scholarly journals Modelling of Flexible Adhesives in Simple Mechanical States with the Use of the Darijani–Naghdabadi Strain Tensors and Kirchhoff–de Saint-Venant Elastic Potential

Polymers ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1639
Author(s):  
Paweł Szeptyński ◽  
Matija Gams ◽  
Arkadiusz Kwiecień
Keyword(s):  
Simple Shear ◽  
Strain Tensor ◽  
Limited Range ◽  
Constitutive Modelling ◽  
Elastic Potential ◽  
Experimental Results ◽  
Constitutive Law ◽  
Stress And Strain ◽  
Simple Tension ◽  
Non Linear

Practical aspects of modelling of flexible adhesives with the energy conjugate measures of stress and strain of the Darijani–Naghdabadi (D-N) family are discussed. A possibility of description of materials exhibiting non-linear physical characteristics with the use of non-linear geometric relationships and linear elastic constitutive law is considered. Nominal stress vs. stretch relations are specified in cases of simple tension and simple shear with the use of the Kirchhoff–de Saint-Venant elastic potential and D-N energy conjugate stress and strain measures. Obtained theoretical estimates were compared with experimental results of simple tension and simple shear tests performed on Sika PM polyurethane (Cracow, Sika Poland). The deformation rate was fixed in order to minimize the influence of viscosity. Values of parameters in the definition of the D-N strain tensor were optimized in order to provide good agreement between model predictions and experimental results. Observed discrepancies indicate that the proposed approach is not appropriate for constitutive modelling of the PM polymer. The presented approach is proposed to be used as a simple design model providing practical formulas describing the behavior of materials of non-linear characteristics in chosen mechanical states. Admissible values of exponents are discussed regarding its bijectivity in a limited range of variation of principal stretches.

Unified Constitutive Modelling of Nonlinear Time-Dependent Materials

1989 ◽  
Vol 42 (11S) ◽  
pp. S78-S82
Author(s):  
P. G. Glockner ◽  
W. Szyszkowski
Keyword(s):  
Strain Softening ◽  
Strain Tensor ◽  
Damage Function ◽  
Constitutive Modelling ◽  
Constitutive Law ◽  
Time Dependent ◽  
Type Integral ◽  
Characteristic Features ◽  
Stress Dependent ◽  
Semi Empirical

A semi-empirical engineering constitutive law modelling in a unified and continuous manner the main characteristic features of time-dependent materials, including creep, strain softening, relaxation and recovery and tensile brittleness, is briefly reviewed. The model, which contains 13 parameters, is a hereditary single Volterra-type integral representation of material response with stress/strain nonlinearity assumed in the form of a power law, the strain tensor dependent on the entire stress history and the stress-anisotropy/brittleness feature handled by means of a tensile-stress dependent damage function. The capability/versatility of the model is illustrated by examples for several materials.

Errors Caused by Non-Work-Conjugate Stress and Strain Measures and Necessary Corrections in Finite Element Programs

2010 ◽  
Vol 77 (4) ◽  
Author(s):  
Wooseok Ji ◽  
Anthony M. Waas ◽  
Zdeněk P. Bažant
Keyword(s):  
Finite Element ◽  
Fiber Composite ◽  
Strain Tensor ◽  
Stress And Strain ◽  
Hencky Strain ◽  
Tangential Stiffness ◽  
Jaumann Rate ◽  
Lagrangian Strain ◽  
Strain Formulation ◽  
Accurate Expression

Many finite element programs including standard commercial software such as ABAQUS use an incremental finite strain formulation that is not fully work-conjugate, i.e., the work of stress increments on the strain increments does not give a second-order accurate expression for work. In particular, the stress increments based on the Jaumann rate of Kirchhoff stress are work-conjugate with the increments of the Hencky (logarithmic) strain tensor but are paired in many finite element programs with the increments of Green’s Lagrangian strain tensor. Although this problem was pointed out as early 1971, a demonstration of its significance in realistic situations has been lacking. Here it is shown that, in buckling of compressed highly orthotropic columns or sandwich columns that are very “soft” in shear, the use of such nonconjugate stress and strain increments can cause large errors, as high as 100% of the critical load, even if the strains are small. A similar situation may arise when severe damage such as distributed cracking leads to a highly anisotropic tangential stiffness matrix, or when axial cracks between fibers severely weaken a uniaxial fiber composite or wood. A revision of these finite element programs is advisable, and will in fact be easy—it will suffice to replace the Jaumann rate with the Truesdell rate. Alternatively, the Green’s Lagrangian strain could be replaced with the Hencky strain.

Influence of pressure-dependent surface viscosity on dynamics of surfactant-laden drops in shear flow

2018 ◽  
Vol 858 ◽  
pp. 91-121 ◽  
Author(s):  
Zheng Yuan Luo ◽  
Xing Long Shang ◽  
Bo Feng Bai
Keyword(s):  
Shear Flow ◽  
Simple Shear ◽  
Surfactant Concentration ◽  
Constitutive Law ◽  
Simple Shear Flow ◽  
Drop Surface ◽  
Shear Surface ◽  
Surface Viscosity ◽  
Principal Axes ◽  
Surfactant Transport

