The arbitrary Lagrangian-Eulerian (ALE) description in non-linear solid mechanics is nowadays standard for hypoelastic-plastic models. An extension to hyperelastic-plastic models is presented here. A fractional-step method - a common choice in ALE analysis - is employed for time-marching: every time-step is split into a Lagrangian phase, which accounts for material effects, and a convection phase, where the relative motion between the material and the finite element mesh is considered. In contrast to previous ALE formulations of hyperelasticity or hyperelastoplasticity, the deformed configuration at the beginning of the time-step, not the initial undeformed configuration, is chosen as the reference configuration. As a consequence, convecting variables are required in the description of the elastic response. This is not the case in previous formulations, where only the plastic response contains convection terms. In exchange for the extra convective terms, however, the proposed ALE approach has a major advantage: only the quality of the mesh in the spatial domain must be ensured by the ALE remeshing strategy; in previous formulations, it is also necessary to keep the distortion of the mesh in the material domain under control. Thus, the full potential of the ALE description as an adaptive technique can be exploited here. These aspects are illustrated in detail by means of three numerical examples: a necking test, a coining test and a powder compaction test.Peer ReviewedPostprint (author’s final draft

This paper presents the formulation of numerical algorithms for the solution of the closest-point projection equations that appear in typical implementations of return mapping algorithms in elastoplasticity. The main motivation behind this work is to avoid the poor global convergence properties of a straight application of a Newton scheme in the solution of these equations, the socalled Newton-CPPM. The mathematical structure behind the closest-point projection equations identified in Part I of this work delineates clearly different strategies for the successful solution of these equations. In particular, primal and dual closest-point projection algorithms are proposed, in non-augmented and augmented Lagrangian versions for the imposition of the consistency condition. The primal algorithms involve a direct solution of the original closest-point projection equations, whereas the dual schemes involve a two level structure by which the original system of equations is staggered, with the imposition of the consistency condition driving alone the iterative process. Newton schemes in combination with appropriate line search strategies are considered, resulting in the desired asymptotically quadratic local rate of convergence and the sought global convergence character of the iterative schemes. These properties, together with the computational performance of the different schemes, are evaluated through representative numerical examples involving different models of finite strain plasticity. In particular, the avoidance of the large regions of no convergence in the trial state observed in the standard Newton-CPPM is clearly illustrated.

Abstract:The Water Poverty Index ͑WPI͒ was created as an interdisciplinary indicator to assess water stress and scarcity, linking physical estimates of water availability with the socioeconomic drivers of poverty. This index has found great relevance in policy making as an effective water management tool, particularly in resources allocation and prioritization processes. Two conceptual weaknesses exist in the current index: ͑1͒ inadequate technique to combine available data and ͑2͒ poor statistical properties of the resulting composite. The purpose of this paper is to propose a suitable methodology to assess water poverty that overcomes these weaknesses. To this end, a number of combinations to create the WPI have been considered, based on indicators selection criteria, simple aggregation functions and multivariate analysis. The approach adopted has been designed for universal application at local scale. To exemplify the utilization of each alternative method, they have been piloted and implemented in the Turkana District ͑Kenya͒ as a case study. The paper concludes that the weighted multiplicative function is the most appropriate aggregation method for estimation of water poverty. It is least eclipsing and ambiguous free function, and it does not allow compensability among different variables of the index.

In this paper, numerical differentiation is applied to integrate plastic constitutive laws and to compute the corresponding consistent tangent operators. The derivatives of the constitutive equations are approximated by means of difference schemes. These derivatives are needed to achieve quadratic convergence in the integration at Gauss-point level and in the solution of the boundary value problem. Numerical differentiation is shown to be a simple, robust and competitive alternative to analytical derivatives. Quadratic convergence is maintained, provided that adequate schemes and stepsizes are chosen. This point is illustrated by means of some numerical examples.

• Engineering academics engaged SD are 'connectors' within and beyond university boundaries. • Engineering academics engaged in SD conduct interdisciplinary research activities. • HEI should explore appropriate policies and mechanisms to engage academics in SD.