Approaches to the modeling of inelasticity and failure of rubberlike materials
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- Tez No: 400835
- Danışmanlar: PROF. MICHAEL KALISKE
- Tez Türü: Doktora
- Konular: İnşaat Mühendisliği, Civil Engineering
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 2012
- Dil: İngilizce
- Üniversite: Technische Universität Dresden
- Enstitü: Yurtdışı Enstitü
- Ana Bilim Dalı: Yapı Malzemesi Ana Bilim Dalı
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 146
Özet
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Özet (Çeviri)
The present thesis aims at developing constitutive approaches for rubberlike materials and numerical algorithms for the implementation in the context of the finite element method. The core of the thesis consists of three main parts. The first part deals with developing a thermodynamically consistent constitutive model for uncured rubber. The second part is devoted to the modeling of failure of rubberlike materials within the framework of continuum mechanics. The final part deals with the finite nonlinear viscoelasticity of rubberlike materials and development of a stable algorithmic implementation in the Eulerian setting. The forming process of uncured rubber is of great interest. However, classical hyperelastic models developed for cross-linked rubber do not apply to uncured rubber due to the lack of cross-links giving the material its elasticity. Experiments show that uncured rubber exhibits strong viscoplastic flow without a distinct yield point accompanied with hardening. We propose a new constitutive model suited for uncured rubber. The kinematic structure of the model is based on the affine micro-sphere model, see MIEHE et al. [110]. The computation of the stretch in the orientation direction follows the Cauchy-Born rule. The micro-sphere enables numerical integration over the sphere via finite summation of the orientation directions corresponding to the integration points over the sphere. This structure replaces the complex three-dimensional formulations, e.g. finite inelasticity models based on multiplicative split of the deformation gradient, by a simpler and more attractive one-dimensional rheological representation at the orientation directions. The rheology of the model consists of two parallel branches. The first branch consists of a spring connected to a Kelvin element where the latter spring models the kinematic hardening. The dashpot describes a time-independent endochronic flow rule based solely on the deformation history. The second branch consists of a spring connected to a Maxwell element in parallel to a dashpot. The two dashpots in the latter branch model the ground-state viscoelasticity and rate-dependent hardening phenomenon. The predictive capabilities of the proposed constitutive model are demonstrated in comparison to homogeneous experiments. The numerical algorithms developed for the proposed material model are demonstrated via boundary value problems. Albeit its complexity, the proposed rheology and the numerical implementation show promising results suitable for large scale FE-based simulations. Rubbery polymers are subjected to severe environmental conditions under service. As a consequence of various ageing mechanisms, the outer surface of rubber components hardens in time and cracking occurs as a result of combined mechanical and chemical processes. Conventional phenomenological hyperelastic constitutive models do not account for material softening. Consequently, the stored energy and stresses tend to infinity as stretch increases. A network alteration for the ageing mechanism of rubberlike materials is introduced along with a micromolecular description of material failure. The need for such a formulation stems from the fact that fracture mechanical II Summary investigations start from an existing crack. Initiation of a crack in rubber parts results from a combined action of ageing and local failure of material, where microscopic cracks and voids lead to a macroscopically visible crack after a number of load cycles. The proposed micro-continuum material model is based on a serial construction of a Langevin-type spring representing the energy storage owing to conformational changes induced by deformation, to a bond potential representing the energy stored in the polymer chain due to the interatomic displacement. For the representation of the micro-macro transition, the non-affine kinematics of the micro-sphere model is used. The Morse potential is utilized for the interatomic bond, which describes the energetic contribution to rubber-like materials and governs the failure of the polymer chain in terms of bond rupture. A novel numerical scheme for the FE implementation of the proposed model is demonstrated. The hardening phenomenon as a result of diffusion limited oxidation of rubber is explained by the principle of mass conservation which dictates simultaneous modulus hardening along with decrease in ultimate stretch observed in aged rubbery polymers. One of the successful approaches to model the time-dependent behaviour of elastomers is proposed by BERGSTRÖM & BOYCE [12]. The model is micromechanically inspired from the relaxation of a single entangled chain in a polymer gel matrix. Although the theory of inelasticity based on multiplicative decomposition of the deformation gradient is well established, the complexity of the nonlinear evolution law as well as the nonlinear equilibrium and non-equilibrium material response necessitates a precise description of the algorithmic setting. We present for the first time a novel numerical implementation of the Bergström-Boyce model (BB model) in the context of finite element analysis and elaborate theoretical aspects of the model. The thermodynamical consistency of the evolution law is proven and a parameter study with respect to the material parameters has been carried out. The agreement of the model with the recent experimental data is investigated. Finally, a new evolution equation is derived in an alternative way from relaxation kinetics of a single polymer chain. The proposed evolution law can be implemented into any type of finite viscoelasticity approach. We replaced the evolution equation in the BB model with the proposed evolution equation and investigated its prediction capacity with existing experimental results in the literature. The present manuscript is organized as follows: First, an overview on the modeling of rubbery polymers will be given in Chapter 1. The fundamental postulates of continuum mechanics on the motion of a deformable body and the key relations and restrictions on the constitutive modeling of elastic and inelastic materials will be discussed in Chapter 2. Chapter 3 is dedicated to the viscoplastic constitutive modeling of uncured rubber and addresses algorithmic issues in the context of finite element method. A micro-continuum mechanical material model for the failure of rubberlike materials will be presented in Chapter 4. Chapter 5 is concerned with finite viscoelasticity of rubberlike materials. A robust algorithmic implementation of BB model and a new evolution law are presented. The manuscript ends with final remarks and conclusions in Chapter 6.
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