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Viscoelasticity

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Full-Text Articles in Mechanical Engineering

Modeling Of Asphalt Concrete For Cross-Anisotropic Visco-Elasticity And Heterogeneity, Zafrul Hakim Khan Dec 2023

Modeling Of Asphalt Concrete For Cross-Anisotropic Visco-Elasticity And Heterogeneity, Zafrul Hakim Khan

Civil Engineering ETDs

Asphalt Concrete (AC) is a cross-anisotropic viscoelastic material. This study has developed a methodology to backcalculate the cross-anisotropic properties of the AC layer from the Falling Weight Deflectometer (FWD) sensor and pavement response data from embedded sensors inside a pavement section. This study has also developed a two-way coupled Multiscale Finite Element Model (MsFEM) with Phase Field Fracture (PFF) to study the microstructural heterogeneity and damage of the AC layer based on the actual field loadings. A Finite Difference Time Domain (FDTD) and Machine learning-based backcalculation algorithm were developed to determine the layer thickness and dielectric constant from air-coupled Ground …


Model Of Surface Waves On A Viscoelastic Material In A Cylindrical Container With Edge Constraints, Phillip Wilson Dec 2023

Model Of Surface Waves On A Viscoelastic Material In A Cylindrical Container With Edge Constraints, Phillip Wilson

All Theses

A theoretical model is developed for the resonant frequencies and mode shapes of pinned edge surface waves on a viscoelastic fluid contained in a finite depth cylindrical container. A boundary integral approach is used to map the governing equations to the domain boundary. The surface waves obey an eigenvalue operator equation that depends on four dimensionless parameters: the cylinder aspect ratio, the Bond number, the Ohnesorge number, and the elastocapillary number. A solution is constructed using a Rayleigh-Ritz variational procedure over a constrained function space, which is able to effectively incorporate the pinned edge boundary condition. Mode shapes are defined …


Extensional Flows Of Polymer Solutions In Planar Microchannels, Mahmud Kamal Raihan Aug 2023

Extensional Flows Of Polymer Solutions In Planar Microchannels, Mahmud Kamal Raihan

All Dissertations

Non-Newtonian fluids such as polymer solutions often flow under microscale extensional conditions in many natural and engineering flow fields such as in microfluidic chips, porous rocks, biological membranes and filters, printheads in additive manufacturing, etc. The changing cross sectional areas of the internal flow passages therein exert additional extension on the flow along with the shearing. Numerous studies have been dedicated to understanding the extensional flows of polymer solutions over the years. However, most of these studies only focused on flexible polymers exhibiting elasticity in their macroscopic rheology, whereas rigid polymers that portray shear-thinning but often elude elasticity in the …


Numerical Study Of The Time-Periodic Electroosmotic Flow Of Viscoelastic Fluid Through A Short Constriction Microchannel, Jianyu Ji, Shizhi Qian, Armani Marie Parker, Xiaoyu Zhang Jan 2023

Numerical Study Of The Time-Periodic Electroosmotic Flow Of Viscoelastic Fluid Through A Short Constriction Microchannel, Jianyu Ji, Shizhi Qian, Armani Marie Parker, Xiaoyu Zhang

Mechanical & Aerospace Engineering Faculty Publications

Electroosmotic flow (EOF) is of utmost significance due to its numerous practical uses in controlling flow at micro/nanoscales. In the present study, the time-periodic EOF of a viscoelastic fluid is statistically analyzed using a short 10:1 constriction microfluidic channel joining two reservoirs on either side. The flow is modeled using the Oldroyd-B (OB) model and the Poisson-Boltzmann model. The EOF of a highly concentrated polyacrylamide (PAA) aqueous solution is investigated under the combined effects of an alternating current (AC) electric field and a direct current (DC) electric field. Power-law degradation is visible in the energy spectra of the velocity fluctuations …


Editorial For The Special Issue On Micromachines For Non-Newtonian Microfluidics, Lanju Mei, Shizhi Qian Jan 2022

Editorial For The Special Issue On Micromachines For Non-Newtonian Microfluidics, Lanju Mei, Shizhi Qian

Mechanical & Aerospace Engineering Faculty Publications

In lieu of an abstract, this is an excerpt from the first page.

Microfluidics has seen a remarkable growth over the past few decades, with its extensive applications in engineering, medicine, biology, chemistry, etc [...]


