Contingent sensitivity to configuration in a nonlinear evolution system

A trans-scopic sensitivity of macroscopic failure to slight differentiation in the meso-scopic structure of a system with nonlinear evolution is reported. A periodical chain following a non-local load-sharing evolution was applied as a propotype in failure study. The results demonstrate that there is a transition region composed of globally stable (GS) and evolution induced catastrophic (EIC) modes. That is different from a critical threshold as predicted by percolation and renormalization group theories. Moreover, the EIC mode shows a distinctive sample specific behaviour. For instance, some neighbouring initial states may evolve into completely different final states, though different initial states can evolve into the same final states. As an example, a marginal configuration of EIC mode, a quasi-Fibonacci skeleton, is constructed.

Evolution induced catastrophe in a nonlinear dynamical model of material failure

In order to study the failure of disordered materials, the ensemble evolution of a nonlinear chain model was examined by using a stochastic slice sampling method. The following results were obtained. (1) Sample-specific behavior, i.e. evolutions are different from sample to sample in some cases under the same macroscopic conditions, is observed for various load-sharing rules except in the globally mean field theory. The evolution according to the cluster load-sharing rule, which reflects the interaction between broken clusters, cannot be predicted by a simple criterion from the initial damage pattern and even then is most complicated. (2) A binary failure probability, its transitional region, where globally stable (GS) modes and evolution-induced catastrophic (EIC) modes coexist, and the corresponding scaling laws are fundamental to the failure. There is a sensitive zone in the vicinity of the boundary between the GS and EIC regions in phase space, where a slight stochastic increment in damage can trigger a radical transition from GS to EIC. (3) The distribution of strength is obtained from the binary failure probability. This, like sample-specificity, originates from a trans-scale sensitivity linking meso-scopic and macroscopic phenomena. (4) Strong fluctuations in stress distribution different from that of GS modes may be assumed as a precursor of evolution-induced catastrophe (EIC).

Evaluación de rendimiento en el cultivo de soja aplicando fosfitos y micronutrientes

Resumen: Lo que se pretende reflejar en este trabajo es la importancia del uso de fosfitos y micronutrientes en el cultivo de soja. El cultivo de esta oleaginosa se ha ido incrementando a lo largo de los últimos años de la mano de la siembra directa, de la genética, del paquete tecnológico para su implantación y protección y del manejo realizado por los profesionales del agro. Este crecimiento en superficie en detrimento de los demás cultivos extensivos que deberían formar parte de la rotación, hizo de la oleaginosa en varias zonas un monocultivo. Esto sumado a la falta de rotación de activos fue generando problemas dentro de los cuales podemos citar: malezas de difícil control, alta presión de enfermedades y plagas. La fertilización, en la generalidad de los casos, está por debajo de los requerimientos por tonelada lograda, generando extracción de macro y micro elementos y agotando los niveles de estos mismos en el perfil edáfico. El aporte de macronutrientes está dado principalmente por fósforo (no en todas las zonas). Asimismo, en algunas zonas dependiendo las deficiencias agregan potasio, azufre y calcio. Así todo se fertiliza por debajo de los rindes objetivos perseguidos, lo cual se comprende que cuando los cultivos superan los mismos, se está haciendo una extracción mayor del sistema suelo que los aportes generados. Lo ideal es realizar un muestreo de cada lote y ambiente, verificar los niveles de nutrientes disponibles y fertilizar pensado en contemplar el rinde perseguido y entregar al sistema suelo un poco más, de manera de hacer una producción no solo rentable en el corto plazo sino sustentable en el tiempo, cuidando el capital suelo. Los macro y meso nutrientes son aportados vía fertilización de base o fondo y la manera más eficiente de aportar los micro elementos, es vía fertilización foliar. Los fosfitos son desde el punto de vista sanitario, la herramienta ideal y complementaria de los fungicidas. Son derivados del ácido fosforoso y tienen dos formas de acción contra los hongos fitopatógenos. Una forma indirecta, aumentando el nivel de defensas de las plantas o Fitoalexinas, impidiendo que las esporas germinen en tejido susceptible. Y una acción directa como fungicidas contra los pseudohongos u Oomicetes. Recordar que los triazoles son una excelente herramienta para controlar hongos verdaderos (Ascomicetes, Basidiomicetes y Deuteromicetes) al igual que las estrobirulinas, pero ambos activos no son específicos para Oomicetes. Generalmente, los fosfitos van combinados con diferentes cationes, que a su vez le confieren diferentes modos de actuar, por ejemplo el fosfito de cobre, actúa desde el punto de vista sanitario elevando las defensas y además presenta el catión cobre como elemento fungistático y bactericida. En el mercado existen diferentes tipos de fosfitos y formas de acción según catión acompañante. Hay fosfitos de Cu, Al, K, Mn, Ca, ect. Uno de los puntos más importantes de los fosfitos es que se translocan vía xilema y floema, llegando rápidamente a los diferentes sitios de la planta. Los fungicidas a diferencia de los fosfitos no pueden realizar la misma labor. Los fungicidas protegen al follaje tratado, pero no al nuevo emergente y el movimiento de los activos se da desde donde impacta la gota asperjada en sentido ascendente, ósea acrópeto, mientras que los fosfitos al recorrer toda la planta realizan una protección integral de la misma. Además, los fosfitos, presentan efecto sinérgico con los fungicidas potenciando la acción de estos. Colaboran en el engrosamiento de tejidos de raíz y tallo, fortaleciéndolos contra el ataque de patógenos. Son de rápida absorción e impactan positivamente en la formación de destinos, como flores y frutos, y fuentes de reservas como raíz. No disponen de valor nutricional para los cultivos extensivos anuales, ya que presentan un tiempo de degradación que excede al desarrollo de estos mismos. Este trabajo, se desarrolla implementando el diseño completamente aleatorio, en el cual la variable respuesta (rendimiento) puede depender de la influencia de un único factor (aplicación de fitoestimulantes), de forma que el resto de las causas de variación se engloban en el error experimental. Se compara los tratamientos contra el testigo, y se hace análisis de la variancia con un nivel de significación del 5%. Dentro de la variable respuesta se analiza el rendimiento en kg/ha. Teniendo en cuenta para este análisis los siguientes datos: 1) Número de granos 2) Peso de 1000 granos Este ensayo consta de cuatro tratamientos y tres repeticiones en un mismo estado fenológico (V10 R2) del cultivo.

