Anisotropic viscous models of large-deformation Mohr-Coulomb failure

We have developed a way to represent Mohr-Coulomb failure within a mantle-convection fluid dynamics code. We use a viscous model of deformation with an orthotropic viscoplasticity (a different viscosity is used for pure shear to that used for simple shear) to define a prefered plane for slip to occur given the local stress field. The simple-shear viscosity and the deformation can then be iterated to ensure that the yield criterion is always satisfied. We again assume the Boussinesq approximation, neglecting any effect of dilatancy on the stress field. An additional criterion is required to ensure that deformation occurs along the plane aligned with maximum shear strain-rate rather than the perpendicular plane, which is formally equivalent in any symmetric formulation. We also allow for strain-weakening of the material. The material can remember both the accumulated failure history and the direction of failure. We have included this capacity in a Lagrangian-integration-point finite element code and show a number of examples of extension and compression of a crustal block with a Mohr-Coulomb failure criterion. The formulation itself is general and applies to 2- and 3-dimensional problems.

An anisotropic viscous representation of Mohr-Coulomb failure for use is modelling coupled mantle-continent dynamics

In mantle convection models it has become common to make use of a modified (pressure sensitive, Boussinesq) von Mises yield criterion to limit the maximum stress the lithosphere can support. This approach allows the viscous, cool thermal boundary layer to deform in a relatively plate-like mode even in a fully Eulerian representation. In large-scale models with embedded continental crust where the mobile boundary layer represents the oceanic lithosphere, the von Mises yield criterion for the oceans ensures that the continents experience a realistic broad-scale stress regime. In detailed models of crustal deformation it is, however, more appropriate to choose a Mohr-Coulomb yield criterion based upon the idea that frictional slip occurs on whichever one of many randomly oriented planes happens to be favorably oriented with respect to the stress field. As coupled crust/mantle models become more sophisticated it is important to be able to use whichever failure model is appropriate to a given part of the system. We have therefore developed a way to represent Mohr-Coulomb failure within a code which is suited to mantle convection problems coupled to large-scale crustal deformation. Our approach uses an orthotropic viscous rheology (a different viscosity for pure shear to that for simple shear) to define a prefered plane for slip to occur given the local stress field. The simple-shear viscosity and the deformation can then be iterated to ensure that the yield criterion is always satisfied. We again assume the Boussinesq approximation - neglecting any effect of dilatancy on the stress field. An additional criterion is required to ensure that deformation occurs along the plane aligned with maximum shear strain-rate rather than the perpendicular plane which is formally equivalent in any symmetric formulation. It is also important to allow strain-weakening of the material. The material should remember both the accumulated failure history and the direction of failure. We have included this capacity in a Lagrangian-Integration-point finite element code and will show a number of examples of extension and compression of a crustal block with a Mohr-Coulomb failure criterion, and comparisons between mantle convection models using the von Mises versus the Mohr-Coulomb yield criteria. The formulation itself is general and applies to 2D and 3D problems, although it is somewhat more complicated to identify the slip plane in 3D.

A simple method to simulate shrinkage-induced cracking in cement-based composites by lattice-type modeling

A new numerical procedure is proposed to investigate cracking behaviors induced by mismatch between the matrix phase and aggregates due to matrix shrinkage in cement-based composites. This kind of failure processes is simplified in this investigation as a purely spontaneous mechanical problem, therefore, one main difficulty during simulating the phenomenon lies that no explicit external load serves as the drive to propel development of this physical process. As a result, it is different from classical mechanical problems and seems hard to be solved by using directly the classical finite element method (FEM), a typical kind of "load -> medium -> response" procedures. As a solution, the actual mismatch deformation field is decomposed into two virtual fields, both of which can be obtained by the classical FEM. Then the actual response is obtained by adding together the two virtual displacement fields based on the principle of superposition. Then, critical elements are detected successively by the event-by-event technique. The micro-structure of composites is implemented by employing the generalized beam (GB) lattice model. Numerical examples are given to show the effectiveness of the method, and detailed discussions are conducted on influences of material properties.

