Mechanics of soft polymers

Understanding the mechanics and physics of soft polymers are essential due to their widespread applications across disciplines. (e.g.-composite materials, bio mechanics, soft robotics etc.) The soft polymers in general inherent lightweight, high stretchability, extreme viscous damping and stimuli responsive behavior. Development of computational modeling strategy to predict their constitutive response, stimuli responsive behavior is indeed helpful for designing novel multifunctional soft composites, artificial mussels/tissues. In this talk I will briefly emphasize how we are developing multiscale-multiphysics based modeling methods for soft polymers to understand their macroscopic deformation mechanism, failure and other mechanical properties. The long term goal is to develop an integrated computation driven-coupled experimental design strategy for polymer based material systems.https://digitalcommons.mtu.edu/techtalks/1021/thumbnail.jp

Constitutive modeling and characterization of nanocomposite hydrogel for blast resistant materials

In the recent trend of advanced material research, manufacturing novel materials with improved properties and multifunctionality is an important focus across disciplines. As a material, hydrogel finds several applications in the area of biomedical engineering. They are used widely in tissue regeneration, scaffolding, drug delivery, etc. However, using hydrogels for mechanical load bearing application is still limited because of its poor stiffness and low toughness. Like other polymers hydrogels have viscoelasticity which indicates it has potentials to be used as an energy absorbing material. Researchers have already been working on producing tough hydrogels by manufacturing double network hydrogels and nanocomposite hydrogels. As expected, the area of research on hydrogels greatly focus on its material science and chemistry perspective and to a lesser extent on constitutive characterization of the material. In order to produce a superior material out of hydrogels, which will have improved mechanical properties and multifunctionality, a mathematical framework needs to be developed for characterizing the constitutive response of these materials. A physically motivated mathematical model would essentially fasten manufacturing novel hydrogels for various engineering applications. In this study, the goal is to develop a constitutive model for predicting the high rate response of nanocomposite hydrogels. The model is proposed in finite deformation framework because deformation associated with hydrogel is substantially higher than other polymers. In order to predict the viscoelastic response of hydrogels a time-dependent nonlinear stress–strain law is proposed where parameters evolve over time. The constitutive model consists of several branches of spring and dashpot combinations to account for the viscoelastic property in terms of multiple characteristic relaxation times. The nonlinear behavior is modeled using Arruda–Boyce hyperelastic potential function to capture the high stretch behavior in hydrogel. Experimental stress relaxation data from literature for covalently crosslinked alginate hydrogel was fitted to find the characteristic relaxation times. The requirement for a blast resistant material is to have moderately high stiffness, high energy absorbing capacity, with significantly high fracture toughness and preferably a self-healing capacity. The model will also be extended to consider the stimuli sensitive behavior of the hydrogels and eventually will focus on providing guidelines for manufacturing hydrogels which can be used as blast resistant materials

Constitutive modeling of ice in the high strain rate regime

AbstractThe objective of the present work is to propose a constitutive model for ice by considering the influence of important parameters such as strain rate dependence and pressure sensitivity on the response of the material. In this regard, the constitutive model proposed by Carney et al. (2006) is considered as a starting basis and subsequently modified to incorporate the effect of brittle cracking within a continuum damage mechanics framework. The damage is taken to occur in the form of distributed cracking within the material during impact which is consistent with experimental observations. At the point of failure, the material is assumed to be fluid-like with deviatoric stress almost dropping down to zero. The constitutive model is implemented in a general purpose finite element code using an explicit formulation. Several single element tests under uniaxial tension and compression, as well as biaxial loading are conducted in order to understand the performance of the model. Few large size simulations are also performed to understand the capability of the model to predict brittle damage evolution in un-notched and notched three point bend specimens. The proposed model predicts lower strength under tensile loading as compared to compressive loading which is in tune with experimental observations. Further the model also asserts the strain rate dependency of the strength behavior under both compressive as well as tensile loading, which also corroborates well with experimental results

Bayesian Calibration and Uncertainty Quantification of a Rate-dependent Cohesive Zone Model for Polymer Interfaces

In the present work, a rate-dependent cohesive zone model for the fracture of polymeric interfaces is presented. Inverse calibration of parameters for such complex models through trial and error is computationally tedious due to the large number of parameters and the high computational cost associated. The obtained parameter values are often non-unique and the calibration inherits higher uncertainty when the available experimental data is limited. To alleviate these difficulties, a Bayesian calibration approach is used for the proposed rate-dependent cohesive zone model in this work. The proposed cohesive zone model accounts for both reversible elastic and irreversible rate-dependent separation sliding deformation at the interface. The viscous dissipation due to the irreversible opening at the interface is modeled using elastic-viscoplastic kinematics that incorporates the effects of strain rate. To quantify the uncertainty associated with the inverse parameter estimation, a modular Bayesian approach is employed to calibrate the unknown model parameters, accounting for the parameter uncertainty of the cohesive zone model. Further, to quantify the model uncertainties, such as incorrect assumptions or missing physics, a discrepancy function is introduced and it is approximated as a Gaussian process. The improvement in the model predictions following the introduction of a discrepancy function is demonstrated justifying the need for a discrepancy term. Finally, the overall uncertainty of the model is quantified in a predictive setting and the results are provided as confidence intervals. A sensitivity analysis is also performed to understand the effect of the variability of the inputs on the nature of the output.Comment: To be submitted for peer-revie

Analysis and optimal design of layered composites with high stiffness and high damping

