Srinivasan M. Sivakumar

Two models to simulate rate-dependent domain switching effects—application to ferroelastic polycrystalline ceramics

The aim of this paper is to study rate-dependent switching in ferroelastic materials. More specifically, a micro-mechanically motivated model is embedded into an iterative three-dimensional and electromechanically coupled finite element framework. An established energy-based criterion serves for the initiation of domain switching processes as based on reduction in (local) Gibbs free energy. Subsequent nucleation and propagation of domain walls is captured via a linear kinetics theory with rate-dependent effects being incorporated in terms of a deformation-dependent limit-time-parameter. With this basic model in hand, two different switching formulations are elaborated in this work: on the one hand, a straightforward volume-fraction-ansatz is applied with the volume-fraction-value depending on the limit-time-parameter; on the other hand, a reorientation-transformation-formulation is proposed, whereby the orientation tensor itself is assumed to depend on the limit-time-parameter. Macroscopic behaviour such as stress versus strains curves or stress versus electrical displacements graphs are obtained by applying straightforward volume-averaging-techniques to the three-dimensional finite-element-based simulation results which provides important insights into the rate-dependent response of the investigated ferroelastic materials. (Less)

A thermodynamically motivated model for ferroelectric ceramics with grain boundary effects

The aim of this paper is to capture the grain boundary effects taking into consideration the nonlinear dissipative effects of ferroelectric polycrystals based on firm thermodynamic principles. The developed micromechanically motivated model is embedded into an electromechanically coupled finite element formulation in which each grain is represented by a single finite element. Initial dipole directions are assumed to be randomly oriented to mimic the virgin state of the unpoled ferroelectric polycrystal. An energy-based criterion using Gibbs free energy is adopted for the initiation of the domain switching process. The key aspect of the proposed model is the incorporation of effects of the constraint imposed by the surrounding grains on a switching grain. This is accomplished by the inclusion of an additional term in the domain switching criterion that is related to the gradient of the driving forces at the boundary of the grains. To study the overall bulk ceramics behavior, a simple volume-averaging technique is adopted. It turns out that the simulations based on the developed finite element formulation with grain boundary effects are consistent with the experimental data reported in the literature.

Interface Fracture Assessment on Sandwich DCB Specimens

This article examines the fracture behavior of sandwich type double cantilever beam (DCB) specimens under monotonic and cyclic loading conditions. The specimen consists of two layers of OFHC copper and one layer of ViaLux 81 photo-definable dry film. The ViaLux 81 is placed in between copper layers. Analytical expression for the strain energy release rate (GI) of the sandwich DCB specimen is derived by following the plate theory based model and compliance method. Finite element analysis has also been carried out on the specimen and the load displacement results for the specified crack or delamination length are obtained. The compliance equation in terms of the delamination length is derived for the specimens for obtaining the strain energy release rate (GI). From the generated R-curve of the interface, the failure load is estimated for the specified delamination length. From the crack growth data, the number of cycles to failure under cyclic loading is estimated for the initial delamination length.

A Performance Study on Configurational Force and Spring-Analogy Based Mesh Optimization Schemes

Assessment of r-adaption algorithms based on configurational force method and spring analogy approach is made. Assessment is made based on qualitative and quantitative aspects of error estimates, convergence rates and mesh quality. Appropriate modifications to node relocation procedures are proposed for enhanced performance. A simple linear projection technique is used to improve convergence characteristics of the material force node relocation algorithm. Performing mesh adaption on initial mesh results in a considerable reduction in gradients of strain energy. Assessment based on suitability of mesh adaption algorithms for structured and unstructured initial meshes has been performed. It has been observed that the configurational force method is more robust. Comparitive study indicates the superiority of the configurational force method. The proposed enhancement to the mesh adaption is based on configuration force method for r-adaption together with weighted Laplacian smoothing and mesh enrichment through h-refinement based on estimated discretization error in energy norm. A further reduction in the potential energy and the relative error norm of the system is found to be achieved with combined r-adaption and mesh enrichment (in the form of h-refinement). Numerical study confirms that the proposed combined r − h adaption is more efficient than a purely h-adaptive approach and more flexible than a purely r-adaptive approach with better convergence characteristics.

