On preconditioning strategies for geotechnics

Iterative solvers are of increasing interest in geomechanics with the move towards 3D finite element modelling. Potentially, these methods can lead to reduced computational complexity as, unlike direct methods, they do not require the full system matrix to be assembled. In general, however, iterative solvers have not been widely adopted in geomechanics due to problems with convergence. This paper reviews the background to iterative methods for elastic and elasto-plastic material models. In some cases, existing numerical methods can be taken from research in the mathematics community. For other systems, further work is needed. The paper provides demonstrations of the capabilities of some strategies

Solution of Elasto-Statics Problems Using the Element-Free Galerkin Method with Local Maximum Entropy Shape Functions

The element free Galerkin method (EFGM) [1] is one of the most robust meshless methods for the solution of elasto-statics problems. In the EFGM, moving least squares (MLS) shape functions are used for the approximation of the field variable. The essential boundary conditions cannot be implemented directly as in the case of Finite Element Method (FEM), because the MLS shape functions do not possess the Kronecker-delta property and use Lagrange multipliers instead. In this paper the recently developed local maximum entropy shape functions are used in the EFGM for the approximation of the field variable instead of MLS. As the local maximum entropy shape functions possess the Kroneckerdelta property at the boundaries so the essential boundary conditions are enforced directly as in the case of FEM. Two benchmark problems, a cantilever beam subjected to parabolic traction at the free end and an infinite plate with circular hole subjected to unidirectional tension are solved to show the implementation and performance of the current approach. The displacement and stresses calculated by the current approach show good agreement with the analytical results

Local Maximum Entropy Shape Functions Based FE-EFGM Coupling

In this paper, a new method for coupling the finite element method (FEM)and the element-free Galerkin method (EFGM) is proposed for linear elastic and geometrically nonlinear problems using local maximum entropy shape functions in theEFG zone of the problem domain. These shape functions possess a weak Kroneckerdelta property at the boundaries which provides a natural way to couple the EFGand the FE regions as compared to the use of moving least square basis functions.In this new approach, there is no need for interface/transition elements between theEFG and the FE regions or any other special treatment for shape function continuity across the FE-EFG interface. One- and two-dimensional linear elastic and two-dimensional geometrically nonlinear benchmark numerical examples are solved by the new approach to demonstrate the implementation and performance of the current approach

Investigation into the shear behaviour of rammed earth using shear box tests.

Scientific investigations into the structural properties of rammed earth (RE) are gaining momentum and a number of parameters (e.g. suction, particle size distribution and water content), influential on material strength and other properties, have been identified and investigated. Cement stabilisation is undergoing continued investigation, while fibrous stabilisation, also known as fibre reinforcement, is beginning to gain attention. Recent experiments have shown that the addition of fibres such as straw or wool to RE or other earthen materials can improve its flexural strength. Less attention, however, has been paid to the fracture behaviour of RE, and to its shearing behaviour. This paper presents a preliminary investigation into the shearing behaviour of stabilised and unstabilised RE reinforced with waste natural fibres. The Direct Shear Test (DST) is used to obtain peak shear stresses and displacements, from which strength parameters (φ’) and cohesion (c’) are obtained. This paper also presents some scanning electron microscope (SEM) images of these materials. The results show that wool fibres decrease the density and peak shear strength of RE. The effect of water, wool and cement content on φ’ and c’ are also discussed

Fast iterative solvers for geomechanics in a commercial FE code

There is a pressing need to improve the feasibility of three-dimensional finite element (FE) methods applied to many problems in civil engineering. This is particularly the case for static analyses in geotechnical engineering: ideally, models would be 3D, follow the actual geometry, use non-linear material formulations and allow simulation of construction sequences, and all of this with a reasonable degree of accuracy. One major obstacle to improvements in this regard is the difficulty in solving of the set of (linearised) algebraic equations which arises from a typical discretisation approach. Very large systems become cumbersome for direct techniques to solve economically. This paper describes the incorporation of iterative (rather than direct) solution techniques, developed through University research, into commercial FE software for geotechnics

Historic rammed earth structures in Spain : construction techniques and a preliminary classification.

Conservation and repair of historic rammed earth sites should only be undertaken if there is a good understanding of the consequences of any intervention technique. Until recently there has been little interest in the characterisation of historic rammed earth construction, yet it is only with this understanding that successful conservation strategies can be adopted. A survey of around 60 historic rammed earth sites in Spain constructed between 967AD and 1837AD has recently been undertaken. While all the sites are built primarily in rammed earth, the construction techniques and state of repair vary greatly. The high density of historic rammed earth structures in the Iberian peninsula is likely due to the Muslim presence there from the 8th century onwards. Initial expansion, a period of civil war and eventual defeat by Christians led to the construction of a large number of fortifications, many constructed in rammed earth. A famous example is the Alhambra at Granada, but there are hundreds of smaller sites throughout Spain. By the end of the 15th century Christians had replaced Muslims through most of Spain, but rammed earth continued to be used in both vernacular and monumental architecture. Examples of historic construction techniques are presented and common features of historic rammed earth construction are identified. A classification is outlined and a clear development of the rammed earth technique is observed

A review of the Material Point Method and its links to other computational methods.

There is considerable interest in development of solid mechanics modelling which can cope with both material and geometric nonlinearity, particularly in areas such as computational geotechnics, for applications such as slope failure and foundation installation. One such technique is the Material Point Method (MPM), which appears to provide an efficient way to model these problems. The MPM models a problem domain using particles at which state variables are kept and tracked. The particles have no restriction on movement, unlike in the Finite Element Method (FEM) where element distortion limits the level of mesh deformation. In the MPM, calculations are carried out on a regular background grid to which state variables are mapped from the particles. It is clear, however, that the MPM is actually closely related to existing techniques, such as ALE and in this paper we review the MPM for solid mechanics and demonstrate these links

70-line 3D finite deformation elastoplastic finite-element code.

Few freeware FE programs offer the capabilities to include 3D finite deformation inelastic continuum analysis; those that do are typically expressed in tens of thousands of lines. This paper offers for the first time compact MATLAB scripts forming a complete finite deformation elasto–plastic FE program. The key modifications required to an infinitesimal FE program in order to include geometric non–linearity are described and the entire code given

On the use of Reuleaux plasticity for geometric non-linear analysis.

Three dimensional analyses including geometric and material non--linearity require robust, efficient constitutive models able to simulate engineering materials. However, many existing constitutive models have not gained widespread use due to their computational burden and lack of guidance on choosing appropriate material constants. Here we offer a simple cone-type elasto-plastic formulation with a new deviatoric yielding criterion based on a modified Reuleaux triangle. The perfect plasticity model may be thought of as a hybrid between Drucker-Prager (D-P) and Mohr-Coulomb (M-C) that provides control over the internal friction angle independent of the shape of the deviatoric section. This surface allows an analytical backward Euler stress integration on the curved surface and exact integration in the regions where singularities appear. The attraction of the proposed algorithm is the improved fit to deviatoric yielding and the one--step integration scheme, plus a fully defined consistent tangent. The constitutive model is implemented within a lean 3D geometrically non-linear finite-element program. By using an updated Lagrangian logarithmic strain--Kirchhoff stress implementation, existing infinitesimal constitutive models can be incorporated without modification