Large Strain Problems Research Articles

Large-Strain Consolidation Analysis for Clayey Sludge Improved by Horizontal Drains

The use of prefabricated horizontal drains (PHDs) with combined surcharge and vacuum preloading is an effective improvement approach for dredged clayey slurries. However, there is no large-strain analysis method for PHD-induced consolidation of high-water-content sludge, even though it is a typical large-strain problem. This study develops a two-dimensional plane strain model based on Gibson’s large-strain theory, considering horizontal and vertical flows, nonlinear hydraulic conductivity, and compressibility during the consolidation process. The alternative direction implicit (ADI) difference method is used to solve the governing equation. The proposed model is verified by the data from an analytical one-dimensional (1D) large-strain model and from field measurements. Compared with the improved small-strain models, the proposed model produces a slower consolidation of sludge. Furthermore, the analyses incorporating geometrical and mechanical nonlinearities show that, in comparison with the external load and the horizontal permeability, the spacing of the PHDs (horizontal and vertical) and the vertical permeability are more crucial factors significantly impacting consolidation efficiency. Specifically, smaller PHD spacing and greater vertical permeability lead to a more efficient consolidation.

Method for calculating horizontal drain induced non-linear and large strain degree of consolidation

Consolidating dredged clay slurries using a combination of vacuum pressure and prefabricated horizontal drains (PHDs) is widely used in practice. This is a large strain problem, but there is no existing large strain theory for PHD induced consolidation. A method with explicit equations has been proposed to consider both mechanical and geometrical non-linearities in analyzing PHD induced consolidation. The method considers stepwise variation of properties using imaginary time concept. An imaginary time is determined by the condition of continuity of degree of consolidation before and after changing the properties. Then the method was applied to analyze a large scale model test of vacuum consolidation with PHD. Two analyses were conducted. One considered both the mechanical and geometrical non-linearity (large strain), and another only considered mechanical non-linearity (small strain). The results of large strain analysis agree with the measured settlement curve and excess pore pressures well. While the small strain analysis under-estimated the rate of consolidation significantly. The results from this study indicate that for analyzing PHD induced consolidation of clay slurries considering the effect of large strain is important, and the proposed method can be a useful design tool.

A Taylor–Hood type virtual element formulations for large incompressible strains

Considerable progress has been made during the last decade with respect to the development of discretization techniques that are based on the virtual element method. Here we construct a new scheme for large strain problems that include incompressible material behavior. The idea is to use a formulations analogous to the classical Taylor–Hood element, Taylor and Hood (1972) which is based on a mixed principle where different interpolation functions are used for the deformation and pressure field. In this paper, a quadratic serendipity ansatz for the displacements is combined with a linear pressure field which leads to new virtual element formulations that are discussed and compared in this paper.

FINITE ELEMENT IMPLEMENTATION OF GEOMETRICALLY NONLINEAR CONTACT

The OOFEM finite element software has been recently updated to include contact algorithms for small strain applications. In this work, we attempt to extend the contact algorithms to large strain problems. Reviewing the current code and comparing it with approaches encountered in literature, we arrive at a specific algorithmic solution and integrate it into the current code base. The current code is explained, the necessary extensions are derived and documented, and the algorithmic changes are described. Tests confirm the functionality and quadratic rate of convergence of the proposed implementation.

Displacement analysis of open pipe piles sinking based on strain path method

The displacement field in the process of opening pipe piles sink has always been a hot issue in the study, especially in the area of pile, the soil body has produced a large strain, regardless of the large deformation effect of the soil, there will be a large calculation error. The strain path method can obtain the flow velocity of the soil because it does not rely on the constitutive relationship of the soil, which is a favorable theory for solving large strain problems. In this paper, the modified strain path method is used as the theoretical basis. The open pipe pile is equivalent to a closed pipe pile through the soil plug effect, and the sunk pile displacement of the open pipe pile is calculated to further reveal the soil plug effect and the soil squeeze effect of the open pipe pile mutual restraint and mutual influence, thus providing a theoretical basis for the pile displacement of open pipe piles.

Implicit stress integration procedure for large strains of the reformulated Shape Memory Alloys material model

Devices made of Shape-Memory Alloys (SMA) often exhibit a superelasticity or a shape memory effect during the exploitation. Both effects include large deformations up to 10% or large rotations, and a large-strain stress integration procedure is necessary for a correct numerical simulation. For this purpose, a reformulation of the existing SMA phenomenological constitutive model is introduced to provide an effective implementation into the Finite Element Method code. All variables are derived in a scalar form, which allows an extension of the small-strain solution to the large-strain problems. The multiplicative decomposition of the deformation gradient is employed to compute the proper strain measure as an input variable for the unified stress integration procedure. An appropriate conjugated stress measure is computed, and the variables necessary for further computation are updated. The verification is presented in several selected examples.

