Dependence of shear yield strain and shear transformation zone on the glass transition temperature in thin film metallic glasses

The dependence of shear yield strain, the activation energy and volume of shear transformation zone on the glass transition temperature was investigated through the analysis of statistical distributions of the first pop-in events during spherical indentation of four different thin film metallic glasses. Only the Cu-Zr metallic glass exhibits a bimodal distribution of the first pop-in loads, whereas W-Ru-B, Zr-Cu-Ni-Al and La-Co-Al metallic glasses show an unimodal distribution. Results show that shear yield strain and activation energy of shear transformation zone decrease whereas the volume of shear transformation zone increases with increasing homologous temperature, indicating that it is the activation energy rather than the volume of shear transformation zone that controls shear yield strain. (C) 2015 Elsevier B.V. All rights reserved.

Effects of Isothermal and Adiabatic Thermal Loadings on Size and Strain Rate Dependence of Copper Nanowire

In the present paper, the size and strain rate effects on ultra-thin < 100 >/{100} Cu nanowires at an initial temperature of 10 K have been discussed. Extensive molecular dynamics (MD) simulations have been performed using Embedded atom method (EAM) to investigate the structural behaviours and properties under high strain rate. Velocity-Verlet algorithm has been used to solve the equation of motions. Two different thermal loading cases have been considered: (i) Isothermal loading, in which Nose-Hoover thermostat is used to maintain the constant system temperature, and (ii) Adiabatic loading, i.e., without any thermostat. Five different wire cross-sections were considered ranging from 0.723 x 0.723 nm(2) to 2.169 x 2.169 nm(2) The strain rates used in the present study were 1 x 10(9) s(-1), 1 x 10(8) s(-1), and 1 x 10(7) s(-1). The effect of strain rate on the mechanical properties of copper nanowires was analysed, which shows that elastic properties are independent of thermal loading for a given strain rate and cross-sectional dimension of nanowire. It showed a decreasing yield stress and yield strain with decreasing strain rate for a given cross- section. Also, a decreasing yield stress and increasing yield strain were observed for a given strain rate with increasing cross-sectional area. Elastic modulus was found to be similar to 100 GPa, which was independent of processing temperature, strain rate, and size for a given initial temperature. Reorientation of < 100 >/{100} square cross-sectional copper nanowire into a series of stable ultra-thin Pentagon copper nanobridge structures with dia of similar to 1 nm at 10 K was observed under high strain rate tensile loading. The effect of isothermal and adiabatic loading on the formation of such pentagonal nanobridge structure has been discussed.

Exploration of the defect’s effect on the mechanical properties of different orientated nanowires

Molecular dynamics (MD) simulations have been carried out to investigate the defect’s effect on the mechanical properties of copper nanowire with different crystallographic orientations, under tensile deformation. Three different crystallographic orientations have been considered. The deformation mechanism has been carefully discussed. It is found that the Young’s modulus is insensitive to the defect, even when the nanowire’s crystallographic orientation is different. However, due to the defect’s effect, the yield strength and yield strain appear a large decrease. The defects have played a role of dislocation sources, the slips or stacking faults are first generated around the locations of the defects. The necking locations have also been affected by different defects. Due to the surface defect, the plastic deformation has received a large influence for the <001>/{110} and <110> orientated nanowires, and a relative small influence is seen for the <111> nanowire.

Two-dimensional graphene heterojunctions: The tunable mechanical properties

We report the mechanical properties of different two-dimensional carbon heterojunctions (HJs) made from graphene and various stable graphene allotropes, including α-, β-, γ- and 6612-graphyne (GY), and graphdiyne (GDY). It is found that all HJs exhibit a brittle behaviour except the one with α-GY, which however shows a hardening process due to the formation of triple carbon rings. Such hardening process has greatly deferred the failure of the structure. The yielding of the HJs is usually initiated at the interface between graphene and graphene allotropes, and monoatomic carbon rings are normally formed after yielding. By varying the locations of graphene (either in the middle or at the two ends of the HJs), similar mechanical properties have been obtained, suggesting insignificant impacts from location of graphene allotropes. Whereas, changing the types and percentages of the graphene allotropes, the HJs exhibit vastly different mechanical properties. In general, with the increasing graphene percentage, the yield strain decreases and the effective Young’s modulus increases. Meanwhile, the yield stress appears irrelevant with the graphene percentage. This study provides a fundamental understanding of the tensile properties of the heterojunctions that are crucial for the design and engineering of their mechanical properties, in order to facilitate their emerging future applications in nanoscale devices, such as flexible/stretchable electronics.

