Peridynamic Modeling of Hyperelastic Membrane Deformation

2017 ◽  
Vol 139 (3) ◽  
Author(s):  
D. J. Bang ◽  
E. Madenci
Keyword(s):  
Energy Density ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Equations Of Motion ◽  
Uniaxial Loading ◽  
Density Functions ◽  
Loading Conditions ◽  
Element Analysis ◽  
Material Parameters ◽  
Loading Case

This study concerns the development of peridynamic (PD) strain energy density functions for a Neo-Hookean type membrane under equibiaxial, planar, and uniaxial loading conditions. The material parameters for each loading case are determined by equating the PD strain energy density to that of the classical continuum mechanics. The PD equations of motion are derived based on the Neo-Hookean model under the assumption of incompressibility. Numerical results concern the deformation of a membrane with a defect in the form of a hole, a crack, and a rigid inclusion under equibiaxial, planar, and uniaxial loading conditions. The PD predictions are verified by comparison with those of finite element analysis.

scholarly journals Peridynamic model for visco-hyperelastic material deformation in different strain rates

2019 ◽  
Author(s):  
Yunke Huang ◽  
Selda Oterkus ◽  
Hong Hou ◽  
Erkan Oterkus ◽  
Zhengyu Wei ◽  
...  
Keyword(s):  
Energy Density ◽  
Density Function ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Surface Defects ◽  
Force Density ◽  
Strain Rates ◽  
Element Analysis ◽  
Material Parameters ◽  
Peridynamic Model

AbstractThis study presents a peridynamic (PD) constitutive model for visco-hyperelastic materials under homogenous deformation. The constitutive visco-hyperelastic model is developed in terms of Yeoh strain energy density function and Prony series. The material parameters in the model are identified by optimizing the classical stress–strain relation and tension test data for different strain rates. The peridynamic visco-hyperelastic force density function is proposed in terms of the peridynamic integral and the Yeoh strain energy density. The time-dependent behaviour for different strain rates is captured by numerical time integration representing the material parameters. The explicit form of peridynamic equation of motion is then constructed to analyse the deformation of visco-hyperelastic membranes. The numerical results concern the deformation and damage prediction for a polyurea membrane and membrane-type acoustic metamaterial with inclusions under homogenous loading. Different surface defects are considered in the simulation. The peridynamic predictions are verified by comparing with finite element analysis results.

On the energy consumption for crack development in fibre wall in disc refining – A micromechanical approach

Holzforschung ◽  
2009 ◽  
Vol 63 (2) ◽  
Author(s):  
Jan-Erik Berg ◽  
Mårten E. Gulliksson ◽  
Per A. Gradin
Keyword(s):  
Energy Density ◽  
Strain Energy ◽  
Microfibril Angle ◽  
Shear Load ◽  
Damage State ◽  
Material Parameters ◽  
Micromechanical Approach ◽  
Damage States ◽  
Loading Case ◽  
Specific Fracture

Abstract An analytical model has been applied to calculate the acquired strain energy density in order to achieve a certain damage state in a softwood fibre by uniaxial tension or shear load. The energy density was found to be dependent on the microfibril angle in the middle secondary wall, the loading case, the thicknesses of the fibre cell wall layers, and conditions, such as moisture content and temperature. At conditions, prevailing at the entrance of the gap between the plates in a refiner and at relative high damage states, more energy is needed to create cracks at higher microfibril angles. The energy density was lower for earlywood compared to latewood fibres. For low microfibril angles, the energy density was lower for loading in shear compared to tension for both earlywood and latewood fibres. Material parameters, such as initial damage state and specific fracture energy, were determined by fitting of input parameters to experimental data.

Thermal Fatigue Prediction for Leadless Solder Joint of TFBGA

2006 ◽  
Author(s):  
Chia-Lung Chang ◽  
Tzu-Jen Lin ◽  
Chih-Hao Lai
Keyword(s):  
Energy Density ◽  
Solder Joint ◽  
Creep Strain ◽  
Thermal Fatigue ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Creep Property ◽  
Inelastic Strain ◽  
Temperature Cycling ◽  
Element Analysis

Nonlinear finite element analysis was performed to predict the thermal fatigue for leadless solder joint of TFBGA Package under accelerated TCT (Temperature Cycling Test). The solder joint was subjected to the inelastic strain that was generated during TCT due to the thermal expansion mismatch between the package and PCB. The solder was modeled with elastic-plastic-creep property to simulate the inelastic deformation under TCT. The creep strain rate of solder was described by double power law. The furthest solder away from the package center induced the highest strain during TCT was considered as the critical solder ball to be most likely damaged. The effects of solder meshing on the damage parameters of inelastic strain range, accumulated creep strain and creep strain energy density were compared to assure the accuracy of the simulation. The life prediction equation based on the accumulated creep strain and creep strain energy density proposed by Syed was used to predict the thermal fatigue life in this study. The agreement between the prediction life and experimental mean life is within 25 per cent. The effect of die thickness and material properties of substrate on the life of solder was also discussed.