Threshold diversity and trans-scales sensitivity in a finite nonlinear evolution model of materials failure

We present a slice-sampling method and study the ensemble evolution of a large finite nonlinear system in order to model materials failure. There is a transitional region of failure probability. Its size effect is expressed by a slowly decaying scaling law. In a meso-macroscopic range (similar to 10(5)) in realistic failure, the diversity cannot be ignored. Sensitivity to mesoscopic details governs the phenomena. (C) 1997 Published by Elsevier Science B.V.

PICES Press, Vol. 12, No. 2, July 2004

The future of PICES [pdf, 1.7 MB] Paris by day - Symposium on "Quantative ecosystem indicators in fisheries management" [pdf, 0.2 MB] The Bering Sea: Current status and recent events [pdf, 0.4 MB] The state of the western North Pacific in the second half of 2003 [pdf, 0.7 MB] The state of the eastern North Pacific entering spring 2004 [pdf, 0.4 MB] PICES-IFEP Workshop on "In-situ iron enrichment experiments in the eastern and western subarctic Pacific" [pdf, 1.4 MB] Canadian SOLAS/PICES-IFEP session on "Response of the upper ocean to meso-scale iron enrichment" [pdf, 0.3 MB] Fisheries and ecosystem responses to recent regime shifts [pdf, 0.8 MB] PICES Interns [pdf, 0.8 MB] Did a regime shift occur in 1998 around Japan?- Highlights from a symposium addressing this question [pdf, 0.8 MB] The Global Ocean Carbon Observing System - Connecting national programs and regional networks [pdf, 1.7 MB] The North Pacific Ecosystem Metadatabase [pdf, 1.2 MB] International GLOBEC Symposium on "Climate variability and Sub-Arctic marine ecosystems" [pdf, 0.2 MB] PICES Calendar [pdf, 0.2 MB] PICES/GLOBEC Symposium on "Climate variability and ecosystem impacts on the North pacific: A basin-scale synthesis" [pdf, 0.2 MB]

“Deborah Numbers”, Coupling Multiple Space and Time Scales and Governing Damage Evolution to Failure

