Viscoelastic Minimum Principles Revisited

1996 ◽  
Vol 63 (2) ◽  
pp. 551-554 ◽  
Author(s):  
S. Hazanov
Keyword(s):  
Effective Properties ◽  
General Algorithm ◽  
Viscoelastic Materials ◽  
Theoretical Evaluation ◽  
Simple Bounds ◽  
Viscoelastic Composites

A problem of viscoelastic counterparts for the elastic minimum theorems is considered. A theorem is proved that gives a general algorithm for the construction of such viscoelastic minimum functionals. The established results are applied for the theoretical evaluation of the effective properties of inhomogeneous viscoelastic materials. As an example, simple bounds on the effective properties of viscoelastic composites are obtained.

Prediction of Microelectronic Substrate Warpage Using Homogenized Thermomechanical Finite Element Models

2005 ◽  
Author(s):  
Parsaoran Hutapea ◽  
Joachim L. Grenestedt ◽  
Mitul Modi ◽  
Michael Mello ◽  
Kristopher Frutschy
Keyword(s):  
Finite Element ◽  
Effective Properties ◽  
Isothermal Condition ◽  
Numerical Approach ◽  
Thermomechanical Properties ◽  
Temperature Changes ◽  
Numerical Predictions ◽  
Homogenization Approach ◽  
Simple Bounds ◽  
Complex Features

High-density microelectronic substrates, used in organic CPU packages, are comprised of several polymer, fiber-weave, and copper layers and are filled with a variety of complex features such as traces, micro-vias, Plated-Through-Holes (PTH), and adhesion holes. When subjected to temperature changes, these substrates may warp, driven by the mismatch in Coefficients of Thermal Expansion (CTE) of the constituent materials. This study focused on predicting substrate warpage in an isothermal condition. The numerical approach consisted of three major steps: estimating homogenized (effective) thermomechanical properties of the features; calculating effective properties of discretized layers using the effective properties of the features; and assembling the layers to create 2D Finite Element (FE) plate models and to calculate warpage of the whole substrates. The effective properties of the features were extracted from 3D unit cell FE models, and closed-form approximate expressions were developed using the numerical results, curve fitting, and some simple bounds. The numerical approach was applied to predict warpage of production substrates, analyzed, and validated against experimentally measured stiffness and CTEs. In this paper, the homogenization approach, numerical predictions, and experimental validation are discussed.

scholarly journals Micromechanical modelling of porous viscoelastic composite materials

2018 ◽  
Vol 191 ◽  
pp. 00007
Author(s):  
Mohamed El Kouri ◽  
Abderrahmane Bakkali ◽  
Lahcen Azrar
Keyword(s):  
Effective Properties ◽  
Methodological Approach ◽  
Micromechanical Model ◽  
Mean Field ◽  
Viscoelastic Composite ◽  
Field Techniques ◽  
Viscoelastic Matrix ◽  
Convolution Products ◽  
Viscoelastic Composites ◽  
Effective Behavior

Modelling and predicting the effective behavior of non-ageing viscoelastic composites have attracted the attention of many researchers. Actually, predicting the effective behavior and the macroscopic overall response while taking into account the constituents properties and shape of inclusions as well as their volume fractions is a challenging topic. In this work, porous viscoelastic composites are considered. The porous effect is introduced as a solid voided inclusions embedded in a viscoelastic matrix. The effective behavior is modelled by delayed integropartial differential equations. The resolution of the resulting equations is done through a methodological approach based on the Volterra tensorial products and the dynamic Green‘s tensor. Thus, the localization equations relating the local and the global fields are derived. After that, the Mori-Tanaka mean field micromechanical model assumptions are applied to derive the Mori-Tanaka‘s localization tensor. Once this step is completed, the effective properties are obtained through mean field techniques. The effective properties are given through tensorial convolution products. A numerical algorithm is elaborated for the computation of direct and inverse tensorial convolution products. For the validation of the developed modelling a comparison with Laplace-Carson approach is done.

Simply supported FPEDs connected by springs for broadband energy harvesting

2020 ◽  
Vol 64 (1-4) ◽  
pp. 201-210
Author(s):  
Yoshikazu Tanaka ◽  
Satoru Odake ◽  
Jun Miyake ◽  
Hidemi Mutsuda ◽  
Atanas A. Popov ◽  
...  
Keyword(s):  
Energy Harvesting ◽  
Evaluation Method ◽  
Energy Harvester ◽  
Vibrational Energy ◽  
Functional Materials ◽  
Vibration Energy ◽  
Theoretical Evaluation ◽  
Vibration Energy Harvester ◽  
Polyvinylidene Difluoride ◽  
Simply Supported

Energy harvesting methods that use functional materials have attracted interest because they can take advantage of an abundant but underutilized energy source. Most vibration energy harvester designs operate most effectively around their resonant frequency. However, in practice, the frequency band for ambient vibrational energy is typically broad. The development of technologies for broadband energy harvesting is therefore desirable. The authors previously proposed an energy harvester, called a flexible piezoelectric device (FPED), that consists of a piezoelectric film (polyvinylidene difluoride) and a soft material, such as silicon rubber or polyethylene terephthalate. The authors also proposed a system based on FPEDs for broadband energy harvesting. The system consisted of cantilevered FPEDs, with each FPED connected via a spring. Simply supported FPEDs also have potential for broadband energy harvesting, and here, a theoretical evaluation method is proposed for such a system. Experiments are conducted to validate the derived model.

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