The multiscale approach to the curing of polymers incorporating viscous and shrinkage effects

Klinge, Sandra; Bartels, Alexander; Steinmann, Paul

doi:10.1016/j.ijsolstr.2012.08.016

Cited by 18 publications

(17 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…An essential difference between the assumptions (2) and (3) is the time-behavior of material parameters: These are time-dependent in the equilibrium part but time-independent in the non-equilibrium part. As a consequence, the constituents of the equilibrium part of the energy density are assumed in the form of convolution integrals [2][3][4][5] …”

Section: Materials Modelmentioning

confidence: 99%

Determination of material parameters of heterogeneous viscoelastic curing polymers

Klinge

Steinmann

2015

Proc Appl Math and Mech

View full text Add to dashboard Cite

Two goals characterize the present contribution: First, the development of a numerical approach for determining the properties of the material microstructure, and second, the shift of the focus of the inverse analysis from investigating a purely elastic material toward the parameter identification related to heterogeneous inelastic materials. As a rule, the constitutive laws in this case involve a greater number of material parameters the determination of which requires different kinds of tests. Material modelThe model proposed incorporates three important properties of curing polymers: the time-dependency of material parameters, the material incompressibility and the viscous effects. In order to achieve these goals, firstly, the free energy density is supposed to be a sum of an equilibrium and a non-equilibrium part:Here, the first part corresponds to the elastic deformations and the second part is caused by the viscous effects. Such a split of the energy is enabled by assuming the multiplicative decomposition of the total deformation gradient F into an elastic F e and a viscous part F v , which is the standard step in the theory of finite deformations: F = F e · F v . In order to avoid the volume locking by simulating the incompressible material behavior, both energy parts are furthermore decomposed into a volumetric and a deviatoric part as proposed by Simo, Taylor and Pister [1]Here, u denotes the deformation, θ is the volumetric change, p is the hydrostatic pressure, C the right Cauchy-Green deformation tensor and J = detF is the Jacobian. Notations "dev" and "vol" indicate the deviatoric and volumetric parts of different quantities. An essential difference between the assumptions (2) and (3) is the time-behavior of material parameters: These are time-dependent in the equilibrium part but time-independent in the non-equilibrium part. As a consequence, the constituents of the equilibrium part of the energy density are assumed in the form of convolution integrals [2-5]where C dev (t) = 4andare the deviatoric elasticity tensor and the bulk modulus defined in terms of strain energy densities Ψ dev and Ψ vol .For the chosen setup, an analysis of the thermodynamic consistency yields the expression for the evolution of viscous deformations. In the present contribution, the solution proposed by Reese and Govindjee [6] is used for this purpose:. Here, T = T (t) represents the relaxation time. It is a time-dependent parameter, which indirectly causes the time-dependency of the non-equilibrium part of the strain energy density. Numerical procedure for the parameter identificationThe numerical approach proposed for the purpose of parameter identification uses the combination of the Levenberg-Marquardt method and the multiscale FEM [7]. The former is a gradient-based method coupling the advantages of the steepest descent method and of the minimization of the Taylor approximation of a function. On the other hand, the multiscale FEM is a numerical homogenization method such that the coupling of the macroscopic and micros...

show abstract

Section: Materials Modelmentioning

confidence: 99%

Determination of material parameters of heterogeneous viscoelastic curing polymers

Klinge

Steinmann

2015

Proc Appl Math and Mech

View full text Add to dashboard Cite

show abstract

“…The variable z(t) is also referred to as intrinsic time scale and is governed by an evolution equation which has been introduced in general form by Eq. (15). Different sources of process dependencies may be defined by choosing appropriate constitutive functions for this evolution equation.…”

Section: Free Energy and Stressesmentioning

confidence: 99%

“…As presented in Section 3.3, the process dependency is accommodated by the intrinsic time scale z(t). The following ansatz for the evolution equation (15) has been choseṅ…”

Section: Process Dependencies Of Mechanical Propertiesmentioning

confidence: 99%

See 1 more Smart Citation

Modelling and simulation of adhesive curing processes in bonded piezo metal composites

et al. 2014

View full text Add to dashboard Cite

This work deals with the modelling and simulation of curing phenomena in adhesively bonded piezo metal composites which consist of an adhesive layer with integrated piezoelectric module and two surrounding metal sheet layers. In a first step, a general modelling framework is proposed which is able to represent curing phenomena in polymers at finite strains. Based on this formulation, a concretized model is deduced for the simulation of curing in one specific epoxy based adhesive. Here, appropriate material functions are specified and the thermodynamic consistency is proved. Regarding the finite element implementation, a numerical integration scheme and a new approach for the consideration of different initial conditions are provided. Finally, finite element simulations of a newly proposed manufacturing process for the production of bonded piezo metal composite structures are conducted. A deep drawing process of the composite with uncured adhesive layer and the subsequent adhesive curing are investigated.Keywords bonded piezo metal composite · curing adhesive · constitutive model · finite element method

show abstract

“…The reason is its applicability to different macroscopic and microscopic problems even with the highly nonlinear material behavior. The authors have already successfully used this strategy for the modeling of reinforced polymers, for the simulation of diffusive processes, and for the investigation of bone tissue …”

Section: Introductionmentioning

confidence: 99%

Multiscale FEM simulations of cross‐linked actin network embedded in cytosol with the focus on the filament orientation

Klinge

Aygün

Gilbert

et al. 2018

Numer Methods Biomed Eng

Self Cite

View full text Add to dashboard Cite

The present contribution focuses on the application of the multiscale finite element method to the modeling of actin networks that are embedded in the cytosol. These cell components are of particular importance with regard to the cell response to external stimuli. The homogenization strategy chosen uses the Hill‐Mandel macrohomogeneity condition for bridging 2 scales: the macroscopic scale that is related to the cell level and the microscopic scale related to the representative volume element. For the modeling of filaments, the Holzapfel‐Ogden β‐model is applied. It provides a relationship between the tensile force and the caused stretches, serves as the basis for the derivation of the stress and elasticity tensors, and enables a novel finite element implementation. The elements with the neo‐Hookean constitutive law are applied for the simulation of the cytosol. The results presented corroborate the main advantage of the concept, namely, its flexibility with regard to the choice of the representative volume element as well as of macroscopic tests. The focus is particularly placed on the study of the filament orientation and of its influence on the effective behavior.

show abstract

The multiscale approach to the curing of polymers incorporating viscous and shrinkage effects

Cited by 18 publications

References 18 publications

Determination of material parameters of heterogeneous viscoelastic curing polymers

Determination of material parameters of heterogeneous viscoelastic curing polymers

Modelling and simulation of adhesive curing processes in bonded piezo metal composites

Multiscale FEM simulations of cross‐linked actin network embedded in cytosol with the focus on the filament orientation

Contact Info

Product

Resources

About