Acoustic Radiation Force And Its Application For Cell Manipulation And Ion Channels Activation, Xiangjun Peng Dec 2021

Acoustic Radiation Force And Its Application For Cell Manipulation And Ion Channels Activation, Xiangjun Peng

McKelvey School of Engineering Theses & Dissertations

Sound is a stress wave that carries energy and momentum flux. Scattered sound waves can generate acoustic radiation force that can be used to manipulate particles or cells. This dissertation demonstrates the physics behind cell manipulation by ultrasound. The work begins with a detailed analysis of the mechanics of using standing surface acoustic waves to fabricate acoustic tweezers for contactless particle manipulation using acoustic radiation force. Models to design and analyze acoustic radiation force have traditionally relied on plane wave theories that cannot predict how standing surface acoustic waves can levitate cells in the direction perpendicular to the substrate. We …


Building A Biomechanical Model Of A Rat Forelimb, Joshua Nathaniel Eric Mak Sep 2021

Building A Biomechanical Model Of A Rat Forelimb, Joshua Nathaniel Eric Mak

Dissertations and Theses

This paper presents a biomechanical model of the rat forelimb to test theories of determining viscoelastic muscle parameters. Several biomechanical models of rat hindlimbs have been developed and have explored the effects of multi-muscle control during locomotion. The forelimb model uses two ball-and-socket joints to model clavicle and scapula movement. A third ball-and-socket joint is used at the shoulder and two hinge joints are used at the elbow and wrist. Scapula motion is further constrained by muscle and spring elements. Each forelimb has 11 degrees of freedom, and 23 Hill-type muscles. The model has been created in Animatlab, which includes …


Research Of Stress-Deformed State Of Multi-Connected Complex Shell Structures, Т.М. Маvlanov, Sh.O. Khudainazarov, B. Yalgashev, O.S. Nurova Mar 2021

Research Of Stress-Deformed State Of Multi-Connected Complex Shell Structures, Т.М. Маvlanov, Sh.O. Khudainazarov, B. Yalgashev, O.S. Nurova

Irrigation and Melioration

Conducting numerical experiments for complex structurally inhomogeneous structures allows us to understand the qualitative picture of the effect of various parameters in a wide range of studies and to give sound recommendations at the design stage for conducting laboratory model and field experiments. In this paper, on the basis of the classical theory of elasticity, the basic equations characterizing the stress-strain state of complex multiply connected shell structures are given and a specific problem is solved. At the same time, some of the structural elements have viscoelastic properties. When solving the problem, the behavior of the structure for the n-th …


Viscoelasticity Of Ptfe-Based Face Seals, Bo Tan Jan 2021

Viscoelasticity Of Ptfe-Based Face Seals, Bo Tan

Theses and Dissertations--Mechanical Engineering

PTFE-based materials are widely used in areas of tribology, particularly in seal and bearing applications because of their outstanding self-lubricating properties. Often in dynamic seal applications there is a need for ultra-low mechanical friction loss between the sealing surfaces. Due to its extremely low friction coefficient, there is interest in employing Polytetrafluoroethylene (PTFE) materials in such applications. One challenging aspect of employing PTFE is that these materials are viscoelastic and plastic. This dissertation concentrates on the modeling of viscoelastic material response when used as mechanical face seals with a focus on PTFE-based materials. First, the viscoelastic characteristics are measured through …


Experiments And Modeling Of The Chemo-Mechanically Coupled Behavior Of Polymeric Gels, Nikola Bosnjak Dec 2020

Experiments And Modeling Of The Chemo-Mechanically Coupled Behavior Of Polymeric Gels, Nikola Bosnjak

Dissertations

Polymeric materials consist of mutually entangled or chemically crosslinked long njitmolecular chains which form a polymer network. Due to their molecular structure, the njitpolymeric materials are known to undergo large deformation in response to various njitenvironmental stimuli, such as temperature, chemical potential and light.