Constitutive Equations for Hyperelastic Materials Based on the Upper Triangular Decomposition of the Deformation Gradient

2018 ◽  
Vol 24 (6) ◽  
pp. 1785-1799 ◽  
Author(s):  
Y. Q. Li ◽  
X.-L. Gao
Keyword(s):  
Energy Density ◽  
Constitutive Equations ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Deformation Gradient ◽  
Density Functions ◽  
Triangular Decomposition ◽  
Deformation Gradient Tensor ◽  
Hyperelastic Materials ◽  
Distortion Tensor

The upper triangular decomposition has recently been proposed to multiplicatively decompose the deformation gradient tensor into a product of a rotation tensor and an upper triangular tensor called the distortion tensor, whose six components can be directly related to pure stretch and simple shear deformations, which are physically measurable. In the current paper, constitutive equations for hyperelastic materials are derived using strain energy density functions in terms of the distortion tensor, which satisfy the principle of material frame indifference and the first and second laws of thermodynamics. Being expressed directly as derivatives of the strain energy density function with respect to the components of the distortion tensor, the Cauchy stress components have simpler expressions than those based on the invariants of the right Cauchy-Green deformation tensor. To illustrate the new constitutive equations, strain energy density functions in terms of the distortion tensor are provided for unconstrained and incompressible isotropic materials, incompressible transversely isotropic composite materials, and incompressible orthotropic composite materials with two families of fibers. For each type of material, example problems are solved using the newly proposed constitutive equations and strain energy density functions, both in terms of the distortion tensor. The solutions of these problems are found to be the same as those obtained by applying the polar decomposition-based invariants approach, thereby validating and supporting the newly developed, alternative method based on the upper triangular decomposition of the deformation gradient tensor.

Elastoplastic Plane Strain Analysis of Stresses and Strains at the Notch Root

1988 ◽  
Vol 110 (3) ◽  
pp. 195-204 ◽  
Author(s):  
G. Glinka ◽  
W. Ott ◽  
H. Nowack
Keyword(s):  
Energy Density ◽  
Plane Strain ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Notch Root ◽  
Equivalent Strain ◽  
Element Analysis ◽  
Elastic Plastic ◽  
Energy Concept ◽  
Notch Tip

For the evaluation of the local elastoplastic strains and stresses at the notch root suitable approximation formulas of sufficient accuracy are often used. In the present study the “equivalent strain energy density” concept for elastic-plastic notch strain-stress analysis has been developed. It was found that the evaluation of the strain energy density in the notch tip plastic zones does not require any input data other than the material stress-strain relation and the elastic stress concentration factor. The concept was verified on the basis of the results obtained from plane strain elastic-plastic finite element analysis using the material model after Mro´z. Comparison of the two sets of results revealed satisfactory accuracy of the equivalent strain energy concept. It was also shown that all stress and strain components in the notch tip can be calculated by complementing the method with Hencky’s equations. Neuber-based calculations were also included in the study. It was found that the energy concept was superior to Neuber’s rule, especially in the presence of high inelastic strains in the notch tip.

scholarly journals A New Constitutive Model for Several Metals Under Arbitrary Temperature and Loading Conditions

1993 ◽  
Author(s):  
P. W. Whaley
Keyword(s):  
Energy Density ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Axial Loading ◽  
Deviatoric Stress ◽  
Loading Conditions ◽  
State Equations ◽  
Temperature Range ◽  
Stress Plane ◽  
Plastic Strain Energy

A new theory of viscoplasticity is described which models yielding as a random phenomenon. A circle on the deviatoric stress plane represents the intensity of yielding with the radius equal to the random yielding microstress. This random model does not utilize a yield surface; yielding intensity is quantified by expected values defined in the deviatoric stress plane. The circle in the deviatoric stress plane with a random radius is a simple way to model multi-axial loading. Approximations for stress, strain energy density and plastic strain energy density are used to improve the computational efficiency of parameter selection and to quantify the flow criterion. The exact state equations are derived which can be manipulated to describe a wide variety of loading conditions for a broad temperature range. Reversed loading, stress relaxation, creep and nonproportional loading are all natural properties of the model which require little additional elaboration. Material properties were specified for five metals, three at room temperature and two over a wide temperature range.

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