Reuleaux plasticity : improving Mohr-Coulomb and Drucker-Prager.

The yielding of soil exhibits both a Lode angle dependency and a dependency on the intermediate principal stress. Ignoring these leads to a loss of realism in geotechnical analysis, yet neither of the widely used Mohr-Coulomb (M-C) or Drucker-Prager (D-P) models include both. This paper presents a simple pressure-dependent plasticity model based on a modified Reuleaux (mR) triangle which overcomes these limitations and yet (like the M-C and D-P formulations) allows for an analytical backward-Euler stress integration solution scheme. This latter feature is not found in more sophisticated (and computationally expensive) models. The mR deviatoric function is shown to provide a significantly improved fit to experimental data when compared with the M-C and D-P functions. Finite deformation finite-element analysis of the expansion of a cylindrical cavity is presented, verifying the use of the mR constitutive model for practical analyses

A ghost-stabilised material point method for large deformation geotechnical analysis

The Material Point Method (MPM) is advertised as the method for large deformation analysis of geotechnical problems. However, the method suffers from several instabilities which are widely documented in the literature, such as: material points crossing between elements, different number of points when projecting quantities between the grid and points, etc. A key issue that has received relatively little attention in the literature is the conditioning of the linear system of equations due to the arbitrary nature of the interaction between the physical body (represented by material points) and the background grid (used to solve the governing equations). This arbitrary interaction can cause significant issues when solving the linear system, making some systems unsolvable or causing them to predict spurious results. This paper presents a cut-FEM (Finite Element Method) inspired ghost-stabilised MPM that removes this issue

On isogeometric yield envelopes

In numerical analysis the failure of engineering materials is controlled through specifying yield envelopes (or surfaces) that bound the allowable stress in the material. Simple examples include the prismatic von Mises (circle) and Tresca (hexagon) yield surfaces. However, each surface is distinct and requires a specific equation describing the shape of the surface to be formulated in each case. These equations impact on the numerical implementation (specifically relating to stress integration) of the models and therefore a separate algorithm must be constructed for each model. This paper presents, for the first time, a way to construct yield surfaces using techniques from isogeometric analysis [1], such that different yield surfaces can be represented within the same framework. These isogeometric surfaces are combined with an implicit backward-Euler-type stress integration algorithm [2] to provide a flexible numerical framework for computational plasticity. The numerical performance of the algorithm is demonstrated using both material point investigations and boundary value analyses

Algorithmic issues for three-invariant hyperplastic Critical State models

Implicit stress integration and the consistent tangents are presented for Critical State hyperplasticity models which include a dependence on the third invariant of stress. An elliptical deviatoric yielding criterion is incorporated within the family of geotechnical models first proposed by Collins and Hilder. An alternative expression for the yield function is proposed and the consequences of different forms of that function are revealed in terms of the stability and efficiency of the stress return algorithm. Errors associated with the integration scheme are presented. It is shown how calibration of the two new material constants is achieved through examining one-dimesional consolidation tests and undrained triaxial compression data. Material point simulations of drained triaxial compression tests are then compared with established experimental results. Strain probe analyses are used to demonstrate the concepts of energy dissipation and stored plastic work along with the robustness of the integration method. Over twenty finite element boundary value problems are then simulated. These include single three-dimensional element tests, plane strain footing analyses and cavity expansion tests. The rapid convergence of the global Newton–Raphson procedure using the consistent tangent is demonstrated in small strain and finite deformation simulations

A high-order material point method

The material point method (MPM) is a version of the particle-in-cell (PIC) which has substantial advantages over pure Lagrangian or Eulerian methods in numerical simulations of problems involving large deformations. Using MPM helps to avoid mesh distortion and tangling problems related to Lagrangian methods and the advection errors associated with Eulerian methods are avoided. In this paper a novel high-order material point method within an isogeomeric analysis (IGA) framework is developed. Utilizing high order basis functions enables more accurate determination of physical state variables e.g. stress. The smooth spline function spaces, B-splines, are used to eliminate the non-physical effects are caused by use of standard high-order finite element basis function i.e. based on Lagrange polynomials

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

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

On the use of plastic inserts in prestressed railway components.

The use of such plastic inserts (such as Vossloh dowels and other soft fastening solutions) in pre-stressed concrete sleepers and crossing bearers has become widespread within the United Kingdom, Europe and the rest of the world. This paper uses a bespoke finite-element analysis tool to, for the first time, investigate the stress state around these plastic inclusions specifically focusing on the likelihood of discontinuity development. Most continuum stress analysis methods are over simplistic, in that they assume that fracture occurs in a direction normal to the major (most tensile) principal stress once it exceeds some limiting threshold. However, simply using a limiting stress approach fails to interpret the problem from the viewpoint of material instability analysis. A more physically realistic approach requires examination of the inelastic material stiffness, to determine the direction in which the initial fractures will propagate. This rigorous continuum-discontinuum approach, combined with an efficient instability search algorithm, is used in this pape

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

Two dimensional configurational-force-driven crack propagation using the discontinuous Galerkin method with rp-adaptivity

This paper presents a quasi-static configurational force (CF) brittle fracture propagation method, [1], using the discontinuous Galerkin (dG) symmetric interior penalty (SIP) method, [2]. The method is derived from the first law of thermodynamics with consideration of the Griffith fracture criterion [1]. The criterion is evaluated by finding the difference between the power applied to the domain and the rate of internal energy change at every point in the domain. If a node within the element mesh satisfies the criterion, a crack will propagate in the CF direction. Around the crack tip the advantage of element specific degrees of freedom in dG methods enables simple p-adaptivity to determine the CF in the spatial domain. In the material domain r-adaptivity is implemented, where the CF direction is used to align element edges, which are then split to propagate the crack