When a polymer network is exposed to a suitable chemical solvent, the solvent molecules are able to diffuse inside the network, causing it to undergo a large volumetric deformation, known as swelling. In addition to volumetric deformation, this process involves the chemical mixing of the polymer network and solvent molecules, and is typically environmentally responsive. A …


Numerical Simulation Of Nonlinear Vibrations Of Discrete Mass With Harmonic Force Perturbation, M. Yusupov, B. A. Akhmedov, Olga Karpova Dec 2020

Numerical Simulation Of Nonlinear Vibrations Of Discrete Mass With Harmonic Force Perturbation, M. Yusupov, B. A. Akhmedov, Olga Karpova

Acta of Turin Polytechnic University in Tashkent

The problem of vibration of a single-mass system under the force excitation of vibration associated with a fixed base by a weightless nonlinear viscoelastic spring is considered. To take into account the rheological properties of the spring material, the Boltzmann-Volterra principle was used. Mathematical models of the problem under consideration are obtained, which are described by integro-differential equations. A solution method based on the use of quadrature formulas has been developed and a computer program has been compiled on its basis, the results obtained are presented in the form of graphs. The influence of nonlinear and rheological properties of a …


Editorial For The Special Issue On Micro/Nano-Chip Electrokinetics, Volume Iii, Shizhi Qian, Xiangchun Xuan Jan 2020

Editorial For The Special Issue On Micro/Nano-Chip Electrokinetics, Volume Iii, Shizhi Qian, Xiangchun Xuan

Mechanical & Aerospace Engineering Faculty Publications

No abstract provided.


Effect Of The Nonlinear Material Viscosity On The Performance Of Dielectric Elastomer Transducers, Yuanping Li Jun 2019

Effect Of The Nonlinear Material Viscosity On The Performance Of Dielectric Elastomer Transducers, Yuanping Li

Electronic Thesis and Dissertation Repository

As a typical type of soft electroactive materials, dielectric elastomers (DEs) are capable of producing large voltage-induced deformation, which makes them desirable materials for a variety of applications in transduction technology, including tunable oscillators, resonators, biomimetics and energy harvesters. The dynamic and energy harvesting performance of such DE-based devices is strongly affected not only by multiple failure modes such as electrical breakdown, electromechanical instability, loss-of-tension and fatigue, but also by their material viscoelasticity. Moreover, as suggested by experiments and theoretical studies, DEs possess nonlinear relaxation processes, which makes modeling of the performance of DE-based devices more challenging.

In this thesis, …


Transient Analysis Of Diffusion-Induced Deformation In A Viscoelastic Electrode, Yaohong Suo, Fuqian Yang Jun 2019

Transient Analysis Of Diffusion-Induced Deformation In A Viscoelastic Electrode, Yaohong Suo, Fuqian Yang

Chemical and Materials Engineering Faculty Publications

In this study, we analyze the transient diffuse-induced-deformation of an electrode consisting of the conducting polymer polypyrrole (PPY) by using the theories of linear viscoelasticity and diffusion-induced stress. We consider two constitutive relationships with dependence of viscosity on strain rate: Kelvin-Voigt model and three-parameter solid model. A numerical method is used to solve the problem of one-dimensional, transient diffusion-induced-deformation under potentiostatic operation. The numerical results reveal that the maximum displacement occurs at the free surface and the maximum stress occurs at the fixed end. The inertia term causes the stress to increase at the onset of lithiation. The stress decreases …


Development Of Material Model Subroutines For Linear And Nonlinear Response Of Elastomers, Asim Gillani Oct 2018

Development Of Material Model Subroutines For Linear And Nonlinear Response Of Elastomers, Asim Gillani

Electronic Thesis and Dissertation Repository

The nature of elastomers has been extensively studied ever since the vulcanization of rubber in the 19th century. Elastomers have been heavily employed in various fields, such as automobile, aerospace, robotics, biomimetics, dynamics and energy harvesting. Due to their molecular nature, these materials display hyperelastic and viscous response when deformed. Their response has been studied in a number of works, which tend to explain their nature through the theory of polymer dynamics or using rheological models. As elastomers are designed as actuators, generators or artificial tissues with complex geometries, the need for finite element analysis to study their response is …


Chemo-Thermo Cure Of Viscoelastic Materials For Semiconductor Packaging Applications, Anjali Pradeep Kumar Aug 2018

Chemo-Thermo Cure Of Viscoelastic Materials For Semiconductor Packaging Applications, Anjali Pradeep Kumar

