Multi-axial deformation

Multi-axial deformation correspondences of shear, tension, and compression at low temperatures... 

The experimental set-up can also be used for the testing of stress relaxation in a plane state of stress. In this test a specified quantity of water is pumped rapidly into the device producing a certain arc height and associated multi-axial deformation. Care must be taken to prevent air cushion formation. The gradual decrease in pressure as a function of time can be obtained from the manometer reading. The test procedure and the evaluation of the relaxation test data can be performed in analogy to the stress relaxation test imder an imposed uniaxial deformation. Figure 3.13 shows such a stress relaxation curve at an imposed multi-axial deformation. 

Multi-axial Deformation Three-Dimensional Non-linear Viscoelasticity... 

The classic way that we perform force versus deformation measurements is to deform a sample at a constant rate, while we record the force induced within it. We normally carry out such tests in one of three configurations tensile, compressive, or flexural, which are illustrated in Fig. 8.1. We can also test samples in torsion or in a combination of two or more loading configurations. For the sake of simplicity, most tests are uni-axial in nature, but we can employ bi-axial or multi-axial modes when needed,... 

An impact modifier is a rubber phase dispersed in particulate form throughout the matrix of a polymer solid. Unlike plasticizers, the rubber particles retain their intrinsic properties as a separate phase. The glass transition temperature of the parent matrix is not lowered by the addition of an impact modifier. The rubber particles do two things to the parent matrix phase (2,3,4) they act as stress concentrators (i.e., a large strain will start in the matrix near the interface) and they enhance the multi-axiality in stress. As multiaxial tensile strength near the interface further enhances dilatation, which shortens the mechanical relaxation time, the otherwise brittle polymer solid of the matrix will undergo plastic deformation in the vicinities of the rubber particles. 

The formation of a tablet during the loading phase causes the system to be under initial stress at the beginning of the deformation analysis. The initial stress has many important implications to the analysis of tablets during unloading and relaxation (99,103,104). For three-dimensional multi-axial loading conditions, Hook s law can be written as ... 

The quantities C and d are the second-order tensors that are an array of nine Cij(iJ = 1,2,3) and dy terms C is known as the Green deformation tensor and d is the rate of deformation tensor. It is always possible to find a principal axis coordinate system where C and d have diagonal forms, that is, where Cy and dy are zero when i is not equal toj. In this principal axis coordinate system, all deformations are representable as multi-axial elongational and may be expressed through extension ratios li, In, and Ini corresponding to these principal axes. 

With this method, the specimen is deformed and the deformation kept constant. Due to the enforced deformation, a single- or multi-axial stress state is created in the specimen, which will decrease due to molecular relaxation processes over the course of time. This type of test is used to evaluate plastics that are subject to longterm, constant deformation in service. 

Rupp, A., and V. V. Grubisic. Reliable Determination of Multi-Axial Road Loads and Tire Deformations on Buses and Heavy Trucks for the Design and Proof Out. Proceedings of the International Truck and Bus Meeting and Exposition, 1997,9-19. 

The multi-stacked actuator is designed to be directly driven by the Maxwell stress without any strain as mentioned above. Its fundamental principle of operation is shown in Fig. 7.1. When a voltage is applied between the two electrode layers, Maxwell stress is produced and thus, the dielectric elastomer is compressed along the axial direction. The compression of each layer results in the lateral expansion of the actuator because of the incompressibility of the polymer. Consequently, the deformation of the multi-stacked actuator is the summation of the deformations of individual layers and, thus, the total deformation is expressed as follows. 

Regarding the shear springs, it is assumed that shear has no effects on the axial force and bending interaction. The hysteretic model for the shear spring is assumed to be multi-linear model, as shown in Fig. 19.7c, where Q is shear force and y the deflection of the shear wall due to shear deformation. The value of the shear force and deflection at cracking and yielding can be calculated according to the formulations proposed by the Architectural Institute of Japan. 

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