A simple implementation of RITSS and its application in large deformation analysis

Abstract

Large deformation finite element (LDFE) analysis is being applied increasingly in geomechanics as it allows numerical interpretation of problems in which the structural element moves a relatively long distance through the soil. The ‘remeshing and interpolation technique with small strain’ (RITSS) method for LDFE analysis, in which the soil domain is periodically remeshed with the stress and material properties interpolated from the old to the new within the standard Lagrangian finite element framework, has been successfully applied to a number of practical applications. It allows any standard finite element theory to be used in the Lagrangian analysis, and because the mesh topography and connectivity are not influenced by the previous deforming increment, large deformations are possible. The major barrier of the RITSS method is that the remeshing and interpolation requires specialised and user-dependent computer code. This has limited its application to specialists and hindered its routine application in engineering practice. This paper proposes a simpler, more practical method to implement RITSS for geotechnical applications. By utilising the ABAQUS in-built procedures for interpolation and remeshing, it avoids any need for user-defined code (although a piece of Python script can be used to automate the iteration instead of operating the ABAQUS user interface). A series of four example problems benchmarking this new approach show it to be robust and numerically accurate.

Introduction

Numerical modelling of large deformations remains one of the most challenging aspects of geotechnical issues, combining geometric nonlinearity and often material constitutive nonlinearity. This is especially the case for offshore engineering, in which applications such as (but not limited to) full flow penetrometers [37], [6], [11], [56], spudcan penetration [7], [42], [20], lateral buckling of pipelines [9], [49], [51], and anchors [35], [41], [50], [4], [53] involve significant relative displacement of the structural element through the soil.

Various approaches for large deformation finite element (LDFE) analysis have been proposed over the last three decades. Early developments from the small strain to finite strain measurements comprised the total Lagrangian [18] and updated Lagrangian [1], [31], [23] approaches, both of which were limited by excessive distortion of elements as the analysis progressed due to the Lagrangian formulation. A radically different formulation is the Eulerian method, which allows material to flow through a fixed spatial mesh. The rare examples of the Eulerian method that can be found in the literature on solid mechanics are the early developments [32], [14], [13], [47] and some recent applications with the commercial software ABAQUS [43], [36], [46]. The challenging obstacles of the Eulerian formulation lie in its poor ability to deal with free surfaces, material interfaces and heterogeneous materials (e.g., offshore sediments exhibiting an increasing shear strength with depth). Combining the merits of both the Lagrangian and Eulerian approaches, the arbitrary Lagrangian Eulerian (ALE) approach has been applied to solid mechanics by, among others, Liu et al. [26], [27], Ghosh [15], [16], and Ghosh and Kikuchi [17] and by Nazem et al. [34] in geomechanics. These ALE developments have tended to follow a formal approach, with finite strain formulations for the Lagrangian steps and incorporating “convection” of the soil relative to the finite element mesh implicitly in the finite element equations [39]. Recently, Kardani et al. [24], [25] incorporated h-adaptive meshing technique into their in-house developed ALE programs to improve the numerical accuracy.

The ‘remeshing and interpolation technique with small strain’ (RITSS) approach proposed by Hu and Randolph [22] falls within the ALE category. However, it has distinct advantages as it is based on standard Lagrangian increments with periodic remeshing, followed by interpolation of all stresses and material properties. Thus, the new mesh topology and connectivity is not influenced by the previous increment. The independence of the remeshing and interpolation from the preceding Lagrangian incremental analysis allows any standard finite element program to be used. These distinct features render RITSS relatively robust and versatile in practical applications (such as, among others, [21], [48], [19], [57], [56], [49], [51], [52]).

The implementation of RITSS generally involves four steps [39]: (1) initial mesh generation, (2) incremental step of Lagrangian analysis, (3) updating boundaries and remeshing, and (4) mapping of stresses and material properties from the old to new mesh. In any analysis, steps (2)–(4) are repeated until completion of the whole LDFE analysis. As a standard Lagrangian analysis process, step (2) can be conducted with any Lagrangian finite element package. Early realisations were built around the finite element program AFENA [3] to fulfil the functionality of step (2). More recently, commercial finite element packages have been employed, including ABAQUS [49], [51] and LS-DYNA [28]. Steps (1) and (3) are essentially pre-processing and preparing the finite element model, which usually can be performed with the affiliated pre-processor of the Lagrangian finite element package or via third party software (e.g., ANSYS was adopted in [54]). The interpolation and mapping procedure of step (4) is pivotal, as it is largely related to the accuracy of the whole RITSS analysis. Currently available RITSS implementations require users to write in-house code for mapping field variables from the old to new mesh, which has been the largest barrier to wider application of the RITSS approach. This is especially challenging for the inexperienced user, as inappropriate or less rigorously coded subroutines in step (4) can lead to unacceptable errors or even numerical instabilities when running the program.

This paper proposes a practical implementation of RITSS using the commercial package ABAQUS that avoids user coding for mapping of stresses and material properties from the old to new mesh (the aforementioned step (4)). This simple implementation approach involves the adoption of an ABAQUS built-in technique, namely ‘mesh-to-mesh solution mapping’ (abbreviated as MSM in this paper). The following sections detail firstly the implementation, followed by four analysis examples to benchmark and validate the approach against available published results. Because the current RITSS implementations require user coding for step (4), the overall goal of this paper is to demonstrate the present simplified RITSS implementation and facilitate readers to conduct their own LDFE analysis.