Coulomb failure criterion, which is widely used in many kinds of materials, into the GB lattice procedure. The improved GB lattice procedure has the capability of modeling both element failures and contact/separation of cracked elements. The numerical examples show its effectiveness in simulating compressive failures. Furthermore, the influences of lateral confinement, friction angle, stiffness of loading platen, inclusion of aggregates on failure processes are respectively analyzed in detail.

Lattice quantum codes and exotic topological phases of matter

This thesis addresses whether it is possible to build a robust memory device for quantum information. Many schemes for fault-tolerant quantum information processing have been developed so far, one of which, called topological quantum computation, makes use of degrees of freedom that are inherently insensitive to local errors. However, this scheme is not so reliable against thermal errors. Other fault-tolerant schemes achieve better reliability through active error correction, but incur a substantial overhead cost. Thus, it is of practical importance and theoretical interest to design and assess fault-tolerant schemes that work well at finite temperature without active error correction.

In this thesis, a three-dimensional gapped lattice spin model is found which demonstrates for the first time that a reliable quantum memory at finite temperature is possible, at least to some extent. When quantum information is encoded into a highly entangled ground state of this model and subjected to thermal errors, the errors remain easily correctable for a long time without any active intervention, because a macroscopic energy barrier keeps the errors well localized. As a result, stored quantum information can be retrieved faithfully for a memory time which grows exponentially with the square of the inverse temperature. In contrast, for previously known types of topological quantum storage in three or fewer spatial dimensions the memory time scales exponentially with the inverse temperature, rather than its square.

This spin model exhibits a previously unexpected topological quantum order, in which ground states are locally indistinguishable, pointlike excitations are immobile, and the immobility is not affected by small perturbations of the Hamiltonian. The degeneracy of the ground state, though also insensitive to perturbations, is a complicated number-theoretic function of the system size, and the system bifurcates into multiple noninteracting copies of itself under real-space renormalization group transformations. The degeneracy, the excitations, and the renormalization group flow can be analyzed using a framework that exploits the spin model's symmetry and some associated free resolutions of modules over polynomial algebras.