Dissertations and Theses

Viscoelastic polymer materials are being actively considered as a novel material for semiconductor packaging applications as a result of their ability to develop strong adhesive bonds at lower temperatures. Viscoelastic thermoset materials are impacted by the stresses generated during the curing process, which is also accompanied by a dissipation of thermal energy. There is a need to develop a generic modeling formulation that is applicable to any material of interest in order to enable the study of different bonding materials and develop optimized curing cycles. This study reports a numerical formulation to evaluate the stress generated and energy dissipated during …


Experimental, Analytical, And Numerical Evaluation Of The Mechanical Properties Of The Brain Tissue, Aref Samadidooki Jun 2018

Experimental, Analytical, And Numerical Evaluation Of The Mechanical Properties Of The Brain Tissue, Aref Samadidooki

LSU Doctoral Dissertations

A true understanding of the mechanisms behind most of the brain diseases is still out of reach. For several years, the interest of scientists has been focused on the genetic and biological causes, however, recent studies unraveled the importance of the biomechanics of the brain growth, folding, impact resistance, and deformation on its pathological conditions. While, a wide range of different methods have been used for characterization of the mechanical properties of the brain at the tissue level, the obtained results from different studies are extremely scattered and sometimes in contrast to one another. Since the brain tissue is extremely …


Effect Of Material Viscoelasticity On Frequency Tuning Of Dielectric Elastomer Membrane Resonators, Liyang Tian Jun 2018

Effect Of Material Viscoelasticity On Frequency Tuning Of Dielectric Elastomer Membrane Resonators, Liyang Tian

Electronic Thesis and Dissertation Repository

Dielectric elastomers (DEs) capable of large voltage-induced deformation show promise for applications such as resonators and oscillators. However, the dynamic performance of such vibrational devices is not only strongly affected by the nonlinear electromechanical coupling and material hyperelasticity, but also significantly by the material viscoelasticity. The material viscoelasticity of DEs originates from the highly mobile polymer chains that constitute the polymer networks of the DE. Moreover, due to the multiple viscous polymer subnetworks, DEs possess multiple relaxation processes. Therefore, in order to predict the dynamic performance of DE-based devices, a theoretical model that accounts for the multiple relaxation processes is …


Radial And Longitudinal Motion Of The Arterial Wall: Their Relation To Pulsatile Pressure And Flow In The Artery, Dan Wang, Linda Vahala, Zhili Hao Jan 2018

Radial And Longitudinal Motion Of The Arterial Wall: Their Relation To Pulsatile Pressure And Flow In The Artery, Dan Wang, Linda Vahala, Zhili Hao

Mechanical & Aerospace Engineering Faculty Publications

The aim of this paper is to analyze the radial and longitudinal motion of the arterial wall in the context of pulsatile pressure and flow, and to understand their physiological implications for the cardiovascular system. A reexamination of the well-established one-dimensional governing equations for axial blood flow in the artery and the constitutive equation for the radial dilation of the arterial wall shows that two waves—a pulsatile pressure wave in the artery and a radial displacement wave in the arterial wall—propagate simultaneously along the arterial tree with the same propagation velocity, explaining why this velocity combines the physical properties and …


Stability And Interfacial Viscoelasticity Of Oil-Water Nanoemulsions Stabilized By Soy 2 Lecithin And Tween 20 For The Encapsulation Of Bioactive Carvacrol, Jerome J. Nash, Kendra Erk Dec 2016

Stability And Interfacial Viscoelasticity Of Oil-Water Nanoemulsions Stabilized By Soy 2 Lecithin And Tween 20 For The Encapsulation Of Bioactive Carvacrol, Jerome J. Nash, Kendra Erk

School of Materials Engineering Faculty Publications

The rheology of oil-in-water (O/W) droplet interfaces stabilized by food-grade emulsifiers (soy lecithin or Tween 20) under controlled aqueous conditions was investigated to elucidate its contribution in the kinetic stabilization of nanoemulsion-based delivery systems containing carvacrol, a naturally-derived antimicrobial compound. Dilational rheology of surfactant-laden O/W interfaces was measured using axisymmetric drop shape analysis. The kinetic stability of corresponding nanoemulsions (containing mixtures of carvacrol and medium-chain triglyceride (MCT) oil dispersed in water (pH 7)) was characterized using dynamic light scattering. Zwitterionic lecithin molecules adsorbed to the O/W interface for 24 h formed a notably viscoelastic layer, compared to nonionic Tween 20 …