Engineering the mechanical properties of graphene nanotube hybrid structures through structural modulation

The excellent multi-functional properties of carbon nanotube (CNT) and graphene have enabled them as appealing building blocks to construct 3D carbon-based nanomaterials or nanostructures. The recently reported graphene nanotube hybrid structure (GNHS) is one of the representatives of such nanostructures. This work investigated the relationships between the mechanical properties of the GNHS and its structure basing on large-scale molecular dynamics simulations. It is found that increasing the length of the constituent CNTs, the GNHS will have a higher Young’s modulus and yield strength. Whereas, no strong correlation is found between the number of graphene layers and Young’s modulus and yield strength, though more graphene layers intends to lead to a higher yield strain. In the meanwhile, the presences of multi-wall CNTs are found to greatly strengthen the hybrid structure. Generally, the hybrid structures exhibit a brittle behavior and the failure initiates from the connecting regions between CNT and graphene. More interestingly, affluent formations of monoatomic chains and rings are found at the fracture region. This study provides an in-depth understanding of the mechanical performance of the GNHSs while varying their structures, which will shed lights on the design and also the applications of the carbon-based nanostructures.

Graphene with patterned fluorination: Morphology modulation and implications

Recent years have witnessed a large volume of works on the modification of graphene; however, an understanding of the associated morphology or mechanical properties changes is still lacking, which is vital for its engineering implementation. By taking the C4F fluorination as an example, we find that the morphology of both graphene sheet (GS) and graphene nanoribbon (GNR) can be effectively tailored by fluorination patterning via molecular dynamics simulations. The fluorine atom produces out-of-plane forces which trigger several intriguing morphology changes to monolayer graphene, including zigzag, folded, ruffle, nanoscroll, and chain structures. Notably, for multilayer GNR, the delamination and climbing phenomena of the surface layer are observed. Further studies show that the fluorination pattern can also be utilized to modulate the mechanical properties of graphene, e.g., about 40% increase of the effective yield strain is observed for the examined GNR with fluorination patterns. This study not only demonstrates the significant impacts on the morphology of graphene from fluorination but also suggests an effective avenue to tailor the morphology and thus mechanical properties of GS and GNR.

Experimental signatures of a nonequilibrium phase transition governing the yielding of a soft glass

We present direct experimental signatures of a nonequilibrium phase transition associated with the yield point of a prototypical soft solid-a binary colloidal glass. By simultaneously quantifying single-particle dynamics and bulk mechanical response, we identified the threshold for the onset of irreversibility with the yield strain. We extracted the relaxation time from the transient behavior of the loss modulus and found that it diverges in the vicinity of the yield strain. This critical slowing down is accompanied by a growing correlation length associated with the size of regions of high Debye-Waller factor, which are precursors to yield events in glasses. Our results affirm that the paradigm of nonequilibrium critical phenomena is instrumental in achieving a holistic understanding of yielding in soft solids.

Toward Understanding Astrophysical Phenomena

Fast radio bursts (FRBs), a novel type of radio pulse, whose physics is not yet understood at all. Only a handful of FRBs had been detected when we started this project. Taking account of the scant observations, we put physical constraints on FRBs. We excluded proposals of a galactic origin for their extraordinarily high dispersion measures (DM), in particular stellar coronas and HII regions. Therefore our work supports an extragalactic origin for FRBs. We show that the resolved scattering tail of FRB 110220 is unlikely to be due to propagation through the intergalactic plasma. Instead the scattering is probably caused by the interstellar medium in the FRB's host galaxy, and indicates that this burst sits in the central region of that galaxy. Pulse durations of order $\ms$ constrain source sizes of FRBs implying enormous brightness temperatures and thus coherent emission. Electric fields near FRBs at cosmological distances would be so strong that they could accelerate free electrons from rest to relativistic energies in a single wave period. When we worked on FRBs, it was unclear whether they were genuine astronomical signals as distinct from `perytons', clearly terrestrial radio bursts, sharing some common properties with FRBs. Recently, in April 2015, astronomers discovered that perytons were emitted by microwave ovens. Radio chirps similar to FRBs were emitted when their doors opened while they were still heating. Evidence for the astronomical nature of FRBs has strengthened since our paper was published. Some bursts have been found to show linear and circular polarizations and Faraday rotation of the linear polarization has also been detected. I hope to resume working on FRBs in the near future. But after we completed our FRB paper, I decided to pause this project because of the lack of observational constraints.