Numerical modeling of the large strain problem in the case of mushrooming projectiles

The paper investigates the capabilities and limitations of five different numerical approaches to the modeling of large strains of mushrooming projectiles on the example of a 9 mm Parabellum. The studies included the following methods: FEM, FEM-Remeshing, ALE-Smoothing, ALE-Euler and SPH. The results of computer simulations are summarized and confronted with experimental data for reduced and nominal impact velocity. The selected methods are compared in terms of predictability, credibility of results, range of application and computational effectiveness. Additionally, practical guidelines for simulation of the soft-core projectile impact problem are given. The most realistic results were registered for the ALE–Euler model, but this incurred the considerable computational cost. FEM is suggested for simulation of projectile impact with reduced velocity as it takes the least CPU time. Selection of other methods should be based on maximum impact velocity and the available computer resources.

Finite element analysis of tensile and puncture behaviours of geosynthetic cementitious composite mat (GCCM)

This paper presents the fundamental mechanical properties that characterise constitutive behaviours of GCCM for large-strain problems in unidirectional tensile and axi-symmetry puncture tests. The 2D nonlinear FEA was conducted to simulate the GCCM behaviour. The optimised stiffness parameters can simulate the elastic behaviour of GCCM. The post-cracking governed by inelasticity of woven geotextile is modelled by bilinear stress-strain relationship. The interface between woven geotextile and cement layer is explained by the existing bond-slip model. The analytical results are presented in terms of load-displacement curves as well as the crack patterns, which are similar to the experimental results.

A Simplified Approach for Estimating Settlement of Soft Clay under Vacuum Consolidation

In general, the ground improvement by Prefabricated Vertical Drains (PVD) consolidation involves a high magnitude of settlement, which results in a change in the consolidation characteristic of the soil during the process of consolidation. Under such circumstances, the consolidation problem must be treated as a large strain problem. The large strain 3-Dimensional consolidation analysis requires a large number of parameters, making it difficult for practicing engineers to carry out such analysis for a practical application. This paper aims to provide a simplified method for estimation of settlement during 3D vacuum consolidation using a single parameter, the coefficient of horizontal Consolidation (Ch). For this, the variation in Ch during the 3D consolidation was back-calculated using Hansbo’s method from a series of large-scale 3D vacuum consolidation tests carried on reconstituted marine clay. As the varying Ch cannot be employed in available analytical models, a simplified finite element analysis is presented to employ varying Ch. The estimated settlement was further compared with settlement obtained utilizing constant Ch, by trial and error method. The paper also demonstrates a potential advantage of the proposed method that the variation in Ch can also be determined from 3D consolidation carried out previously for similar strata, as it requires only basic data, which are usually available.

Discrete numerical simulations of torpedo anchor installation in granular soils

Torpedo anchors are a viable approach for mooring marine hydrokinetic (MHK) energy devices to the seafloor. These anchors can serve to maintain station and to provide the reaction force for an MHK device. The ability of the anchor to perform these duties is a strong function of its penetration depth during installation. This is a large-strain problem not amenable to typical continuum numerical approaches. In the current work, we propose that the discrete element method (DEM) is a more appropriate tool to investigate the shallow penetration of torpedo anchors in sands. The effects of anchor mass, impact velocity, and soil interparticle friction are considered in the DEM simulations. The relative maximum penetration depths for different penetration conditions are quantified and presented. Granular material response at the microscale during penetration are used to provide insight into system response. Energy dissipation in the assembly by both friction and collision at the particle scale are considered. Results show that anchor penetration increases approximately linearly with an increase in impact velocity or anchor weight. Penetration decreases with an increase in interparticle friction (i.e., soil strength). Observations of microscale behaviors and energy calculations are used to provide insight into overall system response.

Numerical integration for nonlinear problems of the finite cell method using an adaptive scheme based on moment fitting

Fictitious domain methods such as the finite cell method simplify the discretization process significantly as the mesh is decoupled from the geometrical description. However, this simplification in the mesh generation results in broken cells, which is why special integration methods are required. Usually, adaptive integration schemes are applied resulting in a large number of integration points and, thus, an expensive numerical integration — especially for nonlinear applications. To perform the numerical integration more efficiently, we propose an adaptive integration method using moment fitting. Thereby, we present a moment fitting approach based on Lagrange polynomials through Gauss–Legendre points to circumvent having to solve the moment fitting equation system. The performance of this integration method is shown by studying several numerical examples of the finite cell method for small and large strain problems in elastoplasticity.

