Simulations of Mechanical Behavior of Polycrystalline Copper with Nano-Twins

Mechanical behavior and microstructure evolution of polycrystalline copper with nano-twins were investigated in the present work by finite element simulations. The fracture of grain boundaries are described by a cohesive interface constitutive model based on the strain gradient plasticity theory. A systematic study of the strength and ductility for different grain sizes and twin lamellae distributions is performed. The results show that the material strength and ductility strongly depend on the grain size and the distribution of twin lamellae microstructures in the polycrystalline copper.

Basic Mechanical Behaviors And Mechanics Of Shear Banding In Bmgs

In this paper, some basic mechanical behaviors of bulk metallic glasses (BMGs) were discussed. It can be found from the discussions that the mechanical behaviors of BMGs are mainly due to the formation and operation of shear bands in BMGs. Furthermore, the relevant mechanics of shear banding were investigated in the paper. The theoretical analysis of deformation coupling thermal softening and free volume creation softening demonstrates that the free volume creation and thermal softening can jointly promote the formation of shear bands in BMGs, and the observed post mortem. shear band width looks more like that governed by free volume creation. (C) 2007 Elsevier Ltd. All rights reserved.

Theory Of Phase Transformation And Reorientation In Single Crystalline Shape Memory Alloys

A constitutive model, based on an (n + 1)-phase mixture of the Mori-Tanaka average theory, has been developed for stress-induced martensitic transformation and reorientation in single crystalline shape memory alloys. Volume fractions of different martensite lattice correspondence variants are chosen as internal variables to describe microstructural evolution. Macroscopic Gibbs free energy for the phase transformation is derived with thermodynamics principles and the ensemble average method of micro-mechanics. The critical condition and the evolution equation are proposed for both the phase transition and reorientation. This model can also simulate interior hysteresis loops during loading/unloading by switching the critical driving forces when an opposite transition takes place.

Thermal stress wave and spallation induced by an electron beam

Thermal stress wave and spallation in aluminium alloy exposed to a high fluency and low energy electron beams are studied theoretically. A simple model for the study of energy deposition of electrons in materials is presented on the basis of some empirical formulae. Under the stress wave induced by energy deposition, microcracks and/or microvoids may appear in target materials, and in this case, the inelastic volume deformation should not vanish. The viscoplastic model proposed by Bodner and Partom with corresponding Gurson's yield function requires modification for this situation. The new constitutive model contains a scalar field variable description of the material damage which is taken as the void volume fraction of the polycrystalline material. Incorporation of the damage parameter permits description of rate-dependent, compressible, inelastic deformation and ductile fracture. The melting phenomenon has been observed in the experiment, therefore one needs to take into account the melting process in the intermediate energy deposition range. A three-phase equation of state used in the paper provides a more detailed and thermodynamical description of metals, particularly, in the melting region. The computational results based on the suggested model are compared with the experimental test for aluminium alloy, which is subjected to a pulsed electron beam with high fluency and low energy. (C) 1997 Elsevier Science Ltd.

Formation of shear bands in plane sheet

The formation of shear bands in plane sheet is studied, both analytically and experimentally, to enhance the fundamental understanding of this phenomenon and to develop a capability for predicting material failure. The evolution of voids is measured and its interaction with the process of shear banding is examined. The evolving dilatancy in plasticity is shown to have a vital role in analysing the shear-band type of bifurcation, and tremendously reduces the theoretical value of critical stresses. The analyses, referring to both localized and diffuse modes of bifurcation, fairly explain the corresponding observations obtained through testing a dual-phase steer sheet and provide a justification of the constitutive model used.

Asymptotic solution of mode-iii crack in damaged softening materials

In this paper, a constitutive model of elasticity coupled with damage suggested by Lemaitre et al, [1] is used. The macroscopic stress-strain response of the model includes two stages: strain hardening and strain softening. The basic equation is derived for the anti-plane shear problem. Several lowest order asymptotic solutions are obtained, and assembled for the crack-tip fields.