The pulsar triple system, J0733+1715, has its orbital parameters fitted to high accuracy owing to the precise timing of the central $\ms$ pulsar. The two orbits are highly hierarchical, namely $P_{\mathrm{orb,1}}\ll P_{\mathrm{orb,2}}$, where 1 and 2 label the inner and outer white dwarf (WD) companions respectively. Moreover, their orbital planes almost coincide, providing a unique opportunity to study secular interaction associated purely with eccentricity beyond the solar system. Secular interaction only involves effect averaged over many orbits. Thus each companion can be represented by an elliptical wire with its mass distributed inversely proportional to its local orbital speed. Generally there exists a mutual torque, which vanishes only when their apsidal lines are parallel or anti-parallel. To maintain either mode, the eccentricity ratio, $e_1/e_2$, must be of the proper value, so that both apsidal lines precess together. For J0733+1715, $e_1\ll e_2$ for the parallel mode, while $e_1\gg e_2$ for the anti-parallel one. We show that the former precesses $\sim 10$ times slower than the latter. Currently the system is dominated by the parallel mode. Although only a little anti-parallel mode survives, both eccentricities especially $e_1$ oscillate on $\sim 10^3\yr$ timescale. Detectable changes would occur within $\sim 1\yr$. We demonstrate that the anti-parallel mode gets damped $\sim 10^4$ times faster than its parallel brother by any dissipative process diminishing $e_1$. If it is the tidal damping in the inner WD, we proceed to estimate its tidal quantity parameter ($Q$) to be $\sim 10^6$, which was poorly constrained by observations. However, tidal damping may also happen during the preceding low-mass X-ray binary (LMXB) phase or hydrogen thermal nuclear flashes. But, in both cases, the inner companion fills its Roche lobe and probably suffers mass/angular momentum loss, which might cause $e_1$ to grow rather than decay.

Several pairs of solar system satellites occupy mean motion resonances (MMRs). We divide these into two groups according to their proximity to exact resonance. Proximity is measured by the existence of a separatrix in phase space. MMRs between Io-Europa, Europa-Ganymede and Enceladus-Dione are too distant from exact resonance for a separatrix to appear. A separatrix is present only in the phase spaces of the Mimas-Tethys and Titan-Hyperion MMRs and their resonant arguments are the only ones to exhibit substantial librations. When a separatrix is present, tidal damping of eccentricity or inclination excites overstable librations that can lead to passage through resonance on the damping timescale. However, after investigation, we conclude that the librations in the Mimas-Tethys and Titan-Hyperion MMRs are fossils and do not result from overstability.

Rubble piles are common in the solar system. Monolithic elements touch their neighbors in small localized areas. Voids occupy a significant fraction of the volume. In a fluid-free environment, heat cannot conduct through voids; only radiation can transfer energy across them. We model the effective thermal conductivity of a rubble pile and show that it is proportional the square root of the pressure, $P$, for $P\leq \epsy^3\mu$ where $\epsy$ is the material's yield strain and $\mu$ its shear modulus. Our model provides an excellent fit to the depth dependence of the thermal conductivity in the top $140\,\mathrm{cm}$ of the lunar regolith. It also offers an explanation for the low thermal inertias of rocky asteroids and icy satellites. Lastly, we discuss how rubble piles slow down the cooling of small bodies such as asteroids.

