Nonlinear Dynamic Response of Piezoelectric Plates Considering Damage Effects

2006 ◽  
Vol 324-325 ◽  
pp. 299-302 ◽  
Author(s):  
Yi Ming Fu ◽  
Xian Qiao Wang
Keyword(s):  
Dynamic Response ◽  
Nonlinear Dynamic ◽  
Internal State ◽  
Constitutive Relations ◽  
Damage Model ◽  
State Variables ◽  
Nonlinear Dynamic Response ◽  
Internal State Variables ◽  
Nonlinear Dynamic Equations ◽  
Piezoelectric Plates

Based on the Talreja’s tensor valued internal state variables damage model and the Helmhotlz free energy of piezoelectric material, the constitutive relations of the piezoelectric plates with damage are derived. Then, the nonlinear dynamic equations of the piezoelectric plates considering damage are established. By using the finite difference method and the Newmark scheme, these equations are solved and the effects of damage and electric loads on the nonlinear dynamic response of piezoelectric plates are discussed.

Nonlinear Dynamic Response and Buckling of Damaged Composite Pipes Under Radial Impact

2006 ◽  
Author(s):  
Wenyong Tang ◽  
Tianlin Wang ◽  
Shengkun Zhang
Keyword(s):  
Dynamic Response ◽  
Shear Deformation ◽  
Nonlinear Dynamic ◽  
Shear Deformation Theory ◽  
Nonlinear Dynamic Response ◽  
Nonlinear Dynamic Equations ◽  
Geometric Deformation ◽  
Initial Geometric Imperfections ◽  
Set Up ◽  
Composite Pipes

In this paper, the nonlinear dynamic response and buckling of damaged composite pipes under radial impact is investigated. A model involving initial geometric deformation, delamination and sub-layer matrix damage is set up for theoretical analysis. Based on the first order shear deformation theory, the nonlinear dynamic equations of the composite pipe considering transverse shear deformation and initial geometric imperfections are obtained by Hamilton’s theory and solved by a semi-analytical finite difference method. The effects of damage on the dynamic response and buckling of composite pipes are discussed.

scholarly journals Modelling of single degree of freedom SMA oscillators by using rheological schemes

2018 ◽  
Vol 196 ◽  
pp. 01049
Author(s):  
Artur Zbiciak ◽  
Kacper Wasilewski
Keyword(s):  
Internal State ◽  
Constitutive Relations ◽  
Degree Of Freedom ◽  
State Variables ◽  
Numerical Application ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Internal State Variables ◽  
Load Removal ◽  
Modelling Approach

The article describes the approach to modelling of single degree of freedom SMA oscillators by using rheological schemes. Certain sets of rheological components are presented and their influence on the oscillator response is examined. Regarding the field of civil engineering, the devices incorporating SMA elements mostly find applications in mitigation of natural disaster hazards, such as earthquakes. The promising results of applications are possible due to unique properties of SMA, such as shape memory effect (recovering of relatively high strains while material is heated) and superelasticity (recovering of strains upon load removal). The most common approach to the formulation of SMAs constitutive relations is a thermomechanical modelling, in which constitutive equations are dependent on internal state variables. One of the advantages of the phenomenological modelling approach presented in the article is a possibility of formulation of constitutive relationships as a set of explicit differential equations. Such system of equations can be easily implemented in mathematical software or in the commercial FEM codes as a user's subroutines. As an example of numerical application of presented approach, the simple one-dimensional oscillator is used in order to solve the case of forced vibrations of a cantilever with embedded SMA reinforcement.

scholarly journals A Reactive Inelasticity Theoretical Framework for modeling Viscoelasticity, Plastic Deformation, and damage in Soft Tissue

2018 ◽  
Author(s):  
Babak N. Safa ◽  
Michael H. Santare ◽  
Dawn M. Elliott
Keyword(s):  
Plastic Deformation ◽  
Soft Tissue ◽  
Internal State ◽  
Constitutive Relations ◽  
Deformation Gradient ◽  
Theoretical Framework ◽  
External Loading ◽  
State Variables ◽  
Mechanical Behaviors ◽  
Internal State Variables

AbstractSoft tissues are biopolymeric materials, primarily made of collagen and water. These tissues have non-linear, anisotropic, and inelastic mechanical behaviors that are often categorized into viscoelastic behavior, plastic deformation, and damage. While tissue’s elastic and viscoelastic mechanical properties have been measured for decades, there is no comprehensive theoretical framework for modeling inelastic behaviors of these tissues that is based on their structure. To model the three major inelastic mechanical behaviors of soft tissue we formulated a structurally inspired continuum mechanics framework based on the energy of molecular bonds that break and reform in response to external loading (reactive bonds). In this framework, we employed the theory of internal state variables and kinetics of molecular bonds. The number fraction of bonds, their reference deformation gradient, and damage parameter were used as internal state variables that allowed for consistent modeling of all three of the inelastic behaviors of tissue by using the same sets of constitutive relations. Several numerical examples are provided that address practical problems in tissue mechanics, including the difference between plastic deformation and damage. This model can be used to identify relationships between tissue’s mechanical response to external loading and its biopolymeric structure.