Crack tip behavior and crack-propagation in ductile materials

Dilatational plastic equations, which can include the effects of ductile damage, are derived based on the equivalency in expressions for dissipated plastic work. Void damage developed internally at the large-strain stage is represented by an effective continuum being strain-softened and plastically dilated. Accumulation of this local damage leads to progressive failure in materials. With regard to this microstructural background, the constitutive parameters included for characterizing material behaviour have the sense of internal variables. They are not able to be determined explicitly by macroscopic testing but rather through computer simulation of experimental curves and data. Application of this constitutive model to mode-I cracking examples demonstrates that a huge strain concentration accompanied by a substantial drop of stress does occur near the crack tip. Eventually, crack propagation is simulated by using finite elements in computations. Two numerical examples show good accordance with experimental data. The whole procedure of study serves as a justification of the constitutive formulation proposed in the text.

Energy Functions And Basic Equations For Ferroelectrics

Energy functions (or characteristic functions) and basic equations for ferroelectrics in use today are given by those for ordinary dielectrics in the physical and mechanical communications. Based on these basic equations and energy functions, the finite element computation of the nonlinear behavior of the ferroelectrics has been carried out by several research groups. However, it is difficult to process the finite element computation further after domain switching, and the computation results are remarkably deviating from the experimental results. For the crack problem, the iterative solution of the finite element calculation could not converge and the solutions for fields near the crack tip oscillate. In order to finish the calculation smoothly, the finite element formulation should be modified to neglect the equivalent nodal load produced by spontaneous polarization gradient. Meanwhile, certain energy functions for ferroelectrics in use today are not compatible with the constitutive equations of ferroelectrics and need to be modified. This paper proposes a set of new formulae of the energy functions for ferroelectrics. With regard to the new formulae of the energy functions, the new basic equations for ferroelectrics are derived and can reasonably explain the question in the current finite element analysis for ferroelectrics.

心肌细胞大变形黏弹性模型及在实验中的应用

在衡量单个细胞力学行为的研究中,越来越多地采用结合实验的数值模拟方法.在连续介质力学框架下,发展了一种新的心肌细胞本构模型,并与微管吮吸实验结合,探讨了心肌细胞的力学特性.本构模型是对普遍使用的仅能用于小变形分析的标准线性固体模型的一种扩展,它将超弹性性能引入到黏弹性模型中,用以描述细胞的大变形黏弹性效应.基于改进的本构模型,对心肌细胞微管吮吸实验过程进行了有限元模拟,并将计算结果与实验结果以及经典理论解进行了对比.结果显示发展的本构模型适合细胞大变形问题的有限元数值模拟.

Dynamics of cell–matrix mechanical interactions in three dimensions

The forces cells apply to their surroundings control biological processes such as growth, adhesion, development, and migration. In the past 20 years, a number of experimental techniques have been developed to measure such cell tractions. These approaches have primarily measured the tractions applied by cells to synthetic two-dimensional substrates, which do not mimic in vivo conditions for most cell types. Many cell types live in a fibrous three-dimensional (3D) matrix environment. While studying cell behavior in such 3D matrices will provide valuable insights for the mechanobiology and tissue engineering communities, no experimental approaches have yet measured cell tractions in a fibrous 3D matrix.

This thesis describes the development and application of an experimental technique for quantifying cellular forces in a natural 3D matrix. Cells and their surrounding matrix are imaged in three dimensions with high speed confocal microscopy. The cell-induced matrix displacements are computed from the 3D image volumes using digital volume correlation. The strain tensor in the 3D matrix is computed by differentiating the displacements, and the stress tensor is computed by applying a constitutive law. Finally, tractions applied by the cells to the matrix are computed directly from the stress tensor.

The 3D traction measurement approach is used to investigate how cells mechanically interact with the matrix in biologically relevant processes such as division and invasion. During division, a single mother cell undergoes a drastic morphological change to split into two daughter cells. In a 3D matrix, dividing cells apply tensile force to the matrix through thin, persistent extensions that in turn direct the orientation and location of the daughter cells. Cell invasion into a 3D matrix is the first step required for cell migration in three dimensions. During invasion, cells initially apply minimal tractions to the matrix as they extend thin protrusions into the matrix fiber network. The invading cells anchor themselves to the matrix using these protrusions, and subsequently pull on the matrix to propel themselves forward.

Lastly, this thesis describes a constitutive model for the 3D fibrous matrix that uses a finite element (FE) approach. The FE model simulates the fibrous microstructure of the matrix and matches the cell-induced matrix displacements observed experimentally using digital volume correlation. The model is applied to predict how cells mechanically sense one another in a 3D matrix. It is found that cell-induced matrix displacements localize along linear paths. These linear paths propagate over a long range through the fibrous matrix, and provide a mechanism for cell-cell signaling and mechanosensing. The FE model developed here has the potential to reveal the effects of matrix density, inhomogeneity, and anisotropy in signaling cell behavior through mechanotransduction.

