[1] Estimating transpiration and water flow in trees remains a major challenge for quantifying water exchange between the biosphere and the atmosphere. We develop a finite element tree crown hydrodynamics (FETCH) model that uses porous media equations for water flow in an explicit three-dimensional branching fractal tree-crown system. It also incorporates a first-order canopy-air turbulence closure model to generate the external forcing of the system. We use FETCH to conduct sensitivity analysis of transpirational dynamics to changes in canopy structure via two scaling parameters for branch thickness and conductance. We compare our results with the equivalent parameters of the commonly used resistor and resistor-capacitor representations of tree hydraulics. We show that the apparent temporal and vertical variability in these parameters strongly depends on structure. We suggest that following empirical calibration and validation, FETCH could be used as a platform for calibrating the ''scaling laws'' between tree structure and hydrodynamics and for surface parameterization in meteorological and hydrological models.

SUMMARYWe examine a bubble-stabilized finite element method for enforcing Dirichlet constraints on embedded interfaces. By 'embedded' we refer to problems of general interest wherein the geometry of the interface is assumed independent of some underlying bulk mesh. As such, the robust imposition of Dirichlet constraints using a Lagrange multiplier field is not trivial. To focus issues, we consider a simple one-sided problem that is representative of a wide class of evolving-interface problems. The bulk field is decomposed into coarse and fine scales, giving rise to coarse-scale and fine-scale one-sided sub-problems. The fine-scale solution is approximated with bubble functions, permitting static condensation and giving rise to a stabilized form bearing strong analogy with a classical method. Importantly, the method is simple to implement, readily extends to multiple dimensions, obviates the need to specify any free stabilization parameters, and can lead to a symmetric, positive-definite system of equations. The performance of the method is then examined through several numerical examples. The accuracy of the Lagrange multiplier is compared to results obtained using a local version of the domain integral method. The variational multiscale approach proposed herein is shown to both stabilize the Lagrange multiplier and improve the accuracy of the post-processed fluxes.

Please cite this article as: Luscher, D.J., Mayeur, J.R., Mourad, H.M., Hunter, A., Kenamond, M.A., Coupling continuum dislocation transport with crystal plasticity for application to shock loading conditions AbstractWe have developed a multi-physics modeling approach that couples continuum dislocation transport, nonlinear thermoelasticity, crystal plasticity, and consistent internal stress and deformation fields to simulate the single-crystal response of materials under extreme dynamic conditions. Dislocation transport is modeled by enforcing dislocation conservation at a slip-system level through the solution of advection-diffusion equations. Nonlinear thermoelasticity provides a thermodynamically consistent equation of state to relate stress (including pressure), temperature, energy densities, and dissipation. Crystal plasticity is coupled to dislocation transport via Orowan's expression where the constitutive description makes use of recent advances in dislocation velocity theories applicable under extreme loading conditions. The configuration of geometrically necessary dislocation density gives rise to an internal stress field that can either inhibit or accentuate the flow of dislocations. An internal strain field associated with the internal stress field contributes to the kinematic decomposition of the overall deformation. The paper describes each theoretical component of the framework, key aspects of the constitutive theory, and some details of a one-dimensional implementation. Results from single-crystal copper plate impact simulations are discussed in order to highlight the role of dislocation transport and pile-up in shock loading regimes. The main conclusions of the paper reinforce the utility of the modeling approach to shock problems.

We present a continuum model for thermally induced volume transitions in stimulus-responsive hydrogels (SRHs). The framework views the transition as proceeding via the motion of a sharp interface separating swollen and collapsed phases of the underlying polymer network. In addition to bulk and interfacial force and energy balances, our model imposes an interfacial normal configurational force balance. To account for the large volume changes exhibited by SRHs during actuation, the governing equations are developed in the setting of finite-strain kinematics. The numerical approximations to the coupled thermomechanical equations are obtained with an extended finite element/level-set method. The solution strategy involves a non-standard operator split and a simplified version of the level-set update. A number of representative problems are considered to investigate the model and compare its predictions to experimental observations. In particular, we consider the thermally induced swelling of spherical and cylindrical specimens. The stability of the interface evolution is also examined.

No abstract

No abstract

SUMMARYThe level set equation is a non-linear advection equation, and standard finite-element and finitedifference strategies typically employ spatial stabilization techniques to suppress spurious oscillations in the numerical solution. We recast the level set equation in a simpler form by assuming that the level set function remains a signed distance to the front/interface being captured. As with the original level set equation, the use of an extensional velocity helps maintain this signed-distance function. For some interface-evolution problems, this approach reduces the original level set equation to an ordinary differential equation that is almost trivial to solve. Further, we find that sufficient accuracy is available through a standard Galerkin formulation without any stabilization or discontinuity-capturing terms. Several numerical experiments are conducted to assess the ability of the proposed assumed-gradient level set method to capture the correct solution, particularly in the presence of discontinuities in the extensional velocity or level-set gradient. We examine the convergence properties of the method and its performance in problems where the simplified level set equation takes the form of a Hamilton-Jacobi equation with convex/non-convex Hamiltonian. Importantly, discretizations based on structured and unstructured finite-element meshes of bilinear quadrilateral and linear triangular elements are shown to perform equally well.

This work presents a crystal plasticity modeling framework that accounts for the influence of material interfaces on the plastic behavior of the two crystals on either side of the interface. Within an interfaceaffected zone (IAZ) extending from both sides of the interface, slip system activity is presumed to be biased towards systems that permit slip transfer across the interface. The preferred slip transfer pathways are determined from the geometric alignment of the slip systems and the stress state within each crystal. The IAZ model is applied to study the plastic stability of Cu-Nb bicrystals under plane strain compression. Our results show that the additional constraints imposed through the enforcement of slip continuity across the interface leads to reduced plastic stability as compared to the case without an IAZ for several of the interfaces studied.