Two different spatial levels are involved concerning damage accumulation to eventual failure. nucleation and growth rates of microdamage nN* and V*. It is found that the trans-scale length ratio c*/L does not directly affect the process. Instead, two independent dimensionless numbers: the trans-scale one * * ( V*)including the * **5 * N c V including mesoscopic parameters only, play the key role in the process of damage accumulation to failure. The above implies that there are three time scales involved in the process: the macroscopic imposed time scale tim = /a and two meso-scopic time scales, nucleation and growth of damage, (* *4) N N t =1 n c and tV=c*/V*. Clearly, the dimensionless number De*=tV/tim refers to the ratio of microdamage growth time scale over the macroscopically imposed time scale. So, analogous to the definition of Deborah number as the ratio of relaxation time over external one in rheology. Let De be the imposed Deborah number while De represents the competition and coupling between the microdamage growth and the macroscopically imposed wave loading. In stress-wave induced tensile failure (spallation) De* < 1, this means that microdamage has enough time to grow during the macroscopic wave loading. Thus, the microdamage growth appears to be the predominate mechanism governing the failure. Moreover, the dimensionless number D* = tV/tN characterizes the ratio of two intrinsic mesoscopic time scales: growth over nucleation. Similarly let D be the “intrinsic Deborah number”. Both time scales are relevant to intrinsic relaxation rather than imposed one. Furthermore, the intrinsic Deborah number D* implies a certain characteristic damage. In particular, it is derived that D* is a proper indicator of macroscopic critical damage to damage localization, like D* ∼ (10–3~10–2) in spallation. More importantly, we found that this small intrinsic Deborah number D* indicates the energy partition of microdamage dissipation over bulk plastic work. This explains why spallation can not be formulated by macroscopic energy criterion and must be treated by multi-scale analysis.

Mechanics of metallic foams: A fractal approach

A fractal approach was proposed to investigate the meso structures and size effect of metallic foams: For a series At foams of different relative densities, the information dimension method was applied to measure meso structures. The generalized sierpinski carpet was introduced to map the meso structures of the foam according to specific dimension. The results show that the fractal-based model can not only reveal the variation of yield strength with specimen size, but also bridge the meso structures and mechanical proper-ties of Al foams directly. Key words: metallic foams; fractal; size effect; meso structures

Distribution and sighting frequency of reef fishes in the Florida Keys National Marine Sanctuary

This study analyzed species richness, distribution, and sighting frequency of selected reef fishes to describe species assemblage composition, abundance, and spatial distribution patterns among sites and regions (Upper Keys, Middle Keys, Lower Keys, and Dry Tortugas) within the Florida Keys National Marine Sanctuary (FKNMS) barrier reef ecosystem. Data were obtained from the Reef Environmental Education Foundation (REEF) Fish Survey Project, a volunteer fish-monitoring program. A total of 4,324 visual fish surveys conducted at 112 sites throughout the FKNMS were used in these analyses. The data set contained sighting information on 341 fish species comprising 68 families. Species richness was generally highest in the Upper Keys sites (maximum was 220 species at Molasses Reef) and lowest in the Dry Tortugas sites. Encounter rates differed among regions, with the Dry Tortugas having the highest rate, potentially a result of differences in the evenness in fishes and the lower diversity of habitat types in the Dry Tortugas region. Geographic coverage maps were developed for 29 frequently observed species. Fourteen of these species showed significant regional variation in mean sighting frequency (%SF). Six species had significantly lower mean %SF and eight species had significantly higher mean %SF in the Dry Tortugas compared with other regions. Hierarchical clustering based on species composition (presence-absence) and species % SF revealed interesting patterns of similarities among sites that varied across spatial scales. Results presented here indicate that phenomena affecting reef fish composition in the FKNMS operate at multiple spatial scales, including a biogeographic scale that defines the character of the region as a whole, a reef scale (~50-100 km) that include meso-scale physical oceanographic processes and regional variation in reef structure and associated reef habitats, and a local scale that includes level of protection, cross-shelf location and a suite of physical characteristics of a given reef. It is likely that at both regional and local scales, species habitat requirements strongly influence the patterns revealed in this study, and are particularly limiting for species that are less frequently observed in the Dry Tortugas. The results of this report serve as a benchmark for the current status of the reef fishes in the FKNMS. In addition, these data provide the basis for analyses on reserve effects and the biogeographic coupling of benthic habitats and fish assemblages that are currently underway. (PDF contains 61 pages.)

