Analysis of Transverse Shear Strains in Pre-Twisted Thick Beams using Variational Asymptotic Method

The cross-sectional stiffness matrix is derived for a pre-twisted, moderately thick beam made of transversely isotropic materials and having rectangular cross sections. An asymptotically-exact methodology is used to model the anisotropic beam from 3-D elasticity, without any further assumptions. The beam is allowed to have large displacements and rotations, but small strain is assumed. The strain energy is computed making use of the beam constitutive law and kinematical relations derived with the inclusion of geometrical nonlinearities and an initial twist. The energy functional is minimized making use of the Variational Asymptotic Method (VAM), thereby reducing the cross section to a point on the beam reference line with appropriate properties, forming a 1-D constitutive law. VAM is a mathematical technique employed in the current problem to rigorously split the 3-D analysis of beams into two: a 2-D analysis over the beam cross-sectional domain, which provides a compact semi-analytical form of the properties of the cross sections, and a nonlinear 1-D analysis of the beam reference curve. In this method, as applied herein, the cross-sectional analysis is performed asymptotically by taking advantage of a material small parameter and two geometric small parameters. 3-D strain components are derived using kinematics and arranged in orders of the small parameters. Closed-form expressions are derived for the 3-D non-linear warping and stress fields. Warping functions are obtained by the minimization of strain energy subject to certain set of constraints that render the 1-D strain measures well-defined. The zeroth-order 3-D warping field thus yielded is then used to integrate the 3-D strain energy density over the cross section, resulting in the 1-D strain energy density, which in turn helps identify the corresponding cross-sectional stiffness matrix. The model is capable of predicting interlaminar and transverse shear stresses accurately up to first order.

Biomechanical Properties of Human Ascending Thoracic Aortic Dissections

Thoracic aortic dissections are associated with a significant risk of morbidity and mortality, and currently challenge our understanding of the biomechanical factors leading to their initiation and propagation. We quantified the biaxial mechanical properties of human type A dissections (n = 16) and modeled the stress-strain data using a microstructurally motivated form of strain energy function. Our results show significantly higher stiffness for dissected tissues as compared to control aorta without arterial disease. Higher stiffness of dissected tissues did not, however, correlate with greater aortic diameter measured prior to surgery nor were there any age dependent differences in the tissue properties.

Multiobjective Optimization of Piezoelectric Bimorph Actuator with Rigid Extension

Production of high tip deflection in a piezoelectric bimorph laminar actuator by applying high voltage is limited by many physical constraints. Therefore, piezoelectric bimorph actuator with a rigid extension of non-piezoelectric material at its tip is used to increase the tip deflection of such an actuator. Research on this type of piezoelectric bending actuator is either limited to first order constitutive relations, which do not include non-linear behavior of piezoelectric element at high electric field, or limited to curve fitting techniques. Therefore, this paper considers high electric field, and analytically models tapered piezoelectric bimorph actuator with a rigid extension of non-piezoelectric material at its tip. The stiffness, capacitance, effective tip deflection, block force, output strain energy, output energy density, input electrical energy and energy efficiency of the actuator are calculated analytically. The paper also discusses the multi-objective optimization of this type of actuator subjected to the mechanical and electrical constraints.

On the critical thickness for non-localized to localized plastic flow transition in metallic glasses: A molecular dynamics study

Molecular dynamics simulations were employed to investigate the specimen thickness-dependent tensile behavior of a series of Cu(x)Z(100-x) (x = 20, 40, 50, 64 and 80 at%) metallic glass (MG) films, with a particular focus on the critical thickness, tc, below which non-localized plastic flow takes place. The simulation results reveal that while the transition occurs in all the alloys examined, t(c) is sensitive to the composition. We rationalize t(c) by postulating that the strain energy stored in the sample at the onset of plastic deformation has to be sufficient for the formation of shear bands. The composition-dependence of t(c) was found to correlate with the average activation energy of the atomic level plastic deformation events. (C) 2015 Elsevier Ltd. All rights reserved.

Electromechanical analysis of piezoelectric bimorph actuator in static state considering the nonlinearity at high electric field

This article contains electromechanical analysis of a piezoelectric bimorph actuator at high electric field by incorporating second-order constitutive equations of piezoelectric material. Tip deflection, block force, block moment, block load, output strain energy, output energy density, input electrical energy, and energy efficiency are analytically derived for the actuator at high electric field. The analysis shows that output energy and energy density increase more rapidly at high electric field, compared to the prediction by the linear model. The analysis shows energy efficiency depends on electric field. Some analytical results are validated with the published experimental results.