Rotational-Mode-Shape-Based Added Mass Identification Using Wavelet Packet Transform

A novel approach is proposed in this article that the combination of rotational mode shape with wavelet packet transform can detect the relatively small added mass (damage) location and its intensity in a beam structure. The rotational mode shapes of added mass state are obtained from a finite element model and used as input in wavelet analysis to capture signatures arising from even small damage in the beam. The proposed algorithm is able to clearly identify single and multiple added mass locations and their intensities in a cantilever beam. It is also tested with noise-contaminated signals to show its feasibility in practical situations.

Nonlinear and time-dependent electromechanical behavior of polyvinylidene fluoride

This paper describes the results from electromechanical tests conducted on polyvinylidene fluoride (PVDF) sheets showing its nonlinear and time-dependent electromechanical behavior. Mechanical and electromechanical tests were carried out for both uniaxially stretched and biaxially stretched PVDF sheets. The tests show nonlinearity in both the stress–strain response and the time-dependent response. Electromechanical dynamic tests were conducted at various superimposed pre-stress conditions. From the dynamical electromechanical tests, it is found that both biaxially stretched and uniaxially stretched PVDF sheets exhibit pre-stress dependence of their electromechanical coefficients. In addition, an attempt has been made to model the mechanical and the electromechanical behavior using a simple three-parameter viscoelastic solid model. The model captures the trends observed in the experiments and is recommended as a useful tool for designs using these materials.

A study on the design and behavior of smart antenna

In this paper, a methodology to control the surface error on a Doppler antenna using the concept of a variable geometry truss structure is proposed. A genetic algorithm is used to find the optimal location and number of actuators with the objective to minimize the construction and runtime costs. The optimization also takes into account the limitations in actuation. A piezoceramic-based actuator is used to demonstrate the effectiveness of the methodology. A simple illustration of 2D trusses, which could form a part of a Doppler antenna structure, is used to show the efficacy of the method. An analysis of the effectiveness of such a design is presented. The influence of the variables in the problem is examined and observations made. This study concludes that the smart antenna concept is a viable, feasible and effective option in design.

Influence of viscoelasticity of protein on the toughness of bone

Bone is an ultrafine composite of protein (collagen) and mineral (hydroxyapatite). An analysis to determine the influence of the viscoelasticity of protein on the toughness of bone at the ultrafine scale is conducted by developing a discrete lattice model appropriate for the ultrafine scale called the incremental continuous damage random fuse model (ICDRFM). Collagen viscoelasticity at ultrafine scale is shown to contribute significantly to the toughness of bone. The results obtained are important in the design of biomimetic ultratough artificial composites.

INFLUENCE OF RELATIVE STRENGTH OF CONSTITUENTS ON THE OVERALL STRENGTH AND TOUGHNESS OF BONE

Biocomposites such as bone exhibit synergistic superior mechanical properties compared to its constituents, protein (collagen) and mineral (hydroxyapatite). The importance of properties of constituents at the submicron scale with regard to the toughness and strength of bone is investigated employing a discrete lattice model. The results show that matrix failure as opposed to platelet breakage provides better toughness to the bone. There is a fairly sudden increase in the toughness of bone when the strength of mineral platelet to that of protein crosses a particular critical value. These could provide clues to the preparation of ultra-tough artificial composites and the treatment of diseases related to fragility of bone.

Energy Based Adaptive Strategy for Plates and Laminates

The objective of this work is the development of a numerical solution strategy for energy–based mesh optimization based on a combined refinement strategy for laminated composite plates. In finite element computations that rely on the principle of minimum potetnial energy, the variational principle itself provides the basis of r-adaptive methods. The numerical solution can be improved by further minimizing the discrete potetnial energy with respect to material node point positions. A new adaptive scheme has been proposed and formulated for adaptive finite element analysis of laminates and plates. It involves a combination of the configurational force based r− adaption and mesh enrichment by h−refinement. These configurational forces are conjugate to the nodal motion and vanish when the potential energy is a minimum or at equilibrium. These forces are evaluated for laminates and plates by considering the weak form of the material force equilibrium. These forces assembled at nodes in a finite element discretization act as error indicators for r− adaption. The h− refinement is based on a modified patch recovery based estimator based on quantities of interest, enhanced by strain energy density ratios. Numerical study confirms that the proposed combined r − h adaption is more efficient than a purely h−adaptive approach and more flexible than a purely r−adaptive approach with better convergence characteristics.