Electromagnetic (EM) follow-up observations of gravitational wave (GW) events will help shed light on the nature of the sources, and more can be learned if the EM follow-ups can start as soon as the GW event becomes observable. In this paper, we propose a computationally efficient time-domain algorithm capable of detecting gravitational waves (GWs) from coalescing binaries of compact objects with nearly zero time delay. In case when the signal is strong enough, our algorithm also has the flexibility to trigger EM observation {\it before} the merger. The key to the efficiency of our algorithm arises from the use of chains of so-called Infinite Impulse Response (IIR) filters, which filter time-series data recursively. Computational cost is further reduced by a template interpolation technique that requires filtering to be done only for a much coarser template bank than otherwise required to sufficiently recover optimal signal-to-noise ratio. Towards future detectors with sensitivity extending to lower frequencies, our algorithm's computational cost is shown to increase rather insignificantly compared to the conventional time-domain correlation method. Moreover, at latencies of less than hundreds to thousands of seconds, this method is expected to be computationally more efficient than the straightforward frequency-domain method.

Size effects in the conical indentation of an elasto-plastic solid

The size effect in conical indentation of an elasto-plastic solid is predicted via the Fleck and Willis formulation of strain gradient plasticity (Fleck, N.A. and Willis, J.R., 2009, A mathematical basis for strain gradient plasticity theory. Part II: tensorial plastic multiplier, J. Mech. Phys. Solids, 57, 1045-1057). The rate-dependent formulation is implemented numerically and the full-field indentation problem is analyzed via finite element calculations, for both ideally plastic behavior and dissipative hardening. The isotropic strain-gradient theory involves three material length scales, and the relative significance of these length scales upon the degree of size effect is assessed. Indentation maps are generated to summarize the sensitivity of indentation hardness to indent size, indenter geometry and material properties (such as yield strain and strain hardening index). The finite element model is also used to evaluate the pertinence of the Johnson cavity expansion model and of the Nix-Gao model, which have been extensively used to predict size effects in indentation hardness. © 2012 Elsevier Ltd.

The main factor influencing the tensile properties of surface nano-crystallized graded materials

The improved mechanical properties of surface nano-crystallized graded materials produced by surface severe plastic deformation ((SPD)-P-2) are generally owing to the effects of the refined structure, work-hardened region and compressive residual stress. However, during the (SPD)-P-2 process, residual stress is produced simultaneously with work-hardened region, the individual contribution of these two factors to the improved mechanical properties remains unclear. Numerical simulations are carried out in order to answer this question. It is found that work hardening predominates in improving the yield strength and the ultimate tensile strength of the surface nano-crystallized graded materials, while the influence of the residual stress mainly emerges at the initial stage of deformation and decreases the apparent elastic modulus of the surface nano-crystallized graded materials, which agrees well with the experimental results. (C) 2010 Elsevier B.V. All rights reserved.

Brittle-ductile transition of particle toughened polymers: influence of the matrix properties

It was theoretically pointed out that the product of the yield stress and yield strain of matrix polymer that determined the brittle-ductile transition (BDT) of particle toughened polymers. For given particle and test condition, the higher the product of the yield stress and the yield strain of the matrix polymer, the smaller the critical interparticle distance (IDc) of the blends was. This was why the IDc (0.15 mum) of the polypropylene (PP)/rubber blends was smaller than that (0.30 mum) of the nylon 66/rubber blends, and the IDc of the nylon 66/rubber blends was smaller than that (0.60 mum) of the high density polyethylene (HDPE)/rubber blends.

Avaliação das equações de predição das exigências de proteína para matrizes pesadas na fase de crescimento

