An implicit boundary finite element method with extension to frictional sliding boundary conditions and elasto-plastic analyses

Implicit boundary methods, which enrich the interpolation structure with implicit weight functions, are straightforward methods for the enforcement of Dirichlet boundary conditions. In this article, we follow the implicit boundary method that uses approximate step functions (the step boundary method) developed by Kumar et al. and provide modifications that have several advantages. Roller boundary conditions have wide practical applications in engineering, however, the step boundary method for roller boundary conditions with inclinations has yet to be fully formulated through to the final linear system of equations. Thus we provide a complete derivation that leads to simplified sti↵ness matrices compared to the original approach, which can be implemented directly in fictitious domain finite element analysis. The approach is then extended, we believe for the first time, to the nonlinear cases of frictional boundary conditions and elasto-plastic material behaviour. The proposed formulation and procedures are validated on a number of example problems that test di↵erent aspects of the method

On Lagrangian mechanics and the implicit material point method for large deformation elasto-plasticity

The material point method is ideally suited to modelling problems involving large deformations where conventional mesh-based methods would struggle. However, total and updated Lagrangian approaches are unsuitable and non-ideal, respectively, in terms formulating equilibrium for the method. This is due to the basis functions, and particularly the derivatives of the basis functions, of material point methods normally being dened based on an unformed, and sometimes regular, background mesh. It is possible to map the basis function spatial derivatives using the deformation at a material point but this introduces additional algorithm complexity and computational expense. This paper presents a new Lagrangian statement of equilibrium which is ideal for material point methods as it satises equilibrium on the undeformed background mesh at the start of a load step. The formulation is implemented using a quasi-static implicit algorithm which includes the derivation of the consistent tangent to achieve optimum convergence of the global equilibrium iterations. The method is applied to a number of large deformation elasto-plastic problems, with a specic focus of the convergence of the method towards analytical solutions with the standard, generalised interpolation and CPDI2 material point methods. For the generalised interpolation method, dierent domain updating methods are investigated and it is shown that all of the current methods are degenerative under certain simple deformation elds. A new domain updating approach is proposed that overcomes these issues. The proposed material point method framework can be applied to all existing material point methods and adopted for implicit and explicit analysis, however its advantages are mainly associated with the former

An efficient and locking-free material point method for three dimensional analysis with simplex elements

The Material Point Method is a relative newcomer to the world of solid mechanicsmodelling. Its key advantage is the ability to model problems having large defor-mations while being relatively close to standard nite element methods, howeverits use for realistic engineering applications will happen only if the material pointcan be shown to be both ecient and accurate (compared to standard nite elementmethods), when modelling complex geometries with a range of material models. Inthis paper we present developments of the standard material point method aimed atrealising these goals. The key contribution provided here is the development of amaterial point method that avoids volumetric locking (arising from elastic or elasto-plastic material behaviour) whilst using low order tetrahedral nite elements forthe background computational mesh, hence allowing unstructured background gridsto be used for complex geometries. We also show that these developments can beeectively parallelised to improve computational ecienc

AMPLE: A Material Point Learning Environment

The Material Point Method is a computational tool ideally suited to modelling solid mechanics problems involving large deformations where conventional mesh-based methods struggle. Explicit and implicit formulations are available, but for both the learning curve for understanding the method and arriving at a useful implementation is severe. Researchers must understand and implement finite element analysis, non-linear material behaviour, finite deformation mechanics and non-linear solution methods before they can even verify their formulations. This issue represents a significant barrier for post-doctoral researchers, graduate students and undergraduate students to start working with (and understanding) the method. This paper presents A Material Point Learning Environment (AMPLE) based around implicit variants of the method, with the aim of softening this steep learning curve via MATLAB-based, accessible and compact scripts. The code is freely available from github.com/wmcoombs/AMPLE

2-dimensional analysis of settlement damage to masonry buildings caused by tunnelling

In current practice, estimating the effects of tunnel construction in soft ground beneath an existing building is usually a two-stage procedure, where interaction between the ground and the building is ignored. This paper describes a study of tunnelling-induced settlement damage to masonry buildings, using a numerical model, in which interaction is included. 2-dimensional finite elements(FEs) are used with non-linear material models for the soil and for a masonry facade. The excavation of a tunnel is simulated, and the resulting damage in the facade, principally cracking, can be observed. This study concentrates on the effect of facade weight and stiffness and the horizontal location of the facade with respect to the tunnel axis. The study finds that increasing facade weight tends to increase damage, owing to the larger horizontal strains. Increasing facade stiffness, however, appears to reduce damage, since the differential settlements under the facade are inhibited

Analysis of tunnel-induced settlement damage to surface structures

Transport developments in cities often involve tunnelling, which inevitably leads to ground movements. These must be carefully predicted if there is a risk of settlement damage to nearby structures. Tunnel-induced settlements may be predicted empirically for greenfield sites, but surface structures modify these movements. Two-dimensional models, often used in practice, neglect the effect of transients as the tunnel is excavated and do not allow realistic models of buildings. Research on a 3-D numerical model of tunnelling is described. This includes a building and a simulation of tunnel construction processes. Interactions between the building and the ground are investigated. Settlement, and structural damage, is studied as the tunnel installation proceeds. An analysis of a building unsymmetrical in plan to the tunnelling direction is presented