基于分形的泡沫金属细观结构与尺寸效应研究

提出采用分形理论对泡沫金属的细现结构及尺寸效应进行研究的方法.针对一系列具有不同相对密度和细观结构的泡沫铝,证明了其细观结构在一定尺度内符合分形特征,比较了小岛分维、计盒分维和信息分维等算法对泡沫金属分形表征的适用性,分析了细观结构特征对分维的影响.结合推广的sierpinski垫片模型研究了泡沫铝的屈服强度与分维的联系,建立了泡沫铝屈服强度的尺寸效应模型.研究结果表明,由于引入了表征细现结构特征的分形维数,该模型除能表征屈服强度随试样尺寸的变化规律外,还在一定程度上直接反映了泡沫金属细观结构特征对力学性能的影响.

Iso-specific Ziegler-Natta polymerization of α-olefins with a single-component organoyttrium catalyst

The synthesis of a sterically tailored ligand array (M)_2((C_5H_2-2-Si(CH_3)_3-4-C(CH_3)_3)S_2i(CH_3)_2]("M_2Bp") (M = Li, 16; K, 19) is described. Transmetallation of Li_2Bp with YCl_3(THF)_3 affords exclusively the C_2 symmetric product rac-[BpY(µ_2-Cl)_2Li(THF)_2], 20. A X-ray crystal structure of 20 has been determined; triclinic, P1, a= 13.110 (8), b = 17.163 (15), c = 20.623 (14) Å, α = 104.02 (7), β = 99.38 (5), γ = 100.24 (6)° , Z = 4, R = 0.056. Transmetallation of K_2Bp with YCl_3(THF)_3 affords the halide free complex rac-BpYCl, 23. The corresponding rac-BpLaCl, 28, is prepared in an anlogous manner. In all cases the achiral meso isomer is not obtained since only for the racemic isomers are the unfavorable steric interactions between the Si(CH3)_3 groups in the narrow portion of the [Cp-M'-Cp] wedge avoided. Alkylation of 20 or 23 with LiCH(Si(CH_3)_3)_2 affords rac-BpYCH(Si(CH_3)_3)_2, 26 in good yield. Alkylation of 28 with LiCH(Si(CH_3)_3)_2 affords rac-BpLaCH(Si(CH_3)_3)_2 29. Hydrogenation of 26 cleanly affords the bridging hydride species [BpY(µ_2-H)]_2, 27, as the homochiral (R,R) and (S,S) dimeric pairs. 26 is an efficient initiator for the polymerization of ethylene to high molecular weight linear polyethylene. 27 catalyzes the polymerization of propylene (25% v/v in methylcyclohexane) and neat samples of 1-butene, 1-pentene, 1-hexene to moderately high molecular weight polymers: polypropylene (M_n = 4,200, PDI 2.32, T_m 157 °C); poly-1-butene (M_n = 8,500, PDI 3.44, T_m 105 °C); poly-1-pentene (M_n = 20,000, PDI 1.99, T_m 73 °C); poly-1-hexene (M_n = 24,000, PDI 1.75, T_m < 25 °C). ^(13)C NMR spectra at the pentad analysis level indicates that the degree of isotacticity is 99% mmmm for all polymer samples. 27 is the first single component iso-specific α-olefin polymerization catalyst. The presumed origins of the high isospecificity are presented.

Interplay of martensitic phase transformation and plastic slip in polycrystals

Inspired by key experimental and analytical results regarding Shape Memory Alloys (SMAs), we propose a modelling framework to explore the interplay between martensitic phase transformations and plastic slip in polycrystalline materials, with an eye towards computational efficiency. The resulting framework uses a convexified potential for the internal energy density to capture the stored energy associated with transformation at the meso-scale, and introduces kinetic potentials to govern the evolution of transformation and plastic slip. The framework is novel in the way it treats plasticity on par with transformation.

We implement the framework in the setting of anti-plane shear, using a staggered implicit/explict update: we first use a Fast-Fourier Transform (FFT) solver based on an Augmented Lagrangian formulation to implicitly solve for the full-field displacements of a simulated polycrystal, then explicitly update the volume fraction of martensite and plastic slip using their respective stick-slip type kinetic laws. We observe that, even in this simple setting with an idealized material comprising four martensitic variants and four slip systems, the model recovers a rich variety of SMA type behaviors. We use this model to gain insight into the isothermal behavior of stress-stabilized martensite, looking at the effects of the relative plastic yield strength, the memory of deformation history under non-proportional loading, and several others.