利用广义应变比能进行结构损伤识别的数值研究

目前结构损伤识别大多是基于位移模态的试验结果进行的，但由于位移模态结果的局限性，很多情况下识别效果并不明显，本文基于应变模态的工作，利用应变模记识别得到的振型和频率结果，提出了广义应变比能（GSED）的概念。将其应用于结构损伤的识别中，具有识别效果明显，物理意义清晰的优点，GSED方法不仅可以判断损伤的存在与否，而且可以对损伤进行较精确的定位，在测试数据充分的情况下还可以大致判断出损伤的程度，最后通过对简支梁的数值仿真计算验证了方法的有效性。

Elastic-plastic constitutive relation of particle reinforced composites

In this paper, a systematic approach is proposed to obtain the macroscopic elastic-plastic constitutive relation of particle reinforced composites (PRC). The strain energy density of PRC is analyzed based on the cell model, and Che analytical formula for the macro-constitutive relation of PRC is obtained. The strength effects of volume fraction of the particle and the strain hardening exponent of matrix material on the macro-constitutive relation are investigated, the relation curve of strain versus stress of PRC is calculated in detail. The present results are consistent; with the results given in the existing references.

Plastic constitutive behavior of short-fiber/particle reinforced composites

A cylindrical cell model based on continuum theory for plastic constitutive behavior of short-fiber/particle reinforced composites is proposed. The composite is idealized as uniformly distributed periodic arrays of aligned cells, and each cell consists of a cylindrical inclusion surrounded by a plastically deforming matrix. In the analysis, the non-uniform deformation field of the cell is decomposed into the sum of the first order approximate field and the trial additional deformation field. The precise deformation field are determined based on the minimum strain energy principle. Systematic calculation results are presented for the influence of reinforcement volume fraction and shape on the overall mechanical behavior of the composites. The results are in good agreement with the existing finite element analyses and the experimental results. This paper attempts to stimulate the work to get the analytical constitutive relation of short-fiber/particle reinforced composites.

On the Formation of Periodic Segmentation Cracks in a Coating Plated on a Substrate with Periodic Subsurface Inclusions

The mechanism of the formation of periodic segmentation cracks of a coating plated on a substrate with periodic subsurface inclusions (PSI) is investigated. The internal stress in coating and subsequently the strain energy release rate (SERR) of the segmentation cracks are computed with finite element method (FEM). And the effect of the geometrical parameters of the PSI is studied. The results indicate that the ratio of the width of the inclusion to the period of the repeated structure has an optimum value, at which the maximum internal tensile stress and SERR arise. On the other hand, the ratio of the max-thickness of the inclusion to the thickness of the coating has a threshold value, above which the further increase of this ratio should seldom influence the internal stress or the SERR.

Study of lateral mode SOI-MEMS resonators for reduced anchor loss

MEMS resonators fabricated in silicon-on-insulator (SOI) technology must be clamped to the substrate via anchoring stems connected either from within the resonator or through the sides, with the side-clamped solution often employed due to manufacturing constraints. This paper examines the effect of two types of commonly used side-clamped, anchoring-stem geometries on the quality factor of three different laterally-driven resonator topologies. This study employs an analytical framework which considers the relative distribution of strain energies between the resonating body and clamping stems. The ratios of the strain energies are computed using ANSYS FEA and used to provide an indicator of the expected anchor-limited quality factors. Three MEMS resonator topologies have been fabricated and characterized in moderate vacuum. The associated measured quality factors are compared against the computed strain energy ratios, and the trends are shown to agree well with the experimental data. © 2011 IOP Publishing Ltd.

Effect Of A Negative Poisson Ratio In The Tension Of Ceramics

The effect of a negative Poisson ratio is experimentally revealed in the tension deformation of a natural layered ceramic. This effect can increase the volume strain energy per unit volume by 1100% and, simultaneously, decrease the deformation strain energy per unit volume by about 44%, so that it effectively enhances the deformation capacity by about 1 order of magnitude in the tension of the material. The present study also shows that the physical mechanisms producing the effect are attributed to the climbing on one another of the nanostructures in the natural material, which provides a guide to the design of synthetic toughening composites.

