Bounding the plastic strength of polycrystalline solids by linear-comparison homogenization methods

The elastoplastic response of polycrystalline metals and minerals above their brittle- ductile transition temperature is idealized here as rigid-perfectly plastic. Bounds on the overall plastic strength of polycrystalline solids with prescribed microstructural statistics and single-crystal plastic strength are computed by means of a linear-comparison homogenization method recently developed by Idiart & Ponte Castañeda (Idiart & Ponte Castañeda 2007 Proc. R. Soc. A 463, 907-924 (doi:10.1098/rspa.2006.1797)). Hashin- Shtrikman and self-consistent results are reported for cubic and hexagonal polycrystals with varying degrees of crystal anisotropy. Improvements over earlier linear-comparison bounds are found to be modest for high-symmetry materials but become appreciable for low-symmetry materials. The largest improvement is observed in self-consistent results for low-symmetry hexagonal polycrystals, exceeding 15 per cent in some cases. In addition to providing the sharpest bounds available to date, these results serve to evaluate the performance of the aforementioned linear-comparison method in the context of realistic material systems.Facultad de Ingenierí

Determinación teórica de la histéresis eléctrica en materiales compuestos ferroeléctricos

En este trabajo se establecen relaciones entre la histéresis eléctrica macroscópica y el comportamiento de las fases constitutivas en materiales compuestos ferroeléctricos con microestructuras complejas y sometidos a historias de carga arbitrarias. El comportamiento ferroeléctrico de cada fase se describe mediante una densidad de energía almacenada y un potencial de disipación en el marco de los ‘materiales estándar generalizados’. Discretizando en el tiempo las ecuaciones diferenciales correspondientes siguiendo un esquema implícito, se obtiene una representación variacional de la respuesta macroscó- pica del compuesto que involucra un solo potencial incremental. Las estimaciones teóricas se obtienen luego mediante ciertas ‘microgeometrías resolubles’ cuyo potencial incremental macroscópico puede determinarse en forma exacta. Por ser exactas para una clase de materiales, estas estimaciones satisfacen automáticamente todos las características comunmente buscadas en una aproximación teórica: estar de acuerdo con restricciones materiales, satisfacer todas las cotas pertinentes, y poseer todas las propiedades de convexidad correspondientes. La metodología propuesta se aplica a sistemas materiales representativos y los resultados se discuten a la luz de observaciones experimentales existentes.Theoretical estimates are given for the overall hysteretic response of two-phase ferroelectric composites with complex particulate microstructures under arbitrary loading histories. The ferroelectric behavior of the constituent phases is described via a stored energy density and a dissipation potential in accordance with the theory of generalized standard materials. An implicit time-discretization scheme is used to generate a variational representation of the overall response in terms of a single incremental potential. Estimates are then generated by constructing sequentially laminated microgeometries of particulate type whose overall incremental potential can be computed exactly. Because they are realizable, by construction, these estimates are guaranteed to conform with any material constraints, to satisfy all pertinent bounds, and to exhibit the required convexity properties with no duality gap. Predictions for composites and porous ferroelectrics are reported and discussed in the light of existing experimental data.Fil: Idiart, Martín Ignacio. Universidad Nacional de la Plata. Facultad de Ingeniería. Departamento de Aeronautica; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Bounding the plastic strength of polycrystalline solids by linear-comparison homogenization methods

The elastoplastic response of polycrystalline metals and minerals above their brittle- ductile transition temperature is idealized here as rigid-perfectly plastic. Bounds on the overall plastic strength of polycrystalline solids with prescribed microstructural statistics and single-crystal plastic strength are computed by means of a linear-comparison homogenization method recently developed by Idiart & Ponte Castañeda (Idiart & Ponte Castañeda 2007 Proc. R. Soc. A 463, 907-924 (doi:10.1098/rspa.2006.1797)). Hashin- Shtrikman and self-consistent results are reported for cubic and hexagonal polycrystals with varying degrees of crystal anisotropy. Improvements over earlier linear-comparison bounds are found to be modest for high-symmetry materials but become appreciable for low-symmetry materials. The largest improvement is observed in self-consistent results for low-symmetry hexagonal polycrystals, exceeding 15 per cent in some cases. In addition to providing the sharpest bounds available to date, these results serve to evaluate the performance of the aforementioned linear-comparison method in the context of realistic material systems.Facultad de Ingenierí