We extend the framework to the generalized 3-D setting, for which the convexified potential is a lower bound on the actual internal energy, and show that the fully implicit discrete time formulation of the framework is governed by a variational principle for mechanical equilibrium. We further propose an extension of the method to finite deformations via an exponential mapping. We implement the generalized framework using an existing Optimal Transport Mesh-free (OTM) solver. We then model the $\alpha$--$\gamma$ and $\alpha$--$\varepsilon$ transformations in pure iron, with an initial attempt in the latter to account for twinning in the parent phase. We demonstrate the scalability of the framework to large scale computing by simulating Taylor impact experiments, observing nearly linear (ideal) speed-up through 256 MPI tasks. Finally, we present preliminary results of a simulated Split-Hopkinson Pressure Bar (SHPB) experiment using the $\alpha$--$\varepsilon$ model.

Studies directed toward the synthesis of palau'amine and axinellamines A-D

The use of spiro [2.4]hepta-4,6-diene-1-methanol 7 as a general precursor for the synthesis of highly functionalized cyclopentyl rings is described. Diene 7 was converted to its silyl protected 4-nitrile derivative 24 in 46% overall yield. The cyclopropyl ring of 24 reacted with soft carbanionic nucleophiles to give ring opened homo-conjugate addition products 25a-h in 76-97% yield without loss of optical purity. The addition products could be further manipulated by selective mono-hydrogenation to give 1,2 substituted cyclopentenes 26a-e in 85-96% yield.

Diene 7 was used as a starting material for studies directed toward the synthesis of the stereochemically dense chloro-cyclopentyl core of palau'amine 1. Two advanced intermediates 50 and 72 were synthesized. Attempts to effect intramolecular chlorine transfer with 50 were unsuccessful. Attempted intramolecular chlorine transfer with 72 led, instead, to an oxygenated species resulting from oxygen radical trapping.

The enantioselective synthesis of the stereochemically dense chloro-cyclopenty l core of axinellamines A-D 2-5 starting from 7 is also described. The core is synthesized in 4.6% yield over 24 steps. Nakamura's radical dehalogenative hydroxylation is applied for the first time to a cyclopropyl carbonyl iodide to give the ring-opened product in 86% yield. Bolm's meso-anhydride desymmetrization is used to introduce asymmetry in a norbornene intermediate. The final step is a diastereoselective intermolecular chlorination using Barton's methodology to achieve chlorine transfer in 76% yield.

Model studies of Ziegler-Natta olefin polymerization using group 3 and group 4 metallocenes

Evidence for the stereochemical isomerization of a variety of ansa metallocene compounds is presented. For the scandocene allyl derivatives described here, we have established that the process is promoted by a variety of salts in both ether and hydrocarbon solvents and is not accelerated by light. A plausible mechanism based on an earlier proposal by Marks, et al., is offered as an explanation of this process. It involves coordination of anions and/or donor solvents to the metal center with cation assistance to encourage metalcyclopentadienyl bond heterolysis, rotation about the Si-Cp bond of the detached cyclopentadienide and recoordination of the opposite face. Our observations in some cases of thermodynamic racemic:meso ratios under the reaction conditions commonly used for the synthesis of the metallocene chlorides suggests that the interchange is faster than metallation, such that the composition of the reaction mixture is determined by thermodynamic, not kinetic, control in these cases.

Two new ansa-scandocene alkenyl compounds react with olefins resulting in the formation of η³-allyl complexes. Kinetics and labeling experiments indicate a tuck-in intermediate on the reaction pathway; in this intermediate the metal is bound to the carbon adjacent to the silyllinker in the rear of the metallocene wedge. In contrast, reaction of permethylscandocene alkenyl compounds with olefins results, almost exclusively, in vinylic C-H bond activation. It is proposed that relieving transition state steric interactions between the cyclopentadienyl rings and the olefin by either linking the rings together or using a larger lanthanide metal may allow for olefin coordination, stabilizing the transition state for allylic σ-bond metathesis.

A selectively isotopically labeled propylene, CH₂CD(¹³CH₃), was synthesized and its polymerization was carried out at low concentration in toluene solution using isospecific metallocene catalysts. Analysis of the NMR spectra (¹³C, ¹H, and ²H) of the resultant polymers revealed that the production of stereoerrors through chain epimerization proceeds exclusively by the tertiaryalkyl mechanism. Additionally, enantiofacial inversion of the terminally unsaturated polymer chain occurs by a non-dissociative process. The implications of these results on the mechanism of olefin polymerization with these catalysts is discussed.

