Constitutive Equation Of Rubber Research Articles

Effect of Silica Coupling Agents on Texture Formation and Strengthening for Silica-Filled Rubber

New finite element homogenization model with nonaffine constitutive equation of rubber is developed to study the deformation behavior of silica-filled rubber under monotonic and cyclic deformation. The obtained results clarified the effect of the volume fraction of the silica coupling agent and the networklike structure connecting the silica particles on essential physical enhancement mechanisms of deformation resistance and hysteresis loss for silica-filled rubber. The finding suggests that the material characteristics of silica-filled rubber are much more controllable than those of carbon-black-filled rubber.

Deformation behaviour of silica filled rubber under monotonic and cyclic straining

A new constitutive equation of rubber is derived by employing a non‐affine molecular chain network model for an elastic deformation behaviour and the reptation theory for a viscoelastic deformation behaviour. The deformation behaviours of two‐dimensional rubber unit cells containing silica fillers under monotonic and cyclic straining are investigated by computational simulation with the proposed constitutive equation and the homogenisation method. The effect of a silica coupling agent, whose condensation reaction creates a cross‐linking agent that increases the number of entangled points, on the deformation behaviour is introduced through the non‐affine constitutive equation of rubber. The precise TEM observation suggests the generation of complex interfillers connecting phases where the characteristics of rubber intricately changed depending on the volume fraction of the silica coupling agent and the location of rubber phase. The obtained results clarified the essential physical enhancement mechanisms of deformation resistance and hysteresis loss, i.e. the Mullins effect, for rubber filled with silica. The volume fraction of the silica coupling agent essentially affects the deformation behaviour of silica filled rubber, suggesting the high controllability of the material characteristics of silica filled rubber compared with carbon black filled rubber.

Strain Rate Dependent Micro- to Macroscopic Deformation Behavior of Carbon-Black Filled Rubber under Monotonic and Cyclic Straining

A constitutive equation of rubber is derived by employing a nonaffine molecular chain network model for an elastic deformation behavior and the reptation theory for a viscoelastic deformation behavior. The results reveal the roles of the individual springs and dashpot, and the strain rate dependence of materials in the monotonic and cyclic deformation behaviors, particularly softening and hysteresis loss, that is, the Mullins effect, occurring in stress-stretch curves under cyclic deformation processes of carbon black filled rubber..

Strain-Rate-Dependent Deformation Behavior of Carbon-Black-Filled Rubber under Monotonic and Cyclic Straining

The constitutive equation of rubber is derived by employing a nonaffine molecular chain network model for an elastic deformation behavior and the reptation theory for a viscoelastic deformation behavior. The results reveal the roles of the individual springs and dashpot, and the strain rate dependence of materials and disentanglement of molecular chains in the monotonic and cyclic deformation behaviors, particularly softening and hysteresis loss, that is, the Mullins effect, occurring in stress-stretch curves under cyclic deformation processes.

1308 ゴムのひずみ速度依存性構成式と繰返し負荷下における変形挙動の評価(OS-13B,OS-13 ポリマの変形と破壊に関するモデリングとシミュレーション)

1308 ゴムのひずみ速度依存性構成式と繰返し負荷下における変形挙動の評価(OS-13B,OS-13 ポリマの変形と破壊に関するモデリングとシミュレーション)

Finite element analysis and design optimization of rubber components for vibration isolation

A constitutive theory, finite element formulation and topology optimization for anti-vibration rubber are presented. Many vibration isolators made of rubbers are operating under small oscillatory load superimposed on large static deformation. A~viscoelastic constitutive equation for rubber is proposed considering the influence of large static pre-deformation on the dynamic properties. The proposed model is derived through linearization of Simo's viscoelastic constitutive model and introduction of static deformation correction factor. And then the model is implemented in a finite element code to analyze the behavior of rubber elements under general loading conditions. Dynamic tests are performed in order to verify the model under multi-axial deformation. The computed results by the FEA code are compared with the experimental results and the suggested constitutive equation with static deformation correction factor shows good agreement with the test values. For the stability and low transmissibility of isolation systems, both static and dynamic performance must be concurrently considered in the design process. The continuum-based design sensitivity analyses (DSA) of both the static hyperelastic model and dynamic viscoelastic model are developed. And then the topology optimization methodology is used in order to generate the system layouts considering both the static and dynamic performance.

A Viscoelastic Constitutive Model of Rubber Under Small Oscillatory Loads Superimposed on Large static Deformation

A viscoelastic constitutive equation of rubber is proposed under small oscillatory load superimposed on large static deformation. The proposed model is derived through linearization of Simos nonlinear viscoelastic constitutive model and reference configuration transformation. Statically pre-deformed state is used as reference configuration. The model is extended to a generalized viscoelastic constitutive equation including widely-used Mormans model. Static deformation correction factor is introduced to consider the influence of pre-strain on the relaxation function. The model is tested for dynamic behavior of rubbers with different carbon black fractions. It is shown that the constitutive equation with static deformation correction factor agrees well with test results.