We study numerically the dynamics of an insoluble surfactant-laden droplet in a simple shear flow taking surface viscosity into account. The rheology of drop surface is modelled via a Boussinesq–Scriven constitutive law with both surface tension and surface viscosity depending strongly on the surface concentration of the surfactant. Our results show that the surface viscosity exhibits non-trivial effects on the surfactant transport on the deforming drop surface. Specifically, both dilatational and shear surface viscosity tend to eliminate the non-uniformity of surfactant concentration over the drop surface. However, their underlying mechanisms are entirely different; that is, the shear surface viscosity inhibits local convection due to its suppression on drop surface motion, while the dilatational surface viscosity inhibits local dilution due to its suppression on local surface dilatation. By comparing with previous studies of droplets with surface viscosity but with no surfactant transport, we find that the coupling between surface viscosity and surfactant transport induces non-negligible deviations in the dynamics of the whole droplet. More particularly, we demonstrate that the dependence of surface viscosity on local surfactant concentration has remarkable influences on the drop deformation. Besides, we analyse the full three-dimensional shape of surfactant-laden droplets in simple shear flow and observe that the drop shape can be approximated as an ellipsoid. More importantly, this ellipsoidal shape can be described by a standard ellipsoidal equation with only one unknown owing to the finding of an unexpected relationship among the drop’s three principal axes. Moreover, this relationship remains the same for both clean and surfactant-laden droplets with or without surface viscosity.

scholarly journals Constitutive Modelling of Polylactic Acid at Large Deformation Using Multiaxial Strains

Polymers ◽  
2021 ◽  
Vol 13 (17) ◽  
pp. 2967
Author(s):  
John Sweeney ◽  
Paul Spencer ◽  
Glen Thompson ◽  
David Barker ◽  
Phil Coates
Keyword(s):  
Steady State ◽  
Stress Relaxation ◽  
Strain Hardening ◽  
Small Strain ◽  
Limited Range ◽  
Constitutive Modelling ◽  
True Stress ◽  
Final Strain ◽  
Transverse Stresses

Sheet specimens of a PLLA-based polymer have been extended at a temperature near to the glass transition in both uniaxial and planar tension, with stress relaxation observed for some time after reaching the final strain. Both axial and transverse stresses were recorded in the planar experiments. In all cases during loading, yielding at small strain was followed by a drop in true stress and then strain hardening. This was followed by stress relaxation at constant strain, during which stress dropped to reach an effectively constant level. Stresses were modelled as steady state and transient components. Steady-state components were identified with the long-term stress in stress relaxation and associated with an elastic component of the model. Transient stresses were modelled using Eyring mechanisms. The greater part of the stress during strain hardening was associated with dissipative Eyring processes. The model was successful in predicting stresses in both uniaxial and planar extension over a limited range of strain rate.

Non-Linear Dynamic Magneto Electric Effects in Ferromagnetic-Ferroelectric Layered Composites

2013 ◽  
Author(s):  
Satenik Harutyunyan ◽  
Davresh Hasanyan
Keyword(s):  
Vibration Frequency ◽  
Strain Distribution ◽  
Longitudinal Vibration ◽  
Three Dimensional ◽  
Low Frequency ◽  
Structure Design ◽  
Experimental Results ◽  
Physical Parameters ◽  
Wide Range ◽  
Non Linear

A non-linear theoretical model including bending and longitudinal vibration effects was developed for predicting the magneto electric (ME) effects in a laminate bar composite structure consisting of magnetostrictive and piezoelectric multi-layers. If the magnitude of the applied field increases, the deflection rapidly increases and the difference between experimental results and linear predictions becomes large. However, the nonlinear predictions based on the present model well agree with the experimental results within a wide range of applied electric field. The results of the analysis are believed to be useful for materials selection and actuator structure design of actuator in actuator fabrication. It is shown that the problem for bars of symmetrical structure is not divided into a plane problem and a bending problem. A way of simplifying the solution of the problem is found by an asymptotic method. After solving the problem for a laminated bar, formula that enable one to change from one-dimensional required quantities to three dimensional quantities are obtained. The derived analytical expression for ME coefficients depend on vibration frequency and other geometrical and physical parameters of laminated composites. Parametric studies are presented to evaluate the influences of material properties and geometries on strain distribution and the ME coefficient. Analytical expressions indicate that the vibration frequency strongly influences the strain distribution in the laminates, and that these effects strongly influence the ME coefficients. It is shown that for certain values of vibration frequency (resonance frequency), the ME coefficient becomes infinity; as a particular case, low frequency ME coefficient were derived as well.

APPLICATION OF FDM® ADDITIVE MANUFACTURING TECHNOLOGY IN THE LEARNING OF ENGINEERING COURSES: ORIENTATION OF STRESS AND STRAIN TENSOR

2020 ◽  
Author(s):  
Miriam Lorenzo-Bañuelos ◽  
Andrés Díaz-Portugal ◽  
Natalia Muñoz-Rujas ◽  
Beatriz Núñez-Angulo ◽  
Wilco M. H. Verbeeten
Keyword(s):  
Additive Manufacturing ◽  
Strain Tensor ◽  
Manufacturing Technology ◽  
Stress And Strain ◽  
Additive Manufacturing Technology

scholarly journals Wavelength dependent nonlinear optical response of tetraphenylethene aggregation-induced emission luminogens

2018 ◽  
Vol 2 (12) ◽  
pp. 2263-2271 ◽  
Author(s):  
Jianbo Xiong ◽  
Xinyue Li ◽  
Chunqing Yuan ◽  
Sergey Semin ◽  
Zhaoquan Yao ◽  
...  
Keyword(s):  
Optical Properties ◽  
Nonlinear Optical ◽  
Theoretical Calculations ◽  
Experimental Results ◽  
Nlo Properties ◽  
Aggregation Induced Emission ◽  
Non Linear ◽  
Potential Applications ◽  
Linear Optical Properties ◽  
Linear Optical

Studies of the non-linear optical properties of classical AIEgens are rare, despite their important potential applications in organic composite photonic circuits. Here, we present experimental results, supported by theoretical calculations, of the non-linear optical (NLO) properties of TPE and its halogenated derivates.

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