Hexahedral-Based Smoothed Finite Element Method Using Volumetric-Deviatoric Split for Contact Problem

A first-order hexahedral (H8)-element-based smoothed finite element method (S-FEM) with a volumetric-deviatoric split for nearly incompressible materials was developed for highly accurate deformation analysis of large-strain problems. In the proposed method, the isovolumetric part of the deformation gradient at the integration point is derived from F based on the beta finite element method (i.e., an S-FEM), whereas the volumetric part of the deformation gradient is derived from F on the basis of the standard FEM with reduced integration elements. This method targets H8 elements that are automatically generated from tetrahedral elements, which makes it quite practical. This is because the FE mesh can be created automatically even if the targeted object has a complex shape. This method eliminates the phenomena of volumetric and shear locking, and reduces pressure oscillations. The proposed method was implemented in the commercial FE software Abaqus and applied to the large-deformation contact problem to verify its effectiveness.

On the formulation of a finite element method for the stiffened multi-layered airfoil/hydrofoil structure: Post buckling analysis for the wings of underwater gliders

A finite element method is developed for the stiffened multi-layered airfoil/hydrofoil structure for the large deformation and finite strain problem. The kinematics of the airfoil/hydrofoil is set up. The Consistent Orthogonal Basis Function Space is applied for the airfoil/hydrofoil structure. Given the airfoil/hydrofoil configuration and boundary conditions, the basis function space can be uniquely determined, such that the diagonal mass matrix is obtained accurately and the basis functions are very identical with the mode shape functions of the structure. In order to satisfy the displacement compatibility condition between adjacent layers of the airfoil/hydrofoil, the traction degree-of-freedom is also induced.The post buckling analysis is presented for the wing (hydrofoil) structure of the underwater glider. The water pressure is applied on the outer surface and the critical buckling pressure is calculated. The post buckling equilibrium path is also given. The results are verified with ANSYS. The present study of the buckling analysis of the airfoil/hydrofoil under water pressure is helpful to the design of underwater glider.

A viscoelastic constitutive model for shape memory polymers based on multiplicative decompositions of the deformation gradient

Shape memory polymers (SMPs) are a class of polymeric smart materials that have the capacity to return from a deformed state (impermanent shape) to their original state (permanent shape) by temperature stimulus. In this work, we propose a novel phase-transition-based viscoelastic model including the time factor for shape memory polymers (SMPs), which has a clearer physical significance. To describe the phase transition phenomenon of SMPs, our new model defines different constitutive structures for above and below transformation temperature separately. As the proposed viscoelastic model is based on multiplicative thermoviscoelasticity, it can not only be used for different types of SMP materials, but also can be used to treat large strain problems. To validate the model's availability and show the model's capability of reproducing the shape memory effect (SME), two testing examples are predicted with this new constitutive model. The prediction results of the simulation are in good agreement with the available experimental results.

Phase field approach to dislocation evolution at large strains: Computational aspects

Computational aspects of the phase field simulations of dislocation nucleation and evolution are addressed. The complete system of equations for the coupled phase field approach to dislocation nucleation and evolution and nonlinear mechanics for large strains is formulated. Analytical solutions for a stationary and propagating single dislocation, dislocation velocity, core energy, and core width are found. Dislocation parameters for nickel are identified based on existing molecular dynamics simulations. In contrast to all previous efforts that are based on the spectral approach, finite element method (FEM) is utilized, which allowed us to treat large strain problems and non-periodic boundary conditions. The single dislocation order parameter profile and the stationary distance between two neighboring dislocations at a semicoherent sharp austenite–martensite interface are in perfect agreement with analytical expressions. The main focus is on proving that the new points of the developed theory can be confirmed in simulations, including possibility of obtaining the desired dislocation height for aligned and inclined dislocations, eliminating spurious stresses, resolving dislocation cores and interaction between cores of different dislocations. Mesh independence of the solutions is demonstrated and the effect of approximating finite element polynomials is analyzed, exhibiting possibility of significant numerical errors when special care is not taken of. Problems of nucleation and evolution of multiple dislocations along the single and multiple slip systems near martensitic lath, and along the sharp austenite –martensite interface, the activity of dislocations with two different orientations in a nanograined material under shear and pressure, and the interaction between two intersecting dislocation systems are studied. Surface-modified partial dislocation was revealed. These problems represent the first step in the future study of interaction of phase transformation and dislocations.