A strain-based failure criterion for pillar stability analysis

Strain-based failure criteria have several advantages over stress-based failure criteria: they can account for elastic and inelastic strains, they utilise direct, observables effects instead of inferred effects (strain gauges vs. stress estimates), and model complete stress-strain curves including pre-peak, non-linear elasticity and post-peak strain weakening. In this study, a strain-based failure criterion derived from thermodynamic first principles utilising the concepts of continuum damage mechanics is presented. Furthermore, implementation of this failure criterion into a finite-element simulation is demonstrated and applied to the stability of underground mining coal pillars. In numerical studies, pillar strength is usually expressed in terms of critical stresses or stress-based failure criteria where scaling with pillar width and height is common. Previous publications have employed the finite-element method for pillar stability analysis using stress-based failure criterion such as Mohr-Coulomb and Hoek-Brown or stress-based scalar damage models. A novel constitutive material model, which takes into consideration anisotropy as well as elastic strain and damage as state variables has been developed and is presented in this paper. The damage threshold and its evolution are strain-controlled, and coupling of the state variables is achieved through the damage-induced degradation of the elasticity tensor. This material model is implemented into the finite-element software ABAQUS and can be applied to 3D problems. Initial results show that this new material model is capable of describing the non-linear behaviour of geomaterials commonly observed before peak strength is reached as well as post-peak strain softening. Furthermore, it is demonstrated that the model can account for directional dependency of failure behaviour (i.e. anisotropy) and has the potential to be expanded to environmental controls like temperature or moisture.

Systemic risk in dynamical networks with stochastic failure criterion

Complex non-linear interactions between banks and assets we model by two time-dependent Erdos-Renyi network models where each node, representing a bank, can invest either to a single asset (model I) or multiple assets (model II). We use a dynamical network approach to evaluate the collective financial failure -systemic risk- quantified by the fraction of active nodes. The systemic risk can be calculated over any future time period, divided into sub-periods, where within each sub-period banks may contiguously fail due to links to either i) assets or ii) other banks, controlled by two parameters, probability of internal failure p and threshold T-h ("solvency" parameter). The systemic risk decreases with the average network degree faster when all assets are equally distributed across banks than if assets are randomly distributed. The more inactive banks each bank can sustain (smaller T-h), the smaller the systemic risk -for some Th values in I we report a discontinuity in systemic risk. When contiguous spreading becomes stochastic ii) controlled by probability p(2) -a condition for the bank to be solvent (active) is stochasticthe- systemic risk decreases with decreasing p(2). We analyse the asset allocation for the U.S. banks. Copyright (C) EPLA, 2014

A coupled elastoplastic-damage constitutive model with Lode angle dependent failure criterion

A coupled elastoplastic-damage constitutive model with Lode angle dependent failure criterion for high strain and ballistic applications is presented. A Lode angle dependent function is added to the equivalent plastic strain to failure definition of the Johnson–Cook failure criterion. The weakening in the elastic law and in the Johnson–Cook-like constitutive relation implicitly introduces the Lode angle dependency in the elastoplastic behaviour. The material model is calibrated for precipitation hardened Inconel 718 nickel-base superalloy. The combination of a Lode angle dependent failure criterion with weakened constitutive equations is proven to predict fracture patterns of the mechanical tests performed and provide reliable results. Additionally, the mesh size dependency on the prediction of the fracture patterns was studied, showing that was crucial to predict such patterns

