Eroding permafrost coasts are likely indicators and integrators of changes in the Arctic System as they are susceptible to the combined effects of declining sea ice extent, increases in open water duration, more frequent and impactful storms, sea-level rise, and warming permafrost. However, few observation sites in the Arctic have yet to link decadal-scale erosion rates with changing environmental conditions due to temporal data gaps. This study increases the temporal fidelity of coastal permafrost bluff observations using near-annual high spatial resolution (<1 m) satellite imagery acquired between 2008-2017 for a 9 km segment of coastline at Drew Point, Beaufort Sea coast, Alaska. Our results show that mean annual erosion for the 2007-2016 decade was 17.2 m yr −1 , which is 2.5 times faster than historic rates, indicating that bluff erosion at this site is likely responding to changes in the Arctic System. In spite of a sustained increase in decadal-scale mean annual erosion rates, mean open water season erosion varied from 6.7 m yr −1 in 2010 to more than 22.0 m yr −1 in 2007, 2012, and 2016. This variability provided a range of coastal responses through which we explored the different roles of potential environmental drivers. The lack of significant correlations between mean open water season erosion and the environmental variables compiled in this study indicates that we may not be adequately capturing the environmental forcing factors, that the system is conditioned by long-term transient effects or extreme weather events rather than annual variability, or that other not yet considered factors may be responsible for the increased erosion occurring at Drew Point. Our results highlight an increase in erosion at Drew Point in the 21st century as well as the complexities associated with unraveling the factors responsible for changing coastal permafrost bluffs in the Arctic.

No abstract

This paper presents a variational formulation of viscoplastic constitutive updates for porous elastoplastic materials. The material model combines von Mises plasticity with volumetric plastic expansion as induced, e.g., by the growth of voids and defects in metals. The finite deformation theory is based on the multiplicative decomposition of the deformation gradient and an internal variable formulation of continuum thermodynamics. By the use of logarithmic and exponential mappings the stress update algorithms are extended from small strains to finite deformations. Thus the time-discretized version of the porous-viscoplastic constitutive updates is described in a fully variational manner. The range of behavior predicted by the model and the performance of the variational update are demonstrated by its application to the forced expansion and fragmentation of U-6%Nb rings.

A constitutive model of bulk metallic glass (BMG) plasticity is developed which accounts for finitedeformation kinematics, the kinetics of free volume, strain hardening, thermal softening, rate-dependency and non-Newtonian viscosity. The model has been validated against uniaxial compression test data; and against plate bending experiments. The model captures accurately salient aspects of the material behavior including: the viscosity of Vitreloy 1 as a function of temperature and strain rate; the temperature and strain-rate dependence of the equilibrium free-volume concentration; the uniaxial compression stress-strain curves as a function of strain rate and temperature; and the dependence of shear-band spacing on plate thickness. Calculations suggest that, under adiabatic conditions, strain softening and localization in BMGs is due both to an increase in free volume and to the rise in temperature within the band. The calculations also suggest that the shear band spacing in plate-bending specimens is controlled by the stress relaxation in the vicinity of the shear bands.

We propose a variational procedure for the recovery of internal variables, in effect extending them from integration points to the entire domain. The objective is to perform the recovery with minimum error and at the same time guarantee that the internal variables remain in their admissible spaces. The minimization of the error is achieved by a three-field finite element formulation. The fields in the formulation are the deformation mapping, the target or mapped internal variables and a Lagrange multiplier that enforces the equality between the source and target internal variables. This formulation leads to an L 2 projection that minimizes the distance between the source and target internal variables as measured in the L 2 norm of the internal variable space. To ensure that the target internal variables remain in their original space, their interpolation is performed by recourse to Lie groups, which allows for direct polynomial interpolation of the corresponding Lie algebras by means of the logarithmic map. Once the Lie algebras are interpolated, the mapped variables are recovered by the exponential map, thus guaranteeing that they remain in the appropriate space.

We advance the Schwarz alternating method as a means for concurrent multiscale coupling in finite deformation solid mechanics. We prove that the Schwarz alternating method converges to the solution of the problem on the entire domain and that the convergence rate is geometric provided that each of the subdomain problems is well-posed, i.e. their corresponding energy density functions are quasi-convex. It is shown that the use of a Newton-type method for the solution of the resultant nonlinear system leads to two kinds of block linearized systems, depending on the treatment of the Dirichlet boundary conditions. The first kind is a symmetric block-diagonal linear system in which each diagonal block is the tangent stiffness of each subdomain, i.e. the off-diagonal blocks are all zero and the coupling terms appear only on the right-hand side. The second kind is a nonsymmetric block system with off-diagonal coupling terms. Several variants of the Schwarz alternating method are proposed for the first kind of linear system, including one in which the Schwarz alternating iterations and the Newton iterations are combined into a single scheme. This version of the method is particularly attractive, as it lends itself to a minimally intrusive implementation into existing finite element codes. Finally, we demonstrate the performance of the proposed variants of the Schwarz alternating method on several one-dimensional and three-dimensional examples.

No abstract

Albany is a multiphysics code constructed by assembling a set of reusable, general components. It is an implicit, unstructured grid finite element code that hosts a set of advanced features that are readily combined within a single analysis run. Albany uses template-based generic programming methods to provide extensibility and flexibility; it employs a generic residual evaluation interface to support the easy addition and modification of physics. This interface is coupled to powerful automatic differentiation utilities that are used to implement efficient nonlinear solvers and preconditioners, and also to enable sensitivity analysis and embedded uncertainty quantification capabilities as part of the forward solve. The flexible application programming interfaces in Albany couple to two different adaptive mesh libraries; it internally employs generic integration machinery that supports tetrahedral, hexahedral, and hybrid meshes of user specified order. We present the overall design of Albany, and focus on the specifics of the integration of many of its advanced features. As Albany and the components that form it are openly available on the internet, it is our goal that the reader might find some of the design concepts useful in their own work. Albany results in a code that enables the rapid development of parallel, numerically efficient multiphysics software tools. In discussing the features and details of the integration of many of the components involved, we show the reader the wide variety of solution components that are available and what is possible when they are combined within a simulation capability.