Tresca Material Research Articles

Large deformation finite element analyses of axially loaded helical piles in cohesive soil

Large deformation finite element (LDFE) analysis is suitable for research on soil-pile interaction. The objectives of this study were to develop an LDFE model for axially loaded double-helix piles and to examine the factors that control their failure modes. The model was implemented with the re-meshing and interpolation technique with a small strain approach. Three types of helical piles in clay modeled as a Tresca material were simulated in an axisymmetric setup. The model was calibrated against the results of centrifuge model tests. Analyses show that the failure mode changed gradually from a cylindrical shear mode (CSM) to a transitional failure mode and then an individual bearing mode (IBM) with increasing inter-helix spacing. Current results suggested that there might not be a unique inter-helix spacing ratio that distinguishes CSM from IBM. Further, the effects of helix embedment depth, inter-helix spacing, and undrained soil shear strength on the failure modes were assessed by parametric analyses. Finally, the failure modes and helix-bearing factors, shown to depend on these parameters, were summarized in several charts for potential practical applications. Results suggested that the lower helix's bearing factors remained unchanged, but the upper helix's bearing factors changed with the embedment depth and failure modes.

Modelling of the Torsional Simple Shear Test with Randomized Tresca Model Properties in Midas GTS NX

The dynamic properties of soil obtained from the torsional simple shear test (TOSS) are assumed to be uniform throughout the specimen. For some exceptional soils, this may hold true, but for the most majority of soils that we examine, it is obviously not the case, and this level of non-uniformity depends on the conditions in which the soil was formed. In this paper, we discuss a method of modelling inherently non-uniform soil specimens by representing them with elements that have an elasto-plastic simple Tresca material model with different properties (Elastic young modulus and yield stresses). The combination of properties that can simulate the nonlinear behaviour of the soil is found and calibrated using a model of the TOSS test built in the finite element software Midas GTS NX. Furthermore, the influence of rigid inclusions in the soil is studied and the results show an increase in stiffness with the increasing percentage of inclusion in the soil.

Cavity expansion in cohesive-frictional soils with limited dilation

The problem of cavity expansion from zero radius has no characteristic length and therefore possesses a similarity solution, in which the cavity pressure remains constant and the continuing deformation is geometrically self-similar. In this case, the incremental velocity approach first used by R. Hill in 1950 to analyse cavity expansion in Tresca materials can be extended to derive a solution for the limiting pressure of cavity expansion in other types of material. In this paper, a rigorous semi-analytical solution is derived, following Hill's incremental velocity method, for the expansion of cavities from zero initial radius in cohesive-frictional soils with limited dilation. In particular, the radius of the elastic–plastic interface c is used in this paper as the timescale and the solution for the limit pressure has been presented. Solutions are evaluated for a number of cases representative of a range of cohesive-frictional and dilatant soils. A comparison is also made between the solutions presented here and previous solutions for cohesive-frictional soils that have unlimited (on-going) plastic dilation. In particular, the influence of limited plastic dilation on the cavity limit pressure is identified and discussed.

Possibilities and limitations of the sequential kinematic method for simulating evolutionary plasticity problems

Evolutionary plasticity processes, such as ploughing and penetrating, widely exist in many geotechnical engineering applications. The simulation of these processes poses considerable challenges due to the occurrence of large deformation, unsteady nature of the material free surface, and inherent coupling between mechanical response and material geometries. This paper explores the possibility of simulating the first-order response of these processes by using sequential kinematic method (SKM) in combination with simple deformation mechanism. The mechanism consists of rigid elements separated by velocity discontinuities. Computations based on the kinematic approach of limit analysis are sequentially performed to evaluate the most likely deformation mode and update material geometries. An r-adaptive kinematic formulation is used that captures versatile velocity fields by optimizing the geometries of simple kinematic mechanism. The modelling methodology is studied in detail for two archetypal evolutionary plasticity problems: wedge ploughing Tresca material and cylinder penetrating undrained clay. The numerical results obtained by using the SKM are compared against existing analytical and numerical solutions, as well as experimental evidence. The paper demonstrates that evolutionary plasticity problems can be simulated in a conceptually simple way using SKM and highlights the potential pitfalls of this technique.