A failure criterion for fillet welds

The work constitutes a study of the strength of mild steel fillet welds subject to static loading, and the behaviour of flange welded beam-column connections under combined bending and shear. Tests are conducted on short welds in the as-welded and stress relieved conditions, and also on full-size beam-column connections. It is shown that welds under compression have a lower strength than when under tension. Failure of the fillet weld is initiated at the weld root, the important factor controlling the initiation being weld ductility. The greater the residual stress, the lower the weld ductility and ultimate strength. Thermal stress relieving increases strength by as much as 30%. Weld failure plane is rarely at the throat and varies from 0° to 45° depending upon loading condition. Failure plane average stresses are related by a circular function which is expressed in terms of externally applied forces at limit state. The tension weld of a flange-welded beam-column connection always fails before the compression weld. The shear load sharing between the welds is a complex function of elastic compression of the web, elastic/plastic deformation of the flanges, load/deformation characteristics, and the type of load application. Bearing forces between the compression flange and column face produce low level bearing stresses and frictional forces which make a negligible contribution to shear load resistance. Three modes of connection failure are possible; 'end mode', 'bending mode' and 'shear mode', with a sudden change taking place between the two latter.

A further step in the modelling of the mechanical behaviour of bagasse

A better understanding of the behaviour of prepared cane and bagasse during the crushing process is believed to be an essential prerequisite for further improvements to the crushing process. Improvements could be made, for example, in throughput, sugar extraction, and bagasse moisture. The ability to model the mechanical behaviour of bagasse as it is squeezed in a milling unit to extract juice would help identify how to improve the current process to reduce final bagasse moisture. However an adequate mechanical model for bagasse is currently not available. Previous investigations have proven with certainty that juice flow through bagasse obeys Darcy’s permeability law, that the grip of the rough surface of the grooves on the bagasse can be represented by the Mohr- Coulomb failure criterion for soils, and that the internal mechanical behaviour of the bagasse is critical state behaviour similar to that for sand and clay. Current Finite Element Models (FEM) available in commercial software have adequate permeability models. However, the same commercial software do not contain an adequate mechanical model for bagasse. Progress has been made in the last ten years towards implementing a mechanical model for bagasse in finite element software code. This paper builds on that progress and carries out a further step towards obtaining an adequate material model.

An additional step towards modelling the mechanical behaviour of sugar cane bagasse

A better understanding of the behaviour of prepared cane and bagasse, especially the ability to model the mechanical behaviour of bagasse as it is squeezed in a milling unit to extract juice, would help identify how to improve the current milling process; for example to reduce final bagasse moisture. Previous investigations have proven with certainty that juice flow through bagasse obeys Darcy’s permeability law, that the grip of the rough surface of the grooves on the bagasse can be represented by the Mohr- Coulomb failure criterion for soils, and that the internal mechanical behaviour of the bagasse can be represented by critical state behaviour similar to that of sand and clay. Current Finite Element Models (FEM) available in commercial software have adequate permeability models. However, commercial software does not contain an adequate mechanical model for bagasse. Progress has been made in the last ten years towards implementing a mechanical model for bagasse in finite element software code. This paper builds on that progress and carries out a further step towards obtaining an adequate material model. In particular, the prediction of volume change during shearing of normally consolidated final bagasse is addressed.

Towards a multi-element simulation of heavily over-consolidated bagasse using a material subroutine

A better understanding of the behaviour of prepared cane and bagasse, and the ability to model the mechanical behaviour of bagasse as it is squeezed in a milling unit to extract juice, would help identify how to improve the current process. There are opportunities to decrease bagasse moisture from a milling unit. The behaviour of bagasse in chutes is poorly understood. Previous investigations have shown that juice flow through bagasse obeys Darcy’s permeability law, that the grip of the rough surface of the grooves on the bagasse can be represented by the Mohr-Coulomb failure criterion for soils, and that the internal mechanical behaviour of the bagasse is critical state behaviour similar to that for sand and clay. Progress has been made in the last 11 years towards implementing a mechanical model for bagasse in finite element software. The objective is to be able to correctly simulate various simple mechanical loading conditions measured in the laboratory. Combining these behaviours together is thought to have a high probability of reproducing the complicated stress conditions in a milling unit. This paper reports on progress made towards modelling the fifth and final (and most challenging) of the simple loading conditions: the shearing of heavily over-consolidated bagasse, using a specific model for bagasse in a multi-element simulation.