Concurrent Spatial Mapping Of The Viscoelastic Behavior Of Heterogeneous Soft Materials Via A Polymer-Based Microfluidic Device, Wenting Gu Apr 2016

Concurrent Spatial Mapping Of The Viscoelastic Behavior Of Heterogeneous Soft Materials Via A Polymer-Based Microfluidic Device, Wenting Gu

Mechanical & Aerospace Engineering Theses & Dissertations

This dissertation presents a novel experimental technique, namely concurrent spatial mapping (CSM), for measuring the viscoelastic behavior of heterogeneous soft materials via a polymer-based microfluidic device. Comprised of a compliant polymer microstructure and an array of electrolyte-enabled distributed resistive transducers, the microfluidic device detects both static and dynamic distributed loads. Distributed loads deform the polymer microstructure and are recorded as resistance changes at the locations of the transducers.

The CSM technique identifies the elastic modulus of soft materials by applying a precisely controlled indentation depth using a rigid probe to a sample placed on the device. The spatially-varying elastic modulus …


Computational Assessment Of Neural Probe And Brain Tissue Interface Under Transient Motion, Michael Polanco, Sebastian Bawab, Hangsoon Yoon Jan 2016

Computational Assessment Of Neural Probe And Brain Tissue Interface Under Transient Motion, Michael Polanco, Sebastian Bawab, Hangsoon Yoon

Mechanical & Aerospace Engineering Faculty Publications

The functional longevity of a neural probe is dependent upon its ability to minimize injury risk during the insertion and recording period in vivo, which could be related to motion-related strain between the probe and surrounding tissue. A series of finite element analyses was conducted to study the extent of the strain induced within the brain in an area around a neural probe. This study focuses on the transient behavior of neural probe and brain tissue interface with a viscoelastic model. Different stages of the interface from initial insertion of neural probe to full bonding of the probe by astro-glial …


Electromechanical Coupling Behavior Of Dielectric Elastomer Transducers, Jianyou Zhou Sep 2015

Electromechanical Coupling Behavior Of Dielectric Elastomer Transducers, Jianyou Zhou

Electronic Thesis and Dissertation Repository

Dielectric elastomer transducers with large deformation, high energy output, light weight and low cost have been drawing great interest from both the research and industry communities, and shown potential for versatile applications in biomimetics, dynamics, robotics and energy harvesting. However, in addition to multiple failure modes such as electrical breakdown, electromechanical instability, loss-of-tension and fatigue, the performance of dielectric elastomer transducers are also strongly influenced by the hyperelastic and viscoelastic properties of the material. Also, the interplay among these material properties and the failure modes is rather difficult to predict. Therefore, in order to provide guidelines for the optimal design …


Temperature Dependence Of Shear Speed In Micellar Fluid, E.G. Sunethra Kumari Dayavansha Jan 2015

Temperature Dependence Of Shear Speed In Micellar Fluid, E.G. Sunethra Kumari Dayavansha

Electronic Theses and Dissertations

Wormlike micellar (WM) fluids are viscoelastic and can support shear waves. Phase transitions of the micellar aggregates are temperature dependent and can manifest as sharp changes in the shear wave speed as a function of temperature. Thus, shear waves provide a good tool for detecting the existence of phase transitions. In this work, the variation of shear speed with temperature of 200mM CTAB/NaSal micellar fluid in a 5:3 ratio was studied. The dependence of shear wave speed on time between fluid synthesis and measurement was also investigated. Shear wave propagation through the fluid was observed as a time varying birefringence …


Thermo-Mechanical Characterization Of Glass And Its Effect On Predictions Of Stress State, Birefringence And Fracture In Precision Glass Molded Lenses, Dhananjay Joshi Dec 2014

Thermo-Mechanical Characterization Of Glass And Its Effect On Predictions Of Stress State, Birefringence And Fracture In Precision Glass Molded Lenses, Dhananjay Joshi

All Dissertations

The Precision Glass Molding (PGM) process was established as an economical and sustainable option for the production of aspherical glass optics to satisfy the increased industrial demand. Applications of precision molded aspherical lenses range from consumer electronics products such as cell phone cameras to defense and medical systems. An aspherical lens can eliminate the spherical and optical aberrations as compared to a spherical lens thus making the lens system more compact and lighter. In spite of being a clean and environmentally friendly process, the lens molding operation suffers from a few drawbacks such as lens profile deviation, stress birefringence/refractive index …


