Peridynamics, a nonlocal extension of continuum mechanics, is unique in its ability to capture pervasive material failure. Its use in the majority of system-level analyses carried out at Sandia, however, is severely limited, due in large part to computational expense and the challenge posed by the imposition of nonlocal boundary conditions. Combined analyses in which peridynamics is em- ployed only in regions susceptible to material failure are therefore highly desirable, yet available coupling strategies have remained severely limited. This report is a summary of the Laboratory Directed Research and Development (LDRD) project "Strong Local-Nonlocal Coupling for Inte- grated Fracture Modeling," completed within the Computing and Information Sciences (CIS) In- vestment Area at Sandia National Laboratories. A number of challenges inherent to coupling local and nonlocal models are addressed. A primary result is the extension of peridynamics to facilitate a variable nonlocal length scale. This approach, termed the peridynamic partial stress, can greatly reduce the mathematical incompatibility between local and nonlocal equations through reduction of the peridynamic horizon in the vicinity of a model interface. A second result is the formulation of a blending-based coupling approach that may be applied either as the primary coupling strategy, or in combination with the peridynamic partial stress. This blending-based approach is distinct from general blending methods, such as the Arlequin approach, in that it is specific to the coupling of peridynamics and classical continuum mechanics. Facilitating the coupling of peridynamics and classical continuum mechanics has also required innovations aimed directly at peridynamic models. Specifically, the properties of peridynamic constitutive models near domain boundaries and shortcomings in available discretization strategies have been addressed. The results are a class of position-aware peridynamic constitutive laws for dramatically improved consistency at domain boundaries, and an enhancement to the meshfree discretization applied to peridynamic models that removes irregularities at the limit of the nonlocal length scale and dramatically improves conver- gence behavior. Finally, a novel approach for modeling ductile failure has been developed, moti- vated by the desire to apply coupled local-nonlocal models to a wide variety of materials, including ductile metals, which have received minimal attention in the peridynamic literature. Software im- plementation of the partial-stress coupling strategy, the position-aware peridynamic constitutive models, and the strategies for improving the convergence behavior of peridynamic models was completed within the Peridigm and Albany codes, developed at Sandia National Laboratories and made publicly available under the open-source 3-clause BSD license.
A notion of material homogeneity is proposed for peridynamic bodies with vari- able horizon but constant bulk properties. A relation is derived that scales the force state according to the position-dependent horizon while keeping the bulk properties un- changed. Using this scaling relation, if the horizon depends on position, artifacts called ghost forces may arise in a body under homogeneous deformation. These artifacts de- pend on the second derivative of horizon and can be reduced by use of a modified equilibrium equation using a new quantity called the partial stress . Bodies with piece- wise constant horizon can be modeled without ghost forces by using a technique called a splice between the regions. As a limiting case of zero horizon, both partial stress and splice techniques can be used to achieve local-nonlocal coupling. Computational examples, including dynamic fracture in a one-dimensional model with local-nonlocal coupling, illustrate the methods.
We develop and analyze an optimization-based method for the coupling of a static peri-dynamic (PD) model and a static classical elasticity model. The approach formulates the coupling as a control problem in which the states are the solutions of the PD and classical equations, the objective is to minimize their mismatch on an overlap of the PD and classical domains, and the controls are virtual volume constraints and boundary conditions applied at the local-nonlocal interface. Our numerical tests performed on three-dimensional geometries illustrate the consistency and accuracy of our method, its numerical convergence, and its applicability to realistic engineering geometries. We demonstrate the coupling strategy as a means to reduce computational expense by confining the nonlocal model to a subdomain of interest, and as a means to transmit local (e.g., traction) boundary conditions applied at a surface to a nonlocal model in the bulk of the domain.
For its advocates, corporate social responsibility (CSR) represents a powerful tool through which business and particularly multinationals can play a more direct role in global sustainable development. For its critics, however, CSR rarely goes beyond business as usual, and is often a cover for business practices with negative implications for communities and the environment. This paper explores the relationship between CSR and sustainable development in the context of mining in Namibia. Drawing upon extant literatures on the geographies of responsibility, and referencing in-country empirical case-study research, a critical relational lens is applied to consider their interaction both historically and in the present.
In recent times social entrepreneurship has proliferated globally, yet research into the phenomenon still lags behind its practice, particularly in the developing world, and especially in Sub-Saharan Africa. In this blog post, we discuss what we know, what we don’t, and what we can learn from studying social entrepreneurship in Sub-Saharan Africa. Our research: a) highlights the important role of the environment in informing social entrepreneurship and its varied manifestations globally; b) provides insights on the nature of social entrepreneurship and enterprises in Sub-Saharan Africa; and c) shows that African data can provide insights for wider understanding of social entrepreneurship.
BOOK REVIEWS Michael Hauskeller, Biotechnology and the Integrity of Life: Taking Public Fears Seriously (DAVID LITTLEWOOD) Sarah B. Pralle, Branching Out, Digging In: Environmental Advocacy and Agenda Setting (VANESSA TIMMER) Greg Kennedy, An Ontology of Trash: The Disposable and its Problematic Nature (PETER LUCAS) BOOKS RECEIVED
This paper explores a segmentation of micro and small enterprises (MSEs) in developing countries within the formal/informal economy nexus that has wide-ranging implications for the targeting of base-of-the-pyramid initiatives and entrepreneurship theory. This proposed segmentation emerges from the analysis of a sample of Kenyan MSEs utilising current and prior business models; the antecedent influences shaping the business model; barriers to entry associated with knowledge, capital and skills; the degree of innovation or imitation evident in the business model linked to the nature of opportunity recognition; and their relationship with the formal institutional business environment.
Research on the informal economy has largely focussed on supply-side issues, addressing questions like what motivates individuals to work in the informal economy and how can governments tackle this phenomenon. To date, much less attention has been given to demand-side aspects, examining issues around who purchases goods and services from the informal economy, why, and to what extent there are variations according to demographic, socio-economic and geographic dimensions. This paper addresses this imbalance by examining the purchasing of goods and services from the informal economy in South-East Europe. Firstly, this paper identifies the prevalence of such informal purchasing in South-East Europe as well as who undertakes such purchasing. Next, it examines the relative significance of cost factors, social factors and failures in the formal economy, in motivating such purchasing. Finally, it explores variability in the significance of these motivators based on individual-level factors, within and across three South-East European countries.