Determining the material properties for heavily over-consolidated bagasse through parameter estimation

A better understanding of the behaviour of prepared cane and bagasse, and the ability to model the mechanical behaviour of bagasse as it is squeezed in a milling unit to extract juice, would help identify how to improve the current process. For example, there are opportunities to decrease bagasse moisture from a milling unit. Also, the behaviour of bagasse in chutes is poorly understood. Previous investigations have shown that juice flow through bagasse obeys Darcy’s permeability law, that the grip of the rough surface of the grooves on the bagasse can be represented by the Mohr-Coulomb failure criterion for soils, and that the internal mechanical behaviour of the bagasse is critical state behaviour similar to that for sand and clay. Progress has been made in the last ten years towards implementing a mechanical model for bagasse in finite element software. The objective has been to be able to simulate simple mechanical loading conditions measured in the laboratory, which, when combined together, have a high probability of reproducing the complicated stress conditions in a milling unit. This paper reports on the successful simulation of part of the fifth and final (and most challenging) loading condition, the shearing of heavily over-consolidated bagasse, and determining material property values through the use of powerful and free parameter estimation software.

Modelling of the mechanical behaviour of heavily over-consolidated bagasse

A better understanding of the behaviour of prepared cane and bagasse, and the ability to model the mechanical behaviour of bagasse as it is squeezed in a milling unit to extract juice, would help identify how to improve the current process, for example to reduce final bagasse moisture. Previous investigations have proven that juice flow through bagasse obeys Darcy’s permeability law, that the grip of the rough surface of the grooves on the bagasse can be represented by the Mohr-Coulomb failure criterion for soils, and that the internal mechanical behaviour of the bagasse is critical state behaviour similar to that for sand and clay. Current Finite Element Models (FEM) available in commercial software have adequate permeability models. However, no commercially available software seems to contain an adequate mechanical model for bagasse. The same software contains a few material models for soil and other materials, while the coding of hundreds of developed models for soil and other materials remains confidential at universities and government research centres. Progress has been made in the last ten years towards implementing a mechanical model for bagasse in finite element software code. This paper builds on that progress and carries out a further step towards obtaining an adequate material model. The fifth and final loading condition outlined previously, shearing of heavily over-consolidated bagasse, is outlined.

Uplift Resistance of Long Pipelines in the Presence of Seismic Forces

The vertical uplift resistance of long pipes buried in sands and subjected to pseudostatic seismic forces has been computed by using the lower-bound theorem of the limit analysis in conjunction with finite elements and nonlinear optimization. The soil mass is assumed to follow the Mohr-Coulomb failure criterion and an associated flow rule. The failure load is expressed in the form of a nondimensional uplift factor F-gamma. The variation of F-gamma is plotted as a function of the embedment ratio of the pipe, horizontal seismic acceleration coefficient (k(h)), and soil friction angle (phi). The magnitude of F-gamma is found to decrease continuously with an increase in the horizontal seismic acceleration coefficient. The reduction in the uplift resistance becomes quite significant, especially for greater values of embedment ratios and lower values of friction angle. The predicted uplift resistance was found to compare well with the existing results reported from the literature. (C) 2014 American Society of Civil Engineers.

Uplift Resistance of Interfering Pipelines Buried in Sand

The vertical uplift resistance of interfering pipelines buried in sands has been computed using the lower-bound limit analysis in conjunction with finite elements and nonlinear optimization. The soil mass is assumed to follow the Mohr-Coulomb failure criterion and an associated flow rule. It is specified that all the pipes fail simultaneously at the same magnitude of the failure load. For different clear spacing (S) between the pipes, the magnitude of the efficiency factor (xi(gamma)) is determined. Because of pipes' interference, with a reduction in the spacing between the pipelines, the magnitude of xi(gamma) is found to decrease continuously. The results were found to compare quite well with the available data from literature for horizontal strip anchors. (C) 2015 American Society of Civil Engineers.