Effect of perforations on the bearing capacity of shallow foundation on clay

As a type of shallow foundation, a mudmat serves as the seabed support structure for subsea wells, pipeline manifolds, and pipeline terminations. The shallow foundations are usually designed with perforations to facilitate installation and removal, but the influence of these perforations has not been fully understood. This paper presents a method to analyze the bearing capacities of both two-dimensional (2D) and three-dimensional (3D) perforated shallow foundations using finite element analysis. The soil was idealized as a Tresca material, with the undrained strength increasing linearly with depth. The outcome indicates that perforations have nonnegligible effects on the bearing capacity of shallow foundations. The bearing capacity decreases with increasing perforation ratio, R, and the degree of reduction increases with the increase of the dimensionless ratio kB/Suo, where k is the shear strength gradient, B is the width of the foundation, and Suo is the shear strength at the mudline. For 2D shallow foundations, there exists a critical perforation ratio, Rc; when the perforation ratio is lower than the critical perforation ratio, the perforated foundation does not lose its bearing capacity. For 3D shallow foundations, the bearing capacity decreases directly with the increase of perforation ratio, R.

Two‐dimensional elastoplastic analysis of cylindrical cavity problems in Tresca materials

SummaryThis paper presents analytical elastic‐plastic solutions for static stress loading analysis and quasi‐static expansion analysis of a cylindrical cavity in Tresca materials, considering biaxial far‐field stresses and shear stresses along the inner cavity wall. The two‐dimensional static stress solution is obtained by assuming that the plastic zone is statically determinate and using the complex variable theory in the elastic analysis. A rigorous conformal mapping function is constructed, which predicts that the elastic‐plastic boundary is in an elliptic shape under biaxial in situ stresses, and the range of the plastic zone extends with increasing internal shear stresses. The major axis of the elliptical elastic‐plastic boundary coincides with the direction of the maximum far‐field compression stress. Furthermore, considering the internal shear stresses, an analytical large‐strain displacement solution is derived for continuous cavity expansion analysis in a hydrostatic initial stress filed. Based on the derived analytical stress and displacement solutions, the influence of the internal shear stresses on the quasi‐static cavity expansion process is studied. It is shown that additional shear stresses could reduce the required normal expansion pressure to a certain degree, which partly explains the great reduction of the axial soil resistance due to rotations in rotating cone penetration tests. In addition, through additionally considering the potential influences of biaxial in situ stresses and shear stresses generated around the borehole during drillings, an improved cavity expansion approach for estimating the maximum allowable mud pressure of horizontal directional drillings (HDDs) in undrained clays is proposed and validated.

Geometry of principal stress trajectories for a Tresca material under axial symmetry

In the case of Tresca’s yield criterion it is usually convenient to subdivide all possible deformations into two subclasses: deformations corresponding to a face of the yield surface and deformation corresponding to an edge of the yield surface. The present paper deals with the second subclass of deformations under conditions of axial symmetry. In this case the stress equations comprising the equilibrium equation and yield criterion can be investigated independently of any flow rule and the final result is also independent of whether elastic strains are included. It is shown that it is always possible to introduce such a principal line coordinate system (i.e. the coordinate system whose coordinate curves coincide with principal stress trajectories) that the product of the scale factors is equal to unity. Using this result the system of equations for mapping between the principal line coordinate and cylindrical coordinate systems is derived and it is shown that this system of equations is hyperbolic.

Upper bound of tunnel face stability using asymmetric yielding

Although significant advancement has been made over recent years with respect to three-dimensional upper bound calculations of tunnel facing, a considerable difference still exists between analytically and empirically based stability values. The current work suggests that the difference may well be the outcome of the traditional use of Tresca yield criterion for the upper bound calculations, which, by definition, does not distinguish among the shearing modes (compression, extension, plane strain). Consequently, this paper suggests and discusses a new yield function, which allows for asymmetric yielding. Such yielding is only beneficial in the case of three-dimensional and continuous velocity fields, and therefore a numerical procedure that generates relevant kinematically admissible fields for classical upper bound calculation is suggested. The procedure involves conversion from a load controlled boundary value problem to a velocity controlled problem at the limit state of collapse. The analysis results in significantly lower upper bound values than those presented earlier (for Tresca material), and the values are much closer to the stability curves of Kimura and Mair (1981), which are commonly used in design.