Anisotropic Analysis of I-Walls in New Orleans

Many numerical analyses of New Orleans levee and floodwall sections adopted mostly isotropic soil models partly due to the inherent simplicity of isotropic models. However, the isotropic models may not be sufficient to properly address the anisotropic behavior of soils. To overcome this imperfection, this study incorporated an anisotropic Modified Cam Clay model in a commercially available finite difference code, FLAC3D, and analyzed a floodwall and levee section in the 17th St. Canal in New Orleans. The analysis showed that the anisotropic model resulted in a similar overall deformation to the Mohr-Coulomb isotropic model. However, the anisotropic model showed more widely spread yielded elements and higher shear strain gradient in the Lacustrine clay layer, reconfirming that the Lacustrine clay layer played a major role for the failure in the 17th St. Canal. This result also signified that the isotropic Mohr-Coulomb model might be good for evaluating overall behavior in moderate deformation problems, while the anisotropic Modified Cam Clay model was good even for large strain problems where more accurate evaluation of yielding is needed.

A new dislocation-density-function dynamics scheme for computational crystal plasticity by explicit consideration of dislocation elastic interactions

Current strategies of computational crystal plasticity that focus on individual atoms or dislocations are impractical for real-scale, large-strain problems even with today’s computing power. Dislocation-density based approaches are a way forward but a critical issue to address is a realistic description of the interactions between dislocations. In this paper, a new scheme for computational dynamics of dislocation-density functions is proposed, which takes full consideration of the mutual elastic interactions between dislocations based on the Hirth–Lothe formulation. Other features considered include (i) the continuity nature of the movements of dislocation densities, (ii) forest hardening, (iii) generation according to high spatial gradients in dislocation densities, and (iv) annihilation. Numerical implementation by the finite-volume method, which is well suited for flow problems with high gradients, is discussed. Numerical examples performed for a single-crystal aluminum model show typical strength anisotropy behavior comparable to experimental observations. Furthermore, a detailed case study on small-scale crystal plasticity successfully captures a number of key experimental features, including power-law relation between strength and size, low dislocation storage and jerky deformation.

Sensitivity analysis based crack propagation criterion for compressible and (near) incompressible hyperelastic materials

Sensitivity analysis of an XFEM crack propagation model is developed for shape and material parameters, where the direct differentiation method is applied to large strain problems with hyperelastic neo-Hookean materials. The presence of level set functions to describe the crack position requires the development of a proper differentiation technique which is also addressed. In order to compute the analytical derivatives of such a complex numerical model the capabilities of the symbolic system AceGen are employed.A crack propagation criterion based on the sensitivity formulation is developed, allowing the direct calculation of the crack growth length and direction without post-processing. Special attention is paid to the ability of satisfying incompressibility and near-incompressibility conditions.The performance of the XFEM sensitivity analysis is assessed by the Cook's Membrane and Pre-crack Plate benchmark tests where sensitivities of displacements and crack propagation criteria based on potential energy have been analysed with respect to crack length and crack growth parameters. The techniques presented in this paper can be extended to anisotropic materials and non-linear materials exhibiting plasticity and viscoplasticity. Additionally, this formulation constitutes a base for further analysis of crack branching and crack joining problems.

Implicit stress integration method of Shape Memory material model

AbstractThe phenomenological SMA material model proposed by Lagoudas [1] is modified and implemented in finite element software PAK [2]. Critical thermodynamic force is derived to match implicit integration method. All variables are derived to depend on effective values of stress, strain and martensitic volume fraction. One scalar equation need to be solved in the integration point using trial stress direction for each time step. The integration in the trial deviatoric stress direction provides possibility to solve large strain problems using the algorithms developed for small strains. Two one‐dimensional and one non‐proportional large strain example verified accuracy of proposed modifications. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

An efficient 3D implicit approach for the thermomechanical simulation of elastic–viscoplastic materials submitted to high strain rate and damage

SUMMARYThis paper aims at presenting a general consistent numerical formulation able to take into account, in a coupled way, strain rate, thermal and damage effects on the behavior of materials submitted to quasistatic or dynamic loading conditions in a large deformation context. The main features of this algorithmic treatment are as follows: A unified treatment for the analysis and implicit time integration of thermo‐elasto‐viscoplastic constitutive equations including damage that depends on the strain rate for dynamic loading conditions. This formalism enables us to use dynamic thermomechanically coupled damage laws in an implicit framework. An implicit framework developed for time integration of the equations of motion. An efficient staggered solution procedure has been elaborated and implemented so that the inertia and heat conduction effects can be properly treated. An operator split‐based implementation, accompanied by a unified method to analytically evaluate the consistent tangent operator for the (implicit) coupled damage–thermo‐elasto‐viscoplastic problem. The possibility to couple any hardening law, including rate‐dependent models, with any damage model that fits into the present framework.All the developments have been considered in the framework of an implicit finite element code adapted to large strain problems. The numerical model will be illustrated by several applications issued from the impact and metal‐forming domains. All these physical phenomena have been included into an oriented object finite element code (implemented at LTAS‐MN 2L, University of Liège, Belgium) named Metafor.Copyright © 2013 John Wiley & Sons, Ltd.