Nonuniform Deformation of Cell Structures Owing to Plastic Stress Wave Propagation

In cell structures, unlike in dense bodies, nonuniform deformation occurs from the impact end, even at velocities in the order of tens to hundreds of meters per second. In this study, we experimentally examine the nonuniform deformation mechanism of cell structures. They prepared two kinds of specimens: nickel foam (Ni foam) and silicone-rubber-filled nickel foam (Ni/silicone foam). As a dynamic and impact test method (compression velocity of 20 m/s or more), we used a dynamic and impact load-measuring apparatus with opposite load cells to evaluate the loads on both ends of the specimen in one test. At compression velocities of 20 m/s or less, no nonuniform deformations were observed in the Ni foam and the Ni/silicone foam, and the loads on the impact and the fixed ends achieved force equilibrium. The Ni foam showed no change with an increasing strain rate, and the Ni/silicone foam showed a strong strain rate dependence of the flow stress. At a compression velocity of approximately 26 m/s, the loads differed at the two ends of the Ni/silicone foam, and we observed nonuniform deformation from the impact end. The results of the visualization of the load and deformation behavior obtained from both ends of the specimen revealed that the velocity of the plastic stress wave and the length of the specimens are important for nonuniform deformation.

Nonuniform Stress Field Determination Based on Deformation Measurement

We demonstrate a technique that, under certain circumstances, will determine stresses associated with a nonuniform deformation field without knowing the detailed constitutive behavior of the deforming material. This technique is based on (1) a detailed deformation measurement of a domain and (2) the observation that for isotropic materials, the strain and the stress, which form the so-called work-conjugate pair, are co-axial, or their eigenvectors share the same direction. The particular measures for strain and stress considered are the Lagrangian strain and the second Piola-Kirchhoff stress. The deformation measurement provides the field of the principal stretch orientation θλ and since the Lagrangian strain and the second Piola-Kirchhoff stress are co-axial, the principal stress orientation θs of the second Piola-Kirchhoff stress is determined. The Cauchy stress is related to the second Piola-Kirchhoff stress through the deformation gradient tensor, which can be measured experimentally. We then show that the principal stress orientation θσ of the Cauchy stress is the sum of the principal stretch orientation θλ and the local rigid-body rotation θq, which is determinable by the deformation gradient through polar decomposition. With the principal stress orientation θσ known, the equation of equilibrium, now in terms of the two principal stresses σ1 and σ2, and θσ, can be solved numerically with appropriate traction boundary conditions. The technique is then applied to the experimental case of nonuniform deformation of a PVC sheet with a circular hole and subject to tension. Limitations and restrictions of the technique and possible extensions will be discussed.

Effects of Constant Amplitude Cyclic Loading on the