Modelling of Fall-cone Tests with Strain-rate Effects

Material Point Method (MPM) is a numerical method, which is well suited for large displacement simulations. Large displacements problems are relatively common in geotechnics, including post-failure behaviour of landslides as well as a wide range of problems involving penetration into the soil body. One of those problems is the fall-cone test, commonly used to establish the undrained shear strength and the sensitivity of saturated fine grained soils.This paper shows a Generalized Interpolation Material Point Method (GIMP) simulation replicating published free-fall cone experiment performed on a kaolin clay. In the fall-cone tests, the penetration characteristics of the cone, such as velocity and total penetration depth depend on the soil properties. Those properties are affected greatly by the strain-rate which must be accounted for in a numerical simulation. Hence, the simulations shown uses a Mohr-Coulomb / Tresca material extended with strain-rate effects.The presentednumerical simulations are compared with the published fall-cone experiment in whichdisplacement and force were measured. The comparison indicates that Generalized Interpolation Material Point Method and Mohr-Coulomb / Tresca model extended with strain-rate effects areableto replicate the fall-cone penetration test very well.

New analytic criterion for porous solids with pressure-insensitive matrix

In this paper, we address the question of how the relative weighting of the two invariants of the plastic deformation of the matrix influence the mechanical response of a porous metallic material. To this end, we first propose a new isotropic potential for description of the plastic behavior of the matrix that depends on both invariants of the strain-rate deviator. The relative weight of the two invariants is described by a material parameter β. Depending on the sign of the parameter β, the new plastic potential for the matrix is either interior to von Mises strain-rate potential (β < 0), coincides with it (β = 0) or it is exterior to it. Next, an analytic criterion for a porous solid with matrix governed by the new strain-rate potential is obtained using rigorous upscaling methods. Analysis is conducted for both tensile and compressive axisymmetric loading scenarios and spherical void geometry. No simplifying approximations are considered when estimating the local and overall plastic dissipation, respectively. It is shown that the value of β has a drastic influence on all aspects of the mechanical response. There is a value β = β*<0 such that there is almost no influence of J3Σ on the mechanical response of the porous solid. If the matrix is characterized by β > β*, the response of the porous material for tensile loadings and J3Σ≥0 is softer than that for loadings at J3Σ≤0. The reverse holds true for β<β*. The noteworthy result is that irrespective of the value of the parameter β, the response of the porous solid is harder than that of a porous Tresca material. However, depending on the value of β the rate of void growth or collapse can be either faster or slower than that of a porous Mises material.

Limit analysis and homogenization of porous materials with Mohr–Coulomb matrix. Part I: Theoretical formulation

The present two-part study aims at investigating the specific effects of Mohr–Coulomb matrix on the strength of ductile porous materials by using a kinematic limit analysis approach. While in the Part II, static and kinematic bounds are numerically derived and used for validation purpose, the present Part I focuses on the theoretical formulation of a macroscopic strength criterion for porous Mohr–Coulomb materials. To this end, we consider a hollow sphere model with a rigid perfectly plastic Mohr–Coulomb matrix, subjected to axisymmetric uniform strain rate boundary conditions. Taking advantage of an appropriate family of three-parameter trial velocity fields accounting for the specific plastic deformation mechanisms of the Mohr–Coulomb matrix, we then provide a solution of the constrained minimization problem required for the determination of the macroscopic dissipation function. The macroscopic strength criterion is then obtained by means of the Lagrangian method combined with Karush–Kuhn–Tucker conditions. After a careful analysis and discussion of the plastic admissibility condition associated to the Mohr–Coulomb criterion, the above procedure leads to a parametric closed-form expression of the macroscopic strength criterion. The latter explicitly shows a dependence on the three stress invariants. In the special case of a friction angle equal to zero, the established criterion reduced to recently available results for porous Tresca materials. Finally, both effects of matrix friction angle and porosity are briefly illustrated and, for completeness, the macroscopic plastic flow rule and the voids evolution law are fully furnished.

Finite element limit analysis of pullout capacity of planar caissons in clay

Rigorous upper and lower bound solutions of pullout capacity for planar caissons in clay are solved by two dimensional plane strain finite element limit analysis. The planar caisson is embedded in a deep clay layer with an undrained shear strength of zero at the mudline that increases linearly with depth. To perform finite element limit analysis, clay is modeled as the triangular element with the rigid-plastic Tresca material in an undrained condition. The planar caisson is modeled as the rigid plate element. Soil-structure interfaces with full tension are used around the contacted length between caisson and clay. Mesh adaptivity is employed to obtain very tight upper and lower bounds on the true pullout load. Parametric studies are carried out for the complete range of input dimensionless variables including adhesion factor and embedment ratio. The results of analyses are summarized in the form of the dimensionless pullout factor which is a function of the dimensionless variables. Empirical closed-form expressions for the dimensionless pullout factor and reverse end bearing factor of a planar caisson are proposed.