Experimental Study Of Nanofiber Production Through Forcespinning, Simon Padron, Arturo Fuentes, Dumitru Caruntu, Karen Lozano Jan 2013

Experimental Study Of Nanofiber Production Through Forcespinning, Simon Padron, Arturo Fuentes, Dumitru Caruntu, Karen Lozano

Mechanical Engineering Faculty Publications and Presentations

A newly developed method of producing nanofibers, called forcespinning, has proven to be a viable alternative to mass produce nanofibers. Unlike electrospinning, the most common method currently being employed (which draws fibers through the use of electrostatic force), forcespinning utilizes centrifugal forces which allow for a host of new materials to be processed into nanofibers (given that electric fields are not required) while also providing a significant increase in yield and ease of production. This work presents a detailed explanation of the fiber formation process. The study is conducted using high speed photography to capture the jet initiation process at …


Characterization And Biomechanical Analysis Of The Human Lumbar Spine With In Vitro Testing Conditions, Dean K. Stolworthy Jan 2012

Characterization And Biomechanical Analysis Of The Human Lumbar Spine With In Vitro Testing Conditions, Dean K. Stolworthy

Theses and Dissertations

Biomechanical testing of cadaveric spinal segments forms the basis for our current understanding of healthy, pathological, and surgically treated spinal function. Over the past 40 years there has been a substantial amount of data published based on a spinal biomechanical testing regimen known as the flexibility method. This data has provided valuable clinical insights that have shaped our understanding of low back pain and its treatments. Virtually all previous lumbar spinal flexibility testing has been performed at room temperature, under very low motion rates, without the presence of a compressive follower-load to simulate upper body weight and the action of …


Mechanical Testing Device For Viscoelastic Biomaterials, Jeff D. Berg Jul 2010

Mechanical Testing Device For Viscoelastic Biomaterials, Jeff D. Berg

Department of Mechanical and Materials Engineering: Dissertations, Theses, and Student Research

Nearly all biologic tissues exhibit viscoelastic behavior. This behavior is characterized by hysteresis in the response of the material to load or strain. This information can be utilized in extrapolation of life expectancy of vascular implant materials including native tissues and synthetic materials. This behavior is exhibited in many engineering materials as well such as the polymers PTFE, polyamide, polyethylene, etc. While procedures have been developed for evaluating the engineering polymers the techniques for biologic tissues are not as mature. There are multiple reasons for this. A major one is a cultural divide between the medical and engineering communities. Biomedical …


Multiscale Modeling Of Glass Fiber Reinforced Viscoelastic Polymers Subjected To Impact Loads, Victor Ferreira Teixeira Jun 2009

Multiscale Modeling Of Glass Fiber Reinforced Viscoelastic Polymers Subjected To Impact Loads, Victor Ferreira Teixeira

Department of Engineering Mechanics: Dissertations, Theses, and Student Research

New applications for polymer composite materials are occurring at a rapid pace today. These include structural components in the energy, transportation, and biomedical fields. Many if not all of these new applications will require that part performance is insured with some degree of sustainable damage. With the growth in the use of composite structures comes the necessity of improved methodologies that can predict more accurately the life and serviceability conditions of composite parts. Damage mechanics in two-phase composite materials is a very complex problem that has challenged researchers for many years. However, most of the available models perform only a …


Multiscale Modeling Of Impact On Heterogeneous Viscoelastic Solids With Evolving Microcracks, Flavio V. Souza Apr 2009

Multiscale Modeling Of Impact On Heterogeneous Viscoelastic Solids With Evolving Microcracks, Flavio V. Souza

Department of Engineering Mechanics: Dissertations, Theses, and Student Research

Multiscale computational techniques play a major role in solving problems related to viscoelastic composite materials due to the complexities inherent to these materials. In the present work, a numerical procedure for multiscale modeling of impact on heterogeneous viscoelastic solids containing evolving microcracks is proposed in which the (global scale) homogenized viscoelastic incremental constitutive equations have the same form as the local scale viscoelastic incremental constitutive equations, but the homogenized tangent constitutive tensor and the homogenized incremental history dependent stress tensor depend on the amount of damage accumulated at the local scale. Furthermore, the developed technique allows the computation of the …