Objetivou-se avaliar as equações para predição das exigências protéicas de matrizes pesadas em crescimento, desenvolvidas em estudos anteriores na Faculdade de Ciências Agrárias e Veterinárias da UNESP, Jaboticabal, tendo como padrão de comparação as recomendações estabelecidas pelo manual de criação da linhagem. Foram utilizadas 288 matrizes pesadas da linhagem Hubbard Hy-Yield, com cinco semanas de idade, em delineamento inteiramente casualizado, com dois tratamentos e seis repetições, sendo 24 aves por unidade experimental até 14 semanas e, de 15 a 20 semanas de idade, 20 aves por unidade experimental. Um tratamento foi representado pelas recomendações protéicas para a linhagem (testemunha) e o outro pelas seguintes equações de predição das exigências de proteína: de 5 a 8 semanas PB (g/ave/dia) = 2,02.P0,75+ 0,350.G, 9 a 14 semanas - PB = 2,02.P0,75 + 0,406.G e de 15 a 20 semanas PB = 2,02.P0,75 + 0,463.G, em que P é o peso corporal (kg) e G, o ganho de peso diário (g). Os resultados indicaram que as equações de predição para proteína, apesar de não comprometerem o peso ou a uniformidade corporal em relação ao tratamento testemunha, determinaram menor porcentagem de peito e maior de gordura abdominal e maior teor de gordura na carcaça, sendo atribuído à menor ingestão de proteína proporcionada pelas equações de predição e, conseqüentemente, deficiência em relação a alguns aminoácidos que não foram suplementados.

Efeito da linhagem e do nível de lisina da dieta sobre a qualidade da carne do peito de frangos de corte

O experimento foi conduzido com o objetivo de avaliar o efeito da linhagem e do nível de lisina da dieta sobre o rendimento e a qualidade da carne de peito de frangos de corte. Foram utilizados 2250 pintos não sexados, de três linhagens comerciais, identificadas como A, B e C, distribuídos em delineamento inteiramente casualizado em esquema fatorial 3x3 (linhagens e níveis de lisina), com cinco repetições de 50 aves. As aves receberam ração à vontade, à base de milho e farelo de soja, suplementadas com 1,18; 1,24 e 1,30% de lisina nas rações pré-iniciais (1 a 7 dias); 1,10; 1,16 e 1,22% nas rações iniciais (7 a 21 dias); 1,0; 1,06 e 1,12% nas rações de crescimento (21 a 35 dias) e 0,85; 0,91 e 0,97% nas rações de terminação (35 a 42 dias). Foram avaliadas as características de rendimento de peito e carne de peito e as medidas de espessura, largura, comprimento, pH, perda de peso por cozimento e força de cisalhamento da carne de peito. Para o rendimento de peito não foram observadas diferenças significativas, enquanto para rendimento de carne de peito houve efeito significativo da linhagem, em que a linhagem A apresentou o maior rendimento e a linhagem B, o menor. Para as medidas físicas da carne do peito, foram encontradas diferenças significativas entre as linhagens para comprimento de peito, com a linhagem C apresentando o maior resultado. O pH da carne diferiu significativamente para linhagens e níveis de lisina. As linhagens tiveram efeito sobre o rendimento, comprimento e pH da carne de peito, em que a linhagem A apresentou maiores valores para rendimento e pH e a linhagem C para comprimento.

Límites de ductilidad y de servicio al cálculo en carga última de estructuras de hormigón armado y de fábrica

