Modeling of curing processes based on a multi-field potential. Single- and multiscale aspects

Klinge, Sandra; Bartels, Alexander; Steinmann, Paul

doi:10.1016/j.ijsolstr.2012.04.034

Cited by 24 publications

(10 citation statements)

References 36 publications

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“…II. PREVIOUS STUDIES ON CURING S. Klinge et al [1] In this paper a particular model for curing of polymers is studied, including the different effects arising at the late stages of the process. This model is Depend on the different parameters of civil engineering.…”

Section: ) Pondingmentioning

confidence: 99%

Advanced Water Curing for Concrete: A Review

Masuldar¹

2019

IJRASET

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This paper reviews research conducted on Different types of curing of Concrete. Various techniques are used worldwide for Residential and commercial structure for curing of concrete. Advancement in water curing for concrete is one of the good enhancements for continuous and proper curing for concrete in minimum cost. This paper represents the review on that analysis of different types of curing techniques. For curing purpose very much amount of water is required. There is a requirement of alternative curing system from which maximum amount of water is saved.

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Section: ) Pondingmentioning

confidence: 99%

Advanced Water Curing for Concrete: A Review

Masuldar¹

2019

IJRASET

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“…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

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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...

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“…The multiplicative decomposition of the deformation gradient F = F e · F i is introduced to define the relationships between the elastic and inelastic deformations. In order to complete the model, the equilibrium energy parts are assumed in the form of convolution integrals, which is substantiated by their dependence on the time-sensitive material parameters [1] Φ eq,dev (t) = 1 2…”

Section: Mechanical Modeling Of Viscoelastic and Shrinkage Effectsmentioning

confidence: 99%

Viscoelastic effects and shrinkage as accompanying phenomena of the curing of polymers. Single‐ and multiscale effects

Klinge¹,

Bartels

Hackl³

et al. 2012

Proc Appl Math and Mech

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The contribution deals with the modeling of two phenomena that are characteristic of the curing of polymers, namely the increasing viscosity and the volume decrease known as autogeneous shrinkage. Both of these processes are caused by the crosslinking of polymer chains during polymerization. In order to model the viscoelastic effects, the free energy consisting of an equilibrium and a non-equilibrium part is proposed. The former is related to the elastic processes and depends on total deformations. The latter is caused by the viscoelastic effects and only depends on the elastic part of deformations. In order to avoid volume locking effects typical of isochoric materials, both parts of the free energy density are furthermore split into a volumetric and a deviatoric part. A multifield description depending on the displacements, volume change and hydrostatic pressure is introduced as well. Different from the viscous process, the modeling of shrinkage effects does not require a new assumption for the free energy but a split of the total deformation gradient into a shrinkage and a mechanical part. The model suitable for simulating both of the mentioned phenomena is implemented in the single-and multiscale FE program. Mechanical modeling of viscoelastic and shrinkage effectsThe curing of polymers is a complex process accompanied by the change of material properties such as stiffness, viscosity or opacity. Within this contribution, the emphasis will first be placed on the viscous effects for the modeling of which the free energy density is decomposed into an equilibrium and a non-equilibrium partIn addition, a decomposition into a volumetric and deviatoric part is introduced since the polymers commonly show an isochoric material behaviorWithin the proposed formulation, Ψ denotes the strain energy density, u the displacement field, θ the volume change, p is the hydrostatic pressure, J = det F is the Jacobian related to the deformation gradient F, C is the right Cauchy-Green deformation tensor, the index "e" denotes the elastic quantities and the notation "iso" represents the isochoric part of the deformations. The remaining notation is self-explanatory. The multiplicative decomposition of the deformation gradient F = F e · F i is introduced to define the relationships between the elastic and inelastic deformations. In order to complete the model, the equilibrium energy parts are assumed in the form of convolution integrals, which is substantiated by their dependence on the time-sensitive material parameters [1]Here, C and K are deviatoric and volumetric stiffnesses. Different from the equilibrium part, the non-equilibrium part depends on the time-insensitive material parameters such that it can directly be equalized with the non-equilibrium strain energy density Φ neq = Ψ neq . The evolution of the elastic deformations is controlled through the evolution of the viscous deformations determined by the approach of Reese andwhere T denotes the relaxation time [2]. Apart from the viscous effects, the behavior of curing poly...

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Modeling of curing processes based on a multi-field potential. Single- and multiscale aspects

Cited by 24 publications

References 36 publications

Advanced Water Curing for Concrete: A Review

Advanced Water Curing for Concrete: A Review

Determination of material parameters of heterogeneous viscoelastic curing polymers

Viscoelastic effects and shrinkage as accompanying phenomena of the curing of polymers. Single‐ and multiscale effects

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