Strength of tantalum at high pressures through Richtmyer-Meshkov laser compression experiments and simulations

Strength at extreme pressures (>1 Mbar or 100 GPa) and high strain rates (106-108 s-1) of materials is not well characterized. The goal of the research outlined in this thesis is to study the strength of tantalum (Ta) at these conditions. The Omega Laser in the Laboratory for Laser Energetics in Rochester, New York is used to create such extreme conditions. Targets are designed with ripples or waves on the surface, and these samples are subjected to high pressures using Omega’s high energy laser beams. In these experiments, the observational parameter is the Richtmyer-Meshkov (RM) instability in the form of ripple growth on single-mode ripples. The experimental platform used for these experiments is the “ride-along” laser compression recovery experiments, which provide a way to recover the specimens having been subjected to high pressures. Six different experiments are performed on the Omega laser using single-mode tantalum targets at different laser energies. The energy indicates the amount of laser energy that impinges the target. For each target, values for growth factor are obtained by comparing the profile of ripples before and after the experiment. With increasing energy, the growth factor increased.

Engineering simulations are used to interpret and correlate the measurements of growth factor to a measure of strength. In order to validate the engineering constitutive model for tantalum, a series of simulations are performed using the code Eureka, based on the Optimal Transportation Meshfree (OTM) method. Two different configurations are studied in the simulations: RM instabilities in single and multimode ripples. Six different simulations are performed for the single ripple configuration of the RM instability experiment, with drives corresponding to laser energies used in the experiments. Each successive simulation is performed at higher drive energy, and it is observed that with increasing energy, the growth factor increases. Overall, there is favorable agreement between the data from the simulations and the experiments. The peak growth factors from the simulations and the experiments are within 10% agreement. For the multimode simulations, the goal is to assist in the design of the laser driven experiments using the Omega laser. A series of three-mode and four-mode patterns are simulated at various energies and the resulting growth of the RM instability is computed. Based on the results of the simulations, a configuration is selected for the multimode experiments. These simulations also serve as validation for the constitutive model and the material parameters for tantalum that are used in the simulations.

By designing samples with initial perturbations in the form of single-mode and multimode ripples and subjecting these samples to high pressures, the Richtmyer-Meshkov instability is investigated in both laser compression experiments and simulations. By correlating the growth of these ripples to measures of strength, a better understanding of the strength of tantalum at high pressures is achieved.

Kautxu birziklatuzko materialek inpaktura duten erantzunaren simulazioa.

[EU]Ondorengo lanean ingeniaritzaren eremuan aurkitzen den eginkizunik garrantzitsuenetako bat egingo da: material berri bat karakterizatu. Hau da, errealitatean ikusten duguna era matematiko batean idatzi, edo beste era batean esanda, modelo matematiko bat lortu. Jorratuko den materiala kautxu birziklatua izango da, pneumatiko zaharretatik abiatuz egiten dena. Material honek, besteak beste, hurrengo abantailak ditu: produzitzeko erraza (beraz, prezio ekonomikoak, lehengaiak hondakin solidoak direla ikusita) eta inpakturako erantzun ona. Kautxu hau, beste erabileren artean, segurtasun-errailetan erabiltzen da, moto-gidariak ebaketetatik babesteko. Modelo matematikoa edo konstitutiboa lortzeko, lege hiperelastiko eta biskoelastikoetatik abiatuz, portaera bisko-hiperelastikorako lege bat proposatuko da. Lege hau deformazio handietarako eta deformazio abiadura handietarako aplikatu egingo da. Honen oinarria aurreko urteetan eskola honetako beste ikasleek eginiko gradu eta karrera amaierako lanak izango dira. Behin hau izanda, elementu finituetako software baten bidez simulatuko da, eta emaitza numerikoak esperimentalekin alderatuko dira. Honen bidez, modeloa hobetu ahal izango dugu, zehaztasun gehiago lortzeko asmoz.

Análise tensão deformação de uma barragem de concreto em solo residual preponderantemente anisotrópico.

