A solution to transient seepage in unsaturated porous media

This paper presents a solution to seepage problems in porous media considering the complete time-dependent transition from fully saturation to partially unsaturated states and vice-versa; therefore capturing the evolution of the free surface (region with zero liquid pressure). A simple and efficient method to implement the seepage face boundary condition for finite element solutions is proposed. The method is based on an analogy to unilateral constraints in Plasticity and, in essence, adds some extra unknowns to the finite elements with boundaries near the seepage face. The free surface is thus automatically predicted. The resulting enriched elements can also account for ponding or infiltration at the external surface. The solution is accomplished by considering the theory of porous media with slightly compressible liquids. The formulation can easily accommodate liquid retention models with hysteresis. Verification examples are presented in addition to simulations of drainage and infiltration illustrating the capabilities of the proposed solution

Efficient isogeometric shell element with through-thickness stretch: application to incremental sheet forming

An isogeometric shell element with through-thickness stretch is applied to a two-point incremental forming problem. The shell element supports full three-dimensional constitutive laws and therefore does not make the plane stress assumption. An anisotropic material model is implemented to account for the sheet rolling direction. Automatically adjusting penalty stiffness is proposed for modeling the contact between the stylus tool and the sheet, whereas the die contact algorithm uses traditional constant penalty stiffness. A comparison is made between experimental results as well as results from a conventional shell formulation

FORM reliability analysis using a parallel evolutionary algorithm

This paper presents a parallel evolutionary algorithm to solve reliability problems with accuracy and repeatability of results. The last characteristic is usually overlooked; however, it is critical to the reliability of the calculation method itself. Note that evolutionary algorithms are stochastic processes and may not always generate identical results. The optimisation problem resulting from the first order reliability method is considered with an implicit state function that can include a call to a finite element analysis (FEA). A strategy to handle failures from the transformation of random variables or from the finite element call during the evolution process is explained in detail. Several benchmark tests are studied, including some involving bounded random variables that introduce strong non-linearities in the mapping to standard Gaussian space. In addition, the solutions of 2D and 3D frame problems using the finite element method illustrate the capabilities of the algorithm including the convenience of the algorithm in handling discrete limit state functions. Finally, the ability to obtain similar results after many runs is demonstrated

The subloading isotropic plasticity as a variable modulus model

The subloading concept is an extension of mathematical plasticity which defines an internal surface to the conventional yield surface. It is indeed a versatile approach, especially for the modelling of soils under quasi-static cycles with smooth transitions from pure elastic to elastoplastic behaviour. For the case of isotropic hardening models, this paper demonstrates that the subloading isotropic plasticity is equivalent to a variable modulus approach and therefore a simpler and equivalent methodology can be adopted instead. In addition to demonstrating this equivalence, an alternative formulation that was presented elsewhere and that uses only one surface is briefly discussed. The alternative formulation can then be easily applied to popular models for soils such as the Cam clay model. Finally, some numerical predictions are presented in order to illustrate the capabilities of the subloading isotropic plasticity and the corresponding variable modulus approach

A consistent u-p formulation for porous media with hysteresis

This paper presents a continuum formulation based on the theory of porous media for the mechanics of liquid unsaturated porous media. The hysteresis of the liquid retention model is carefully modelled, including the derivation of the corresponding consistent tangent moduli. The quadratic convergence of Newton's method for solving the highly nonlinear system with an implicit finite element code is demonstrated. A u-p formulation is proposed where the time discretisation is carried out prior to the space discretisation. In this way, the derivation of all consistent moduli is fairly straightforward. Time integration is approximated with the Theta and Newmark's methods, and hence the fully coupled nonlinear dynamics of porous media is considered. It is shown that the liquid retention model requires also the consistent second-order derivative for quadratic convergence. Some predictive simulations are presented illustrating the capabilities of the formulation, in particular to the modelling of complex porous media behaviour

Isogeometric thickness stretchable shell: efficient formulation for nonlinear dynamic problems

An isogeometric shell element with through-thickness stretch is introduced and applied to quasi-static and dynamic problems. The shell element supports full three-dimensional constitutive laws, ie, the plane stress assumption is not required. An updated Lagrangian rate formulation is adopted, and biquadratic spline-based interpolation functions are used for in-plane interpolation. The concept of fiber mass scaling is proposed to lower the highest eigenfrequencies to improve the performance of the formulation. Clamped and unclamped knot vectors are compared, and the advantages of using unclamped knot vectors are demonstrated. The shell element is validated using several benchmark tests, which indicate good performance of the proposed formulation

Quadrature rules for isogeometric shell formulations: study using a real-world application about metal forming

This paper studies quadrature rules for simulating large deformations of shells using isogeometric analysis. Several recently proposed rules and their effects on a real-world application known as incremental sheet forming are investigated. It is observed that, when tackling real-world applications, unexpected problems arise and, therefore, theoretical studies only with manufactured solutions are not enough for a complete verification of a method. The chosen application reveals problems with certain quadratures and that some simple stabilization strategies cannot completely suppress hourglass modes. Additionally, the effects of quadrature rules on the total computational costs are demonstrated and the influence of the maximum stable time step is assessed using a highly demanding simulation

Extended Barcelona Basic Model for unsaturated soils under cyclic loadings

The Barcelona Basic Model (BBM) is an extension of the Cam clay model that has become popular in applications involving unsaturated soils and, in particular, in simulations using the finite element method. Partially saturated soils can be loaded in different ways, for instance, mechanically and/or hydraulically. In addition, cycles of loading and unloading can be applied. The present work introduces a modification of the BBM in order to simplify its computer implementation and also to allow the simulation of elastoplastic behaviour during cycles of both mechanical and hydraulic loading. A unique smooth yield surface is introduced and a two-yield surfaces concept is applied in order to represent the cyclic behaviour. The influence of the intermediate principal stress on the strength is also accounted for. Finally, the numerical integration (stress update) of the extended BBM is briefly discussed. (C) 2011 Elsevier Ltd. All rights reserved

Automatic calibration of soil–water characteristic curves using genetic algorithms

An automatic technique for the determination of the coefficients of models for soil-water characteristic curves (SWCC) or water retention curves (WRC) is presented. The technique is based on optimisation using genetic algorithms, in which the error between predictions and experimental data is minimised by varying the model parameters. The method is powerful and reasonably efficient in finding the best parameters. Four models are analysed including one accounting for hysteresis behaviour. Details of a simple genetic algorithm (SGA) and its complete application are explained. To account for the hysteresis of the SWCC, the models are programmed in a rate form, in which numerical integration is employed to advance the state variables. One advantage of the optimisation presented is that the best curves averaging both the drying and wetting paths are obtained when hysteresis is present