Métodos sin malla aplicados a problemas dinámicos en materiales de construcción y suelos
- Autores: Pedro Navas Almodóvar
- Directores de la Tesis: Chengxiang Yu (dir. tes.), Bo Li (codir. tes.), Susana López Querol (codir. tes.)
- Lectura: En la Universidad de Castilla-La Mancha ( España ) en 2017
- Idioma: español
- Tribunal Calificador de la Tesis: Manuel Pastor Pérez (presid.), Marcos Arroyo Álvarez de Toledo (secret.), Lorenzo Sanavia (voc.)
- Programa de doctorado: Programa de Doctorado en Territorio, Infraestructuras y Medio Ambiente por la Universidad de Castilla-La Mancha
- Materias:
- Texto completo no disponible (Saber más ...)
- Resumen
The behavior of civil engineering materials such as concrete or soils is often dynamic and lies in large deformation regime. Consequently, it is essential for numerical models to be able to capture such phenomena. Meshfree methodologies, in comparison to their finite element counter- parts, are known to be particularly suitable for dealing with large strain problems. The main purpose of this thesis is precisely to develop a mesh- free implementation of finite deformation theory of solids, with the corre- sponding time integration schemes, to simulate dynamic behavior of soils and concrete.
For spatial discretization, the shape functions based on the local principle of maximum entropy within the Optimal Transportation Meshfree (OTM) framework is employed for its numerous advantages in comparison to its alternatives. For example, the exact mass transport, the satisfaction of the continuity equation, exact linear and angular momentum conservation make it possible to solve different problems such as spurious modes, tensile instabilities and unknown convergence or stability properties. Since the deformation and velocity fields are interpolated from nodal values using local max-ent shape functions, the Kronecker-delta property at the bound- ary facilitates the direct application of essential boundary conditions. In addition, the parameters pertinent to the local maximum entropy are ob- tained efficiently and robustly, independently of the number of nodes in the support, through a combination of the Newton Raphson method and the Nelder-Mead algorithm. The latter has been improved in order to obtain better convergence property. B-bar and F-bar methodologies are specifically developed in the OTM framework for small and large strain problems in order to avoid locking.
For time integration, both implicit and explicit schemes are implemented. In particular, a unified method is established to combine six classical integration schemes. The validation of both schemes is carried out by performing benchmark examples with available analytical or experimental solutions with excellent results. Some of them are also enhanced with the employment of contact algorithms in order to model the interaction between two different bodies.
In the geotechnical field the assessment of both dry and saturated soils subjected to dynamic loading is presented. Different elastic and plastic material models are applied within the complete formulation of the Biot’s equations, which enables us to simulate high frequency loads with high accuracy. The Drucker-Prager failure criterion is employed within the OTM framework for the first time. In addition, the first implementation of the complete formulation of the Biot’s equations within a large strain framework is carried out. An innovative explicit algorithm is proposed for a biphase medium meanwhile the linearization of the linear momen- tum balance derivatives is performed in order to build the implicit time integration scheme for the u − w formulation.
Regarding the application to concrete, the dynamic fracture propagation of a three-point bending beam impacted by a drop-weight device at three different velocities is simulated. It is shown that the eigenerosion ap- proach to fracture is able to capture crack patterns and reaction forces in mode-I but fails to predict realistic stress and strain values. An eigen- softening algorithm is thus developed to simulate the softening behavior of quasi-brittle materials. The new methodology is applied to model both mode-I and mixed-mode fracture in plain and fiber-reinforced concrete and excellent results are obtained.