Dynamic Response of the Fiber Metal Laminated (FML) Plate with Interfacial Damage in Unstable Temperature Field

2014 ◽  
Vol 490-491 ◽  
pp. 403-411
Author(s):  
Yi Ming Fu ◽  
Xue Fei Shao
Keyword(s):  
Dynamic Response ◽  
Nonlinear Dynamic ◽  
Constitutive Relations ◽  
Thin Layers ◽  
Interfacial Damage ◽  
Nonlinear Dynamic Response ◽  
Motion Equations ◽  
Nonlinear Motion ◽  
Fiber Metal ◽  
Unstable Temperature

During the past decades, increasing requirement in aircraft for high-performance, lightweight structures have caused strong interests on the development of fiber-metal laminates (FMLs), which are manufractured from thin layers of glass fibre reinforced composite and alluminium alloy. In this paper, the nonlinear dynamic response problem of the FML plate subjected to unstable temperature with interfacial damage is analyzed. Based on the weak bonded theory, the interfacial constitutive relations of the FML are constructed. According to the Hamiltons variance principle, the nonlinear motion equations of the FML with interfacial damages subjected to the unstable thermal field are obtained. And then, the finite difference, Newmark-and the iteration method are applied to solve the nonlinear motion equations. In the numerical examples, the effects of the interface damage, the amplitude and frequency of imposed loads and the temperature fields on the nonlinear dynamic response of the FML plates are investigated. And in conclusion, the effects of various type of temperature on the nonlinear dynamic response of FML plate are different obviously.

Damage Coupled With Heat Conduction in Uniaxially Reinforced Composites

1988 ◽  
Vol 55 (3) ◽  
pp. 641-647 ◽  
Author(s):  
Y. Weitsman
Keyword(s):  
Heat Conduction ◽  
Mechanical Response ◽  
Internal State ◽  
Constitutive Relations ◽  
Damage Model ◽  
Irreversible Thermodynamics ◽  
Continuum Damage ◽  
State Variables ◽  
Damage Growth ◽  
Continuum Damage Model

This paper presents a continuum damage model for a unidirectionally reinforced composite based upon fundamental concepts of continuum mechanics and irreversible thermodynamics. Damage is incorporated by two symmetric, second-rank, tensor-valued, internal state variables which represent the total areas of “active” and “passive” cracks contained within a representative material volume element. Constitutive relations are derived for both the mechanical response and heat flux in the presence of damage. It is shown that damage growth contributes to dissipation in the coupled heat conduction process. A specific fracture mechanics solution is employed to relate “microlevel” crack growth processes to “macrolevel” damage growth expressions. This approach lends itself to a probabilistic formulation of the continuum damage model.

Nonlinear Dynamic Response of Piezoelectric Beam Reinforced with BNNTs under Electro-Thermo-Mechanical Loadings

2014 ◽  
Vol 1065-1069 ◽  
pp. 1083-1086
Author(s):  
Jin Hua Yang ◽  
Wen Liang Fan
Keyword(s):  
Variational Principle ◽  
Dynamic Response ◽  
Nonlinear Dynamic ◽  
Constitutive Relations ◽  
Boron Nitride Nanotubes ◽  
Governing Equations ◽  
Nonlinear Dynamic Response ◽  
Numerical Examples ◽  
Piezoelectric Beam ◽  
The Finite Difference Method

This paper presents an investigation on the nonlinear dynamic response of piezoelectric beam reinforced with boron nitride nanotubes (BNNTs) under combined electro-thermo-mechanical loadings. By employing nonlinear strain and utilizing piezoelectric theory, the constitutive relations of the piezoelectric beam reinforced with BNNTs are established. Then the dynamic governing equations of the structure are derived through variational principle and resolved by applying the finite difference method. In numerical examples, the effects of geometric nonlinear, voltage etc. on the nonlinear dynamic response of piezoelectric beam reinforced with BNNTs are discussed.

A Continuum Damage Model for Viscoelastic Materials

1988 ◽  
Vol 55 (4) ◽  
pp. 773-780 ◽  
Author(s):  
Y. Weitsman
Keyword(s):  
Degrees Of Freedom ◽  
Internal State ◽  
Constitutive Relations ◽  
Damage Model ◽  
Uniaxial Stress ◽  
Continuum Damage ◽  
State Variables ◽  
Viscoelastic Materials ◽  
Continuum Damage Model ◽  
Special Cases

This paper presents a continuum damage model for viscoelastic materials. “Damage” is expressed by two symmetric, second rank tensors which are related to the total areas of “active” and “passive” microcracks within a representative volume element of the multifractured material. Viscoelasticity is introduced through scalar valued internal state variables that represent the internal degrees-of-freedom associated with the motions of long chain polymeric molecules. The constitutive relations are established from basic considerations of continuum mechanics and irreversible thermodynamics, with detailed expressions derived for the case of initially isotropic materials. It is shown that damage causes softening of the material moduli as well as changes in material symmetry. The special cases of uniaxial damage under uniaxial stress and the interaction of damage with moisture diffusion are also considered.

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