A model problem concerning the ionic transport in microstructured solid electrolytes

We consider ionic transport by diffusion and migration through microstructured solid electrolytes. The effective response is determined by homogenizing the relevant field equations via the notion of multi-scale convergence. The theory is applied to semi-crystalline polymer electrolytes with spherulitic morphologies. Predictions support recent experimental observations on doped poly-ethylene-oxide (PEO) systems which suggest that the anisotropic crystalline phase can actually support faster ion transport than the amorphous phase along certain directions dictated by the morphology of the polymeric chains.Facultad de Ingenierí

A model problem concerning ionic transport in microstructured solid electrolytes

We consider ionic transport by diffusion and migration through microstructured solid electrolytes. The assumed constitutive relations for the constituent phases follow from convex energy and dissipation potentials which guarantee thermodynamic consistency. The effective response is determined by homogenizing the relevant field equations via the notion ofmulti-scale convergence. The resulting homogenized response involves several effective tensors, but they all require the solution of just one standard conductivity problem over the representative volume element. A multi-scale model for semicrystalline polymer electrolytes with spherulitic morphologies is derived by applying the theory to a specific class of two-dimensional microgeometries for which the effective response can be computed exactly. An enriched model accounting for a random dispersion of filler particles with interphases is also derived. In both cases, explicit expressions for the effective material parameters are provided. The models are used to explore the effect of crystallinity and filler content on the overall response. Predictions support recent experimental observations on doped poly-ethylene-oxide systems which suggest that the anisotropic crystalline phase can actually support faster ion transport than the amorphous phase along certain directions dictated by the morphology of the polymeric chains. Predictions also support the viewpoint that ceramic fillers improve ionic conductivity and cation transport number via interphasial effects.Facultad de IngenieríaDepartamento de Aeronáutic

Determinación teórica de la histéresis eléctrica en materiales compuestos ferroeléctricos

En este trabajo se establecen relaciones entre la histéresis eléctrica macroscópica y el comportamiento de las fases constitutivas en materiales compuestos ferroeléctricos con microestructuras complejas y sometidos a historias de carga arbitrarias. El comportamiento ferroeléctrico de cada fase se describe mediante una densidad de energía almacenada y un potencial de disipación en el marco de los ‘materiales estándar generalizados’. Discretizando en el tiempo las ecuaciones diferenciales correspondientes siguiendo un esquema implícito, se obtiene una representación variacional de la respuesta macroscó- pica del compuesto que involucra un solo potencial incremental. Las estimaciones teóricas se obtienen luego mediante ciertas ‘microgeometrías resolubles’ cuyo potencial incremental macroscópico puede determinarse en forma exacta. Por ser exactas para una clase de materiales, estas estimaciones satisfacen automáticamente todos las características comunmente buscadas en una aproximación teórica: estar de acuerdo con restricciones materiales, satisfacer todas las cotas pertinentes, y poseer todas las propiedades de convexidad correspondientes. La metodología propuesta se aplica a sistemas materiales representativos y los resultados se discuten a la luz de observaciones experimentales existentes.Theoretical estimates are given for the overall hysteretic response of two-phase ferroelectric composites with complex particulate microstructures under arbitrary loading histories. The ferroelectric behavior of the constituent phases is described via a stored energy density and a dissipation potential in accordance with the theory of generalized standard materials. An implicit time-discretization scheme is used to generate a variational representation of the overall response in terms of a single incremental potential. Estimates are then generated by constructing sequentially laminated microgeometries of particulate type whose overall incremental potential can be computed exactly. Because they are realizable, by construction, these estimates are guaranteed to conform with any material constraints, to satisfy all pertinent bounds, and to exhibit the required convexity properties with no duality gap. Predictions for composites and porous ferroelectrics are reported and discussed in the light of existing experimental data.Facultad de Ingenierí

Bounding the plastic strength of polycrystalline solids by linear-comparison homogenization methods