En este trabajo se aborda una cuestión central en el diseño en carga última de estructuras de hormigón armado y de fábrica: la posibilidad efectiva de que las deformaciones plásticas necesarias para verificar un estado de rotura puedan ser alcanzadas por las regiones de la estructura que deban desarrollar su capacidad última para verificar tal estado. Así, se parte de las decisiones de diseño que mediante mera estática aseguran un equilibrio de la estructura para las cargas últimas que deba resistir, pero determinando directamente el valor de las deformaciones necesarias para llegar a tal estado. Por tanto, no se acude a los teoremas de rotura sin más, sino que se formula el problema desde un punto de vista elastoplástico. Es decir, no se obvia el recorrido que la estructura deba realizar en un proceso de carga incremental monótono, de modo que las regiones no plastificadas contribuyen a coaccionar las libres deformaciones plásticas que, en la teoría de rotura, se suponen. En términos de trabajo y energía, se introduce en el balance del trabajo de las fuerzas externas y en el de la energía de deformación, aquella parte del sistema que no ha plastificado. Establecido así el balance energético como potencial del sistema es cuando la condición de estacionariedad del mismo hace determinados los campos de desplazamientos y, por tanto, el de las deformaciones plásticas también. En definitiva, se trata de un modo de verificar si la ductilidad de los diseños previstos es suficiente, y en qué medida, para verificar el estado de rotura previsto, para unas determinadas cargas impuestas. Dentro del desarrollo teórico del problema, se encuentran ciertas precisiones importantes. Entre ellas, la verificación de que el estado de rotura a que se llega de manera determinada mediante el balance energético elasto-plástico satisface las condiciones de la solución de rotura que los teoremas de carga última predicen, asegurando, por tanto, que la solución determinada -unicidad del problema elásticocoincide con el teorema de unicidad de la carga de rotura, acotando además cuál es el sistema de equilibrio y cuál es la deformada de colapso, aspectos que los teoremas de rotura no pueden asegurar, sino sólo el valor de la carga última a verificar. Otra precisión se basa en la particularidad de los casos en que el sistema presenta una superficie de rotura plana, haciendo infinitas las posibilidades de equilibrio para una misma deformada de colapso determinada, lo que está en la base de, aparentemente, poder plastificar a antojo en vigas y arcos. Desde el planteamiento anterior, se encuentra entonces que existe una condición inherente a cualquier sistema, definidas unas leyes constitutivas internas, que permite al mismo llegar al inicio del estado de rotura sin demandar deformación plástica alguna, produciéndose la plastificación simultánea de todas las regiones que hayan llegado a su solicitación de rotura. En cierto modo, se daría un colapso de apariencia frágil. En tal caso, el sistema conserva plenamente hasta el final su capacidad dúctil y tal estado actúa como representante canónico de cualquier otra solución de equilibrio que con idéntico criterio de diseño interno se prevea para tal estructura. En la medida que el diseño se acerque o aleje de la solución canónica, la demanda de ductilidad del sistema para verificar la carga última será menor o mayor. Las soluciones que se aparten en exceso de la solución canónica, no verificarán el estado de rotura previsto por falta de ductilidad: la demanda de deformación plástica de alguna región plastificada estará más allá de la capacidad de la misma, revelándose una carga de rotura por falta de ductilidad menor que la que se preveía por mero equilibrio. Para la determinación de las deformaciones plásticas de las rótulas, se ha tomado un modelo formulado mediante el Método de los Elementos de Contorno, que proporciona un campo continuo de desplazamientos -y, por ende, de deformaciones y de tensiones- incluso en presencia de fisuras en el contorno. Importante cuestión es que se formula la diferencia, nada desdeñable, de la capacidad de rotación plástica de las secciones de hormigón armado en presencia de cortante y en su ausencia. Para las rótulas de fábrica, la diferencia se establece para las condiciones de la excentricidad -asociadas al valor relativo de la compresión-, donde las diferencias entres las regiones plastificadas con esfuerzo normal relativo alto o bajo son reseñables. Por otro lado, si bien de manera un tanto secundaria, las condiciones de servicio también imponen un límite al diseño previo en carga última deseado. La plastificación lleva asociadas deformaciones considerables, sean locales como globales. Tal cosa impone que, en estado de servicio, si la plastificación de alguna región lleva asociadas fisuraciones excesivas para el ambiente del entorno, la solución sea inviable por ello. Asimismo, las deformaciones de las estructuras suponen un límite severo a las posibilidades de su diseño. Especialmente en edificación, las deformaciones activas son un factor crítico a la hora de decidirse por una u otra solución. Por tanto, al límite que se impone por razón de ductilidad, se debe añadir el que se imponga por razón de las condiciones de servicio. Del modo anterior, considerando las condiciones de ductilidad y de servicio en cada caso, se puede tasar cada decisión de diseño con la previsión de cuáles serán las consecuencias en su estado de carga última y de servicio. Es decir, conocidos los límites, podemos acotar cuáles son los diseños a priori que podrán satisfacer seguro las condiciones de ductilidad y de servicio previstas, y en qué medida. Y, en caso de no poderse satisfacer, qué correcciones debieran realizarse sobre el diseño previo para poderlas cumplir. Por último, de las consecuencias que se extraen de lo estudiado, se proponen