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A Rubber Experiment and the Constitutive Model
Published in Jie Zhang, Chuanjun Han, Rubber Structures in Oil and Gas Equipment, 2022
The image theory treats rubber material as a continuous unity. Based on the assumption that the rubber is isotropic and the volume is approximately incompressible, a unified physical quantity is used to characterize its mechanical properties. This physical quantity is called the strain energy density function. This function is a scalar function of strain tensor, and the derivative of its corresponding variable component is the corresponding stress component, and its expression is: Sij=∂W∂E where, Sij is II Piola-Kirchhoff stress level. W is strain energy density function per unit volume. E is Lagrange strain sheet.
Theory of Linear Elasticity
Published in Irving H. Shames, Clive L. Dym, Energy and Finite Element Methods in Structural Mechanics, 2017
Irving H. Shames, Clive L. Dym
The function 𝒰 under such circumstances is called the strain energy density function. We now pose two queries: What physical attributes can be ascribed to this function, and when does it exist? As to the first query, consider an infinitesimal rectangular parallelepiped under the action of normal stresses, as shown in Fig. 1.23. The displacements on faces 1 and 2 in the x direction are given as ux and ux + (∂ux/∂x)dx, respectively, so that the increment of mechanical work done by the stresses on the element during deformation is
Hyperelastic limiting chain extensibility constitutive models for rubber: A brief review
Published in Per-Erik Austrell, Leif Kari, Constitutive Models for Rubber IV, 2017
Mechanical properties of elastomeric materials are usually represented in terms of a strain-energy density function W (Ogden 1984). The state of strain is characterized by the principal stretches λ1, λ2, λ3 of the deformation or equivalently by introducing a strain measure such as the right Cauchy-Green strain tensor C = FTF. Here F is the gradient of the deformation. For an isotropic hyperelastic material, W is a function of the strain invariants
Pounding responses of a base-isolated liquid storage tank under bidirectional earthquakes
Published in Journal of Asian Architecture and Building Engineering, 2023
Wei Jing, Jie Feng, Xuansheng Cheng
From the above analysis, when concrete LST collides with moat wall, the wall tensile stress and liquid sloshing height are increased. Especially under the action of bidirectional earthquake, the pounding will make the wall tensile stress close to or exceed concrete tensile strength, so failure mode caused by wall cracking will occur. Therefore, in order to improve the effectiveness of the sliding isolation LST, it is necessary to study the mitigation measure for the pounding. A simple and inexpensive method is to add a rubber cushion at the bottom of LST, as shown in Figure 15. The thickness and height of buffer cushion are 0.1 m and 0.3 m. Similar to structure, 3D solid is also used for the rubber. Hyperelastic Mooney–Rivlin material model is used to simulate rubber cushion (Major and Major 2015), which is effective and can be preferred in the analysis of incompressible media and inelastic materials (specifically for materials in which Poisson’s ratio is close to 0.5, for rubber-like materials and for elasto-plastic materials). The strain energy density function W that is described by the invariant of the deformation tensor is
Non-linear elasticity experiment and analysis of acrylic material used for human occupied vehicle
Published in Ships and Offshore Structures, 2023
Bingxiong Zhao, Fang Wang, Youjie Li, Yu Wu, Jinfei Zhang, Ruilong Luo, Oleg Gaidai, Weicheng Cui
As shown in Figure 3, the yield points are far from the straight line of linear elastic modulus. The linear elastic model does not accurately describe the observed behaviour for acrylic. Stress–strain relationship of acrylic can be defined as non-linearly elastic, isotropic and incompressible. A hyperelastic material is a type of constitutive model for elastic material for which the stress–strain relationship is derived from a strain energy density function. Ronald Rivlin and Melvin Mooney developed the first hyperelastic forms, named Neo-Hookean and Mooney–Rivlin forms. Many other hyperelastic forms, such as Marlow, Ogden, Arruda–Boyce and Polynomial, have been developed. The polynomial form is widely used for many hyperelastic materials (Guo and Sluys 2008). In this paper, the polynomial hyperelastic form is used to describe the stress–strain relationship of acrylic.
Stability analysis of conveying-nanofluid CNT under magnetic field based on nonlocal couple stress theory and fluid-structure interaction
Published in Mechanics Based Design of Structures and Machines, 2023
Sayed Reza Ramezani, Afsaneh Mojra
According to the nonlocal elasticity theory, the structural stiffness of a nanomaterial is smaller than that of the corresponding value for the bulk material. Contrary to the nonlocal elasticity theory, the couple stress theory predicts the structural stiffness of a nanomaterial larger than that of the corresponding value for the bulk material. In this theory, the curvature tensor is added to the strain tensor in the strain energy density function. A combination of these two theories can cover the material behavior at the nano-scale. Based on the nonlocal couple stress theory, the constitutive equation of motion is expressed as follows: where, and are the couple-stress sizing effect parameter, nonlocal sizing effect parameter, modulus of elasticity and modulus of rigidity, respectively. Moreover, and represent the stress and couple-stress tensors, whereas, and denote the strain and curvature tensors, respectively.