The elastoplastic response of polycrystalline metals and minerals above their brittle- ductile transition temperature is idealized here as rigid-perfectly plastic. Bounds on the overall plastic strength of polycrystalline solids with prescribed microstructural statistics and single-crystal plastic strength are computed by means of a linear-comparison homogenization method recently developed by Idiart & Ponte Castañeda (Idiart & Ponte Castañeda 2007 Proc. R. Soc. A 463, 907-924 (doi:10.1098/rspa.2006.1797)). Hashin- Shtrikman and self-consistent results are reported for cubic and hexagonal polycrystals with varying degrees of crystal anisotropy. Improvements over earlier linear-comparison bounds are found to be modest for high-symmetry materials but become appreciable for low-symmetry materials. The largest improvement is observed in self-consistent results for low-symmetry hexagonal polycrystals, exceeding 15 per cent in some cases. In addition to providing the sharpest bounds available to date, these results serve to evaluate the performance of the aforementioned linear-comparison method in the context of realistic material systems.Facultad de Ingenierí

Influence of metallic inclusions on the electromechanical response of ferroelectric ceramics

Theoretical estimates are given for the overall dissipative response of ferroelectric ceramics with random dispersions of metallic inclusions under arbitrary loading histories. The fer- roelectric behavior of the matrix is described via a stored energy density and a dissipation potential in accordance with the theory of generalized standard materials. An implicit time- discretization scheme is used to generate a variational representation of the overall response in terms of a single incremental potential. Estimates are then generated by constructing se- quentially laminated microgeometries of particulate type whose overall incremental potential can be computed exactly. Because they are realizable, by construction, these estimates are guaranteed to conform with any material constraints, to satisfy all pertinent bounds, and to exhibit the required convexity properties with no duality gap. Sample results for isotropic composites are reported and discussed.Facultad de Ingenierí

Fiber-reinforced hyperelastic solids: a realizable homogenization constitutive theory

A new homogenization theory to model the mechanical response of hyperelastic solids reinforced by a random distribution of aligned cylindrical fibers is proposed. The central idea is to devise a special class of microstructures—by means of an iterated homogenization procedure in finite elasticity together with an exact dilute result for sequential laminates—that allows to compute exactly the macroscopic response of the resulting fiber-reinforced materials. The proposed framework incorporates direct microstructural information up to the two-point correlation functions, and requires the solution to a Hamilton–Jacobi equation with the fiber concentration and the macroscopic deformation gradient playing the role of “time” and “spatial” variables, respectively. In addition to providing constitutive models for the macroscopic response of fiber-reinforced materials, the proposed theory also gives information about the local fields in the matrix and fibers, which can be used to study the evolution of microstructure and the development of instabilities. As a first application of the theory, closed-form results for the case of Neo-Hookean solids reinforced by a transversely isotropic distribution of anisotropic fibers are worked out. These include a novel explicit criterion for the onset of instabilities under general finite-strain loading conditions.Facultad de Ingenierí

Une méthode d’homogénéisation sécante généralisée pour des matériaux polycristallins viscoplastiques en déformations imposées

Homogenization estimates for viscoplastic polycrystals are derived by applying the generalized-secant linearization scheme of Liu and Ponte Castañeda (2004) to the constitutive description with strain rates as primary variables. The resulting estimates are thus particularly suitable for simulating mechanical processes where deformations are imposed and where the material softens. Their accuracy is preliminarily assessed in the context of a model material system. Good agreement with previous estimates is found.Des estimations relatives à l’homogénéisation de polycristaux viscoplastiques sont obtenues en appliquant la méthode de linéarisation sécante généralisée de Liu et Ponte Castañeda (2004) au cas d’une relation constitutive où les taux de déformation sont des variables primaires. Les estimations obtenues sont particulièrement adaptées pour simuler des chargements mécaniques où les déformations sont imposées et où le matériau s’adoucit. La précision de ces estimations est évaluée au préalable dans le cas d’un système matériau modèle. Un bon accord est obtenu avec des estimations antérieures.Facultad de IngenieríaDepartamento de Aeronáutic