Extracting material response from simple mechanical tests on hardening-softening-hardening viscoplastic solids

Compliant foams are usually characterized by a wide range of desirable mechanical properties. These properties include viscoelasticity at different temperatures, energy absorption, recoverability under cyclic loading, impact resistance, and thermal, electrical, acoustic and radiation-resistance. Some foams contain nano-sized features and are used in small-scale devices. This implies that the characteristic dimensions of foams span multiple length scales, rendering modeling their mechanical properties difficult. Continuum mechanics-based models capture some salient experimental features like the linear elastic regime, followed by non-linear plateau stress regime. However, they lack mesostructural physical details. This makes them incapable of accurately predicting local peaks in stress and strain distributions, which significantly affect the deformation paths. Atomistic methods are capable of capturing the physical origins of deformation at smaller scales, but suffer from impractical computational intensity. Capturing deformation at the so-called meso-scale, which is capable of describing the phenomenon at a continuum level, but with some physical insights, requires developing new theoretical approaches.

A fundamental question that motivates the modeling of foams is ‘how to extract the intrinsic material response from simple mechanical test data, such as stress vs. strain response?’ A 3D model was developed to simulate the mechanical response of foam-type materials. The novelty of this model includes unique features such as the hardening-softening-hardening material response, strain rate-dependence, and plastically compressible solids with plastic non-normality. Suggestive links from atomistic simulations of foams were borrowed to formulate a physically informed hardening material input function. Motivated by a model that qualitatively captured the response of foam-type vertically aligned carbon nanotube (VACNT) pillars under uniaxial compression [2011,“Analysis of Uniaxial Compression of Vertically Aligned Carbon Nanotubes,” J. Mech.Phys. Solids, 59, pp. 2227–2237, Erratum 60, 1753–1756 (2012)], the property space exploration was advanced to three types of simple mechanical tests: 1) uniaxial compression, 2) uniaxial tension, and 3) nanoindentation with a conical and a flat-punch tip. The simulations attempt to explain some of the salient features in experimental data, like
1) The initial linear elastic response.
2) One or more nonlinear instabilities, yielding, and hardening.

The model-inherent relationships between the material properties and the overall stress-strain behavior were validated against the available experimental data. The material properties include the gradient in stiffness along the height, plastic and elastic compressibility, and hardening. Each of these tests was evaluated in terms of their efficiency in extracting material properties. The uniaxial simulation results proved to be a combination of structural and material influences. Out of all deformation paths, flat-punch indentation proved to be superior since it is the most sensitive in capturing the material properties.

Strength, Deformation and Fracture in Metallic Nanostructures

An understanding of the mechanics of nanoscale metals and semiconductors is necessary for the safe and prolonged operation of nanostructured devices from transistors to nanowire- based solar cells to miniaturized electrodes. This is a fascinating but challenging pursuit because mechanical properties that are size-invariant in conventional materials, such as strength, ductility and fracture behavior, can depend critically on sample size when materials are reduced to sub- micron dimensions. In this thesis, the effect of nanoscale sample size, microstructure and structural geometry on mechanical strength, deformation and fracture are explored for several classes of solid materials. Nanocrystalline platinum nano-cylinders with diameters of 60 nm to 1 μm and 12 nm sized grains are fabricated and tested in compression. We find that nano-sized metals containing few grains weaken as sample diameter is reduced relative to grain size due to a change from deformation governed by internal grains to surface grain governed deformation. Fracture at the nanoscale is explored by performing in-situ SEM tension tests on nanocrystalline platinum and amorphous, metallic glass nano-cylinders containing purposely introduced structural flaws. It is found that failure location, mechanism and strength are determined by the stress concentration with the highest local stress whether this is at the structural flaw or a microstructural feature. Principles of nano-mechanics are used to design and test mechanically robust hierarchical nanostructures with structural and electrochemical applications. 2-photon lithography and electroplating are used to fabricate 3D solid Cu octet meso-lattices with micron- scale features that exhibit strength higher than that of bulk Cu. An in-situ SEM lithiation stage is developed and used to simultaneously examine morphological and electrochemical changes in Si-coated Cu meso-lattices that are of interest as high energy capacity electrodes for Li-ion batteries.