A homogenization based yield criterion for a porous Tresca material with ellipsoidal voids

This paper presents a rate-independent ana- lytical model for porous Tresca ( J3 -dependent) mate- rials containing general ellipsoidal voids. The model is based on the nonlinear variational homogenization method which uses a linear comparison material to esti- mate the response of the nonlinear porous solid and is denoted as “MVAR”. Specifically, the model is derived by an original approach starting from a novel porous single crystal model (Mbiakop et al. in Int J Solids Struct 64–65:100–119, 2015b, J Mech Phys Solids 84:436–467, 2015c) by considering the limiting case of infinite slip systems which leads readily to the cor- responding Tresca criterion. The MVAR yield surface is then validated using FEM on different unit-cells and various parameters including several porosity levels, several stress triaxiality ratios, different Lode angle and general void shapes and orientations. The MVAR model is found to be in good agreement with the finite element results for all cases considered in this study. Both the MVAR and the FEM computations reveal a strong sensitivity upon the microstructure anisotropy (void shape and orientation), and a dependence of the effective behavior on the third invariant of the applied stress. To the best knowledge of the authors, this is the first model in the literature that is able to deal with porous Tresca material and general void shapes and orientations. Moreover, the MVAR is used in a pre- dictive manner to investigate the complex response of porous Tresca cases with strong coupling between the J3-dependent matrix behavior and the (morphologi- cal) anisotropy induced by the shape and orientation of the voids. The simplicity of the present analytical study opens the possibility to adapt the present model to experimental results for various materials.

Effect of strain rate and strain softening on embedment depth of a torpedo anchor in clay

Torpedo anchors (of diameter ~1m) are released from a height of 50–100m from the seabed, achieving velocities up to 35m/s at impacting the sediment. The strain rates induced in the surrounding soil by this dynamic installation is therefore significantly higher than those associated with installation of other offshore foundations and anchoring systems. The high strain rates enhance the mobilised undrained shear strength compared to that measured by in-situ penetrometer or laboratory tests. This paper reports the results from dynamic installation of a torpedo anchor in strain softening, rate dependent soft clays, quantifying the effects relative to results for ideal Tresca material. The three-dimensional dynamic large deformation finite element (LDFE) analyses were carried out using the coupled Eulerian–Lagrangian approach. The simple elastic-perfectly plastic Tresca soil model was modified to allow strain softening and strain rate dependency of the shear strength. Parametric analyses were undertaken varying the strain rate parameter, the sensitivity and ductility of the soil, and the soil undrained shear strength. Overall, embedment depth for rate dependent, strain softening clays lay below that for ideal Tresca material. Increased strain rate dependency of the soil led to marked reduction in embedment depth, only partly compensated by brittleness. Key results have been presented in the form of design charts, fitted by simple expressions to estimate the embedment depth of a torpedo anchor.

The ratchet–shakedown diagram for a thin pressurised pipe subject to additional axial load and cyclic secondary global bending

The ratchet and shakedown boundaries are derived analytically for a thin cylinder composed of elastic-perfectly plastic Tresca material subject to constant internal pressure with capped ends, plus an additional constant axial load, F, and a cycling secondary global bending load. The analytic solution is in good agreement with solutions found using the linear matching method. When F is tensile, ratcheting can occur for sufficiently large cyclic bending loads in which the pipe gets longer and thinner but its diameter remains the same. When F is compressive, ratcheting can occur in which the pipe diameter increases and the pipe gets shorter, but its wall thickness remains the same. When subject to internal pressure and cyclic bending alone (F = 0), no ratcheting is possible, even for arbitrarily large bending loads, despite the presence of the axial pressure load. The reason is that the case with a primary axial membrane stress exactly equal to half the primary hoop membrane stress is equipoised between tensile and compressive axial ratcheting, and hence does not ratchet at all. This remarkable result appears to have escaped previous attention.