Estudos de fundações de obras de arte, como barragens de concreto-gravidade e barragens de terra, devem contemplar todos os esforços atuantes no maciço de fundação, principalmente as tensões e as deformações esperadas durante todo o processo construtivo e no período pós-construtivo. Quando essas estruturas são apoiadas sobre rochas de boa sanidade, a escolha do barramento geralmente favorece a implantação de barragens de concreto. Entretanto, quando os maciços de fundação são formados por solos, a opção técnica geralmente mais bem aceita é quanto à utilização de barragens de terra. Em ambos os casos, as análises de estabilidade e de deformação são desenvolvidas por métodos analíticos bem consolidados na prática. Nas condições mais adversas de fundação, seja em rochas ou em solos com marcante anisotropia e estruturas reliquiares herdadas da rocha-mãe, a utilização de modelos constitutivos anisotrópicos em análises por elementos finitos propicia simulações mais realistas dessas feições estruturais, contribuindo para o seu melhor conhecimento. O presente trabalho teve por objetivo demonstrar a utilização de um modelo constitutivo anisotrópico no estudo da fundação da Barragem San Juan, localizada na República Dominicana, que foi concebida como uma estrutura tipo concreto-gravidade apoiada sobre solos residuais jovens altamente anisotrópicos. Nessa obra, apesar de sua pequena altura, a presença marcante de descontinuidades ensejou um estudo mais detalhado do comportamento tensão-deformação da fundação, levando em conta o levantamento detalhado da atitude das descontinuidades presentes no maciço e os resultados de ensaios de resistência em planos paralelos e normais às descontinuidades. Para a estimativa de deformações, os respectivos módulos de Young (Es) foram estimados com base em correlações com a resistência à penetração SPT desenvolvidas nesta dissertação, a partir de um estudo estatístico baseado em várias publicações disponíveis na literatura. As análises numéricas por elementos finitos foram desenvolvidas através do programa Plaxis 2D, utilizando-se como modelo constitutivo aquele denominado The Jointed Rock Model, que é particularmente recomendado para análises de estabilidade e deformação de materiais anisotrópicos. Os resultados das análises numéricas foram comparados com as análises de equilíbrio limite elaboradas para o projeto executivo da referida barragem, pelo programa Slope, utilizando o método rigoroso de Morgenstern e Price, que se mostrou conservador. Os resultados das análises numéricas mostraram sua inequívoca versatilidade para a escolha de opções de reforço da fundação, através de dentes que objetivavam o aumento das condições de estabilidade da barragem.

Finite element modelling of the sismic behaviour of water front structures

Water front structures have suffered significant damage in many of the recent earthquakes. These include gravity type quay walls, vertically composite walls, cantilever retaining walls, anchored bulkheads and similar structures. One of the primary causes for the poor performance of these classes of structures is the liquefaction of the foundation soil and in some instances liquefaction of the backfill soil. The liquefaction of the soil in-front of the quay wall tends to cause large lateral displacements and rotation of the wall. Often such gravity walls are placed on rubble mound deposited onto the sea bed.This paper presents finite element analyses of such a problem in which strength degradation of the foundation soil and the backfill material will be modelled using PZ mark III constitutive model. The performance of the wall in terms of its lateral displacement, vertical settlement and/or the rotation suffered by the wall will be presented. In addition, the contours of the horizontal and vertical effective stresses and the excess pore pressure ratio will be presented at different time instants together with hyrdraulic gradients. Immediately after the earthquake, the hydraulic gradients indicate migration of pore water into the region below the wall, suggesting further softening of the foundation soil below the wall.

Experimental and numerical investigation of fracture mechanics of bitumen beams

This work presents an experimental and numerical investigation to characterise the fracture properties of pure bitumen (the binder in asphalt paving materials). The paper is divided into two parts. The first part describes an experimental study of fracture characterisation parameters of pure bitumen as determined by three-point bend tests. The second part deals with modelling of fracture and failure of bitumen by Finite Element analysis. Fracture mechanics parameters, stress intensity factor, KIC, fracture energy, GIC, and J-integral, JIC, are used for evaluation of bitumen's fracture properties. The material constitutive model developed by Ossa et al. [40,41] which was implemented into a FE code by Costanzi [18] is combined with cohesive zone models (CZM) to simulate the fracture behaviour of pure bitumen. Experimental and numerical results are presented in the form of failure mechanism maps where ductile, brittle and brittle-ductile transition regimes of fracture behaviour are classified. The FE predictions of fracture behaviour match well with experimental results. © 2012 Elsevier Ltd.