ciertas líneas de estudio y de experimentación para poder llegar a completar o expandir de manera práctica los resultados obtenidos. ABSTRACT This work deals with a main issue for the ultimate load design in reinforced concrete and masonry structures: the actual possibility that needed yield strains to reach a ultimate state could be reached by yielded regions on the structure that should develop their ultimate capacity to fulfill such a state. Thus, some statically determined design decisions are posed as a start for prescribed ultimate loads to be counteracted, but finding out the determined value of the strains needed to reach the ultimate load state. Therefore, ultimate load theorems are not taken as they are, but a full elasto-plastic formulation point of view is used. As a result, the path the structure must develop in a monotonus increasing loading procedure is not neglected, leading to the fact that non yielded regions will restrict the supposed totally free yield strains under a pure ultimate load theory. In work and energy terms, in the overall account of external forces work and internal strain energy, those domains in the body not reaching their ultimate state are considered. Once thus established the energy balance of the system as its potential, by imposing on it the stationary condition, both displacements and yield strains appear as determined values. Consequently, what proposed is a means for verifying whether the ductility of prescribed designs is enough and the extent to which they are so, for known imposed loads. On the way for the theoretical development of the proposal, some important aspects have been found. Among these, the verification that the conditions for the ultimate state reached under the elastoplastic energy balance fulfills the conditions prescribed for the ultimate load state predicted through the ultimate load theorems, assuring, therefore, that the determinate solution -unicity of the elastic problemcoincides with the unicity ultimate load theorem, determining as well which equilibrium system and which collapse shape are linked to it, being these two last aspects unaffordable by the ultimate load theorems, that make sure only which is the value of the ultimate load leading to collapse. Another aspect is based on the particular case in which the yield surface of the system is flat -i.e. expressed under a linear expression-, turning out infinite the equilibrium possibilities for one determined collapse shape, which is the basis of, apparently, deciding at own free will the yield distribution in beams and arches. From the foresaid approach, is then found that there is an inherent condition in any system, once defined internal constitutive laws, which allows it arrive at the beginning of the ultimate state or collapse without any yield strain demand, reaching the collapse simultaneously for all regions that have come to their ultimate strength. In a certain way, it would appear to be a fragile collapse. In such a case case, the system fully keeps until the end its ductility, and such a state acts as a canonical representative of any other statically determined solution having the same internal design criteria that could be posed for the that same structure. The extent to which a design is closer to or farther from the canonical solution, the ductility demand of the system to verify the ultimate load will be higher or lower. The solutions being far in excess from the canonical solution, will not verify the ultimate state due to lack of ductility: the demand for yield strains of any yielded region will be beyond its capacity, and a shortcoming ultimate load by lack of ductility will appear, lower than the expected by mere equilibrium. For determining the yield strains of plastic hinges, a Boundary Element Method based model has been used, leading to a continuous displacement field -therefore, for strains and stresses as well- even if cracks on the boundary are present. An important aspect is that a remarkable difference is found in the rotation capacity between plastic hinges in reinforced concrete with or without shear. For masonry hinges, such difference appears when dealing with the eccentricity of axial forces -related to their relative value of compression- on the section, where differences between yield regions under high or low relative compressions are remarkable. On the other hand, although in a certain secondary manner, serviceability conditions impose limits to the previous ultimate load stated wanted too. Yield means always big strains and deformations, locally and globally. Such a thing imposes, for serviceability states, that if a yielded region is associated with too large cracking for the environmental conditions, the predicted design will be unsuitable due to this. Furthermore, displacements must be restricted under certain severe limits that restrain the possibilities for a free design. Especially in building structures, active displacements are a critical factor when chosing one or another solution. Then, to the limits due to ductility reasons, other limits dealing with serviceability conditions shoud be added. In the foresaid way, both considering ductility and serviceability conditions in every case, the results for ultimate load and serviceability to which every design decision will lead can be bounded. This means that, once the limits are known, it is possible to bound which a priori designs will fulfill for sure the prescribed ductility and serviceability conditions, and the extent to wich they will be fulfilled, And, in case they were not, which corrections must be performed in the previous design so that it will. Finally, from the consequences derived through what studied, several study and experimental fields are proposed, in order to achieve a completeness and practical expansion of the obtained results.