A direct approach for continuous topology optimization subject to admissible loading

In the present paper, a method is proposed for topology optimization of continuum structures subject to static and plastic admissibility conditions relative to a prescribed load. A key feature of the method is that, using a finite-element discretization, the form of the resulting topology optimization problem is similar to that of the direct static approach of the limit analysis problem. The proposed method is formulated in plane strain using Tresca materials and is illustrated on example problems taken from the literature.

REDUCED SHAKEDOWN FORMULATION IN PLANE STRESS PROBLEMS

Shakedown theory determines the load limits for structures under variable loads. Our recently-constructed reduced shakedown kinematic formulations are re-examined, with particular expressions constructed for plane stress problems in both cases of Mises and Tresca materials. While the possibilities for numerical implementations of the reduced forms are to be explored, we illustrate the applications of the forms to estimate the nonshakedown loads for a circular hollow disk under variable pressure and temperature fields.

Importance of the consideration of the specificities of local plastic deformation on the response of porous solids with Tresca matrix

Abstract Based on rigorous limit-analysis theorems, very recently, Cazacu et al. (2014) have deduced an analytic plastic potential for porous solids with Tresca matrix. Key in the model development was the consideration of the specificities of the plastic flow of the matrix. In this paper, finite element calculations are conducted for a voided cubic cell obeying Tresca's criterion and compared with the predictions of the new model. The numerical calculations confirm the centro-symmetry of the yield locus of the porous Tresca material and the combined effects of the mean stress and the third-invariant of the stress deviator on void evolution. In particular, it is shown that the rate of void growth is faster for axisymmetric loading histories corresponding to the third-invariant J 3 Σ ≥ 0 than for those corresponding to J 3 Σ ≤ 0 , while void collapse occurs faster for loadings such that J 3 Σ ≤ 0 than for those characterized by J 3 Σ ≥ 0. Irrespective of the loading history, it is found that neglecting the local plastic heterogeneity leads to a drastic underestimation of the rate of void evolution.

Limit analysis of the undrained bearing capacity of offshore pipelines

The ultimate bearing capacity of a rigid, plane-strain pipe segment embedded in undrained clay is studied using numerical limit analysis. The pipe is considered to be ‘wished in place' at invert penetrations ranging from zero to five pipe diameters, thus providing coverage of both on-bottom (partially embedded) and trenched (fully embedded) offshore pipelines. The soil is modelled as a rigid-plastic Tresca material with either uniform strength or strength proportional to depth. The effects of soil weight, interface roughness and interface tensile capacity are investigated in a systematic manner. All calculations are performed using the finite-element limit analysis code OxLim, which uses adaptive mesh refinement to compute tightly bracketed lower- and upper-bound plasticity solutions. The velocity fields from the upper-bound analyses provide the corresponding failure mechanisms. The paper initially focuses on purely vertical loading (penetration and uplift), and then addresses combined vertical and horizontal loading. A comprehensive set of design curves and failure envelopes is presented, with the results explained in terms of the changing failure mechanisms. These results are immediately applicable in practice. In particular, current industry-standard procedures for design against pipeline upheaval are critically reviewed, and are shown to have potentially unconservative shortcomings.

A direct complementarity approach for the elastoplastic analysis of plane stress and plane strain structures

SUMMARYThis paper presents a direct complementarity approach for carrying out the elastoplastic analysis of plane stress and plane strain structures. Founded on a traditional finite‐step formulation, our approach, however, avoids the typically cumbersome implementation of iterative predictor–corrector procedures associated with the ubiquitous return mapping algorithm. Instead, at each predefined step, the governing formulation—cast in its most natural mathematical programming format known as a mixed complementarity problem—is directly solved by using a complementarity solver run from within a mathematical modeling system. We have chosen the industry‐standard General Algebraic Modeling System/PATH mixed complementarity problem solver that is called from within the General Algebraic Modeling System environment. We consider both von Mises and Tresca materials, with perfect or hardening (kinematic and isotropic) behaviors. Our numerical tests, five (benchmark) examples of which are presented in this paper, have been carried out using models constructed from the mixed finite element of Capsoni and Corradi (Comput. Methods Appl. Mech. Eng. 1997; 141:67–93), which beneficially offers a locking‐free behavior and coarse‐mesh accuracy. The results indicate, in addition to an isochoric locking‐free behavior, good accuracy and the ability to circumvent the difficult singularity problem associated with the corners of Tresca yield surfaces. Copyright © 2012 John Wiley &amp; Sons, Ltd.