On the mechanism of void growth and the effect of straining mode in ductile materials

Finite element analysis is employed to investigate void growth embedded in elastic-plastic matrix material. Axisymmetric and plane stress conditions are considered. The simulation of void growth in a unit cell model is carried out over a wide range of triaxial tensile stressing or large plastic straining for various strain hardening materials to study the mechanism of void growth in ductile materials. Triaxial tension and large plastic strain encircling around the void are found to be of most importance for driving void growth. The straining mode of incremental loading which favors the necessary strain concentration around void for its growth can be characterized by the vanishing condition of a parameter called "the third invariant of generalized strain rate". Under this condition, it accentuates the internal strain concentration and the strain energy stored/dissipated within the material layer surrounding the void. Experimental results are cited to justify the effect of this loading parameter. (C) 2000 Elsevier Science Ltd. All rights reserved.

Long-range automaton models of earthquakes: Power-law accelerations, correlation evolution, and mode-switching

We introduce a conceptual model for the in-plane physics of an earthquake fault. The model employs cellular automaton techniques to simulate tectonic loading, earthquake rupture, and strain redistribution. The impact of a hypothetical crustal elastodynamic Green's function is approximated by a long-range strain redistribution law with a r(-p) dependance. We investigate the influence of the effective elastodynamic interaction range upon the dynamical behaviour of the model by conducting experiments with different values of the exponent (p). The results indicate that this model has two distinct, stable modes of behaviour. The first mode produces a characteristic earthquake distribution with moderate to large events preceeded by an interval of time in which the rate of energy release accelerates. A correlation function analysis reveals that accelerating sequences are associated with a systematic, global evolution of strain energy correlations within the system. The second stable mode produces Gutenberg-Richter statistics, with near-linear energy release and no significant global correlation evolution. A model with effectively short-range interactions preferentially displays Gutenberg-Richter behaviour. However, models with long-range interactions appear to switch between the characteristic and GR modes. As the range of elastodynamic interactions is increased, characteristic behaviour begins to dominate GR behaviour. These models demonstrate that evolution of strain energy correlations may occur within systems with a fixed elastodynamic interaction range. Supposing that similar mode-switching dynamical behaviour occurs within earthquake faults then intermediate-term forecasting of large earthquakes may be feasible for some earthquakes but not for others, in alignment with certain empirical seismological observations. Further numerical investigation of dynamical models of this type may lead to advances in earthquake forecasting research and theoretical seismology.

A field model interpretation of crack initiation and growth behavior in ferroelectric ceramics: change of poling direction and boundary condition

Strain energy density expressions are obtained from a field model that can qualitatively exhibit how the electrical and mechanical disturbances would affect the crack growth behavior in ferroelectric ceramics. Simplification is achieved by considering only three material constants to account for elastic, piezoelectric and dielectric effects. Cross interaction of electric field (or displacement) with mechanical stress (or strain) is identified with the piezoelectric effect; it occurs only when the pole is aligned normal to the crack. Switching of the pole axis by 90degrees and 180degrees is examined for possible connection with domain switching. Opposing crack growth behavior can be obtained when the specification of mechanical stress sigma(infinity) and electric field E-infinity or (sigma(infinity), E-infinity) is replaced by strain e and electric displacement D-infinity or (epsilon(infinity), D-infinity). Mixed conditions (sigma(infinity),D-infinity) and (epsilon(infinity),E-infinity) are also considered. In general, crack growth is found to be larger when compared to that without the application of electric disturbances. This includes both the electric field and displacement. For the eight possible boundary conditions, crack growth retardation is identified only with (E-y(infinity),sigma(y)(infinity)) for negative E-y(infinity) and (D-y(infinity), epsilon(y)(infinity)) for positive D-y(infinity) while the mechanical conditions sigma(y)(infinity) or epsilon(y)infinity are not changed. Suitable combinations of the elastic, piezoelectric and dielectric material constants could also be made to suppress crack growth. (C) 2002 Published by Elsevier Science Ltd.

Electrothermal stress in conductive body with collinear cracks

The temperature and stress field in a thin plate with collinear cracks interrupting an electric current field are determined. This is accomplished by using a complex function method that allows a direct means of finding the distribution of the electric current, the temperature and stress field. Temperature dependency for the heat-transfer coefficient, coefficient of linear expansion and the elastic modulus are considered. As an example, temperature distribution is calculated for an alloy (No. GH2132) plate with two collinear cracks under high temperature. Relationships between the stress, temperature, electric density and crack length are obtained. Crack trajectories emanating from existing crack are predicted by application of the strain energy density criterion which can also be used for finding the load carrying capacity of the cracked plate. (C) 2003 Elsevier Ltd. All rights reserved.