AbstractIn this paper we investigate the design of composite materials with simultaneously high stiffness and high damping. We consider layered composite materials with parallel plane layers made of a stiff constituent and a lossy polymer. We analyze the response of these composites to a dynamic load with an arbitrary direction. Using the viscoelastic correspondence principle and linear frequency domain viscoelastic models, we derive an expression for the effective complex modulus of layered composites of infinite size at infinitesimal strains. The dependence of the effective dynamic modulus and loss factor on the geometrical parameters and on the tensile and bulk loss factors of the lossy constituent is analyzed. Moreover we determine the magnitude of the strains in the lossy constituent and demonstrate that the combination of high stiffness and high damping of these composites is due to the high normal and/or shear strains in the lossy material. We use nonlinear constrained optimization to design layered composites with simultaneously high stiffness and high damping while constraining the strains in the polymer. To determine the range of validity of the linear viscoelastic model, simulations using finite deformations models are compared to the theoretical results. Finally, we compute the effective properties of composites of finite size using finite element methods and determine the minimum size required to approach the formulae derived for composites of infinite size

Phase Field Based Cohesive Zone Fracture Approach to Model Anisotropic Effect and Interface Fracture in Fiber Reinforced Polymer Composites

Among multiple damage mechanisms in fiber reinforced polymer composites (FRPCs), delamination is the major failure mode that occurs very often due to low interlaminar strength of these materials. Prediction of this failure mode through computational modeling is not straight forward. In this work we aim to use the phase field fracture method (PFF) to model interfacial fracture in FRPCs. In PFF, the crack is assumed as a diffused entity rather than discrete discontinuities. In the present work, a unified phase field based cohesive zone model (PF-CZM) has been utilized to characterize the interlaminar fracture of carbon fiber reinforced epoxy composite. A Double cantilever beam (DCB) geometry has been simulated for 0? fiber orientation to determine mode I interfacial fracture toughness. To meet the requirement, two laminas of unidirectional FRP were bonded together using an adhesive (resin rich region) for different adhesive layer thicknesses and the corresponding energy release rates are computed. The area method suggested by Whitney [1982] was used to measure the energy release rate (R-curve). The results show different GI values for different thickness of adhesive layer and remains within a specified limit. The peak load is also different for different thicknesses of adhesive. Prior to the DCB simulations, open hole tension (OHT) simulations for different fiber orientations (0?, 45? and 90?) were also performed for carbon-fiber reinforced epoxy composite to validate the PF-CZM model prediction with the experimental data available in literature

A thermo-mechanically coupled constitutive model for curing of polymers

Thermoplastics and Thermosetting polymers have found wide variety of applications these days in automotive, electronics, healthcare and aerospace industries due to their lightweight, easy formability etc. One of the major challenge in the manufacturing and processing of thermosets and thermoplastics is curing, through which the liquid polymer transitions into a state of visco-elastic and/or viscoplastic solid. The curing process is a coupled thermo-chemo-mechanical conversion process which requires a thorough understanding of the constitutive behavior to predict cure dependent mechanical behavior of the solid polymer. In this work, a thermodynamically consistent, frame indifferent, coupled chemo-mechanical continuum level constitutive framework is proposed for thermally cured glassy polymers. The constitutive framework considers the thermodynamics of chemical reactions, as well as the material behavior for a glassy polymer. This work considers a definition for the degree of cure based on the chemistry of the curing reactions. A simplified version of the proposed model has been numerically implemented, and simulations are used to understand the capabilities of the model and framework in typical composites specimen

A homogenized large deformation constitutive model for high temperature oxidation in fiber-reinforced polymer composites

In the present work we develop a thermodynamically consistent, large deformation homogenized constitutive model to predict high-temperature oxidation in fiber-reinforced polymer matrix composites (FRPMCs). The presence of fibers introduces anisotropy in the diffusion and the chemical reactions prevailing oxidation for these composite materials, resulting in heterogeneous shrinkage and stress distribution within the representative material volume. To model such behavior, we develop a homogenized approach considering a unidirectional composite RVE as a mixture of fibers and matrix, represented by the fiber volume fractions and their respective orientations. In what follows, we develop a coupled chemo-mechanical model to predict the oxidation response of this highly anisotropic composite material, based on an earlier developed multiphysics theory of bulk polymer\u27s oxidation. We numerically implement the proposed model in finite elements by writing a user element subroutine (UEL) in ABAQUS/Standard and perform various simulations in 2-D and 3-D composites RVE. The results demonstrate that the proposed model is capable of predicting several important characteristics of oxidation in fiber-reinforced composites, such as, preferential growth of oxide layer, heterogeneous distribution of residual stress, and the effect of fiber volume fraction on the oxidation process

A reaction-driven evolving network theory coupled with phase-field fracture to model polymer oxidative aging

High-temperature oxidation in polymers is a complex phenomenon, driven by the coupled diffusion–reaction process, causing changes in the amorphous network structure and resulting in property degradation. Prolonged oxidation in polymers results in the formation of a coarse, oxide layer on the outer surface and induces spontaneous cracking inside the material. In this paper, we present a chemical reaction-driven evolving network theory coupled with phase-field fracture to describe the effect of oxidation in polymers across different length scales. Guided by the statistical mechanics, the network theory has been introduced to model the reaction induced chain scissions and crosslinking events causing significant changes in the three-dimensional network structure. Further, these microscale events have been considered as the reason behind macroscopic mechanical property degradation, namely oxidative embrittlement. Finally the network theory is coupled with a phase-field fracture to model the macroscale damage initiation and propagation in the polymer under mechanical stress. The specific constitutive forms for all the physical–chemical processes are derived for the coupled system and numerically implemented in finite elements by writing ABAQUS user-defined element (UEL) subroutine. To present the model\u27s capability, various numerical examples with standard fracture geometries have been studied. The simulation results have demonstrated the model\u27s capability of predicting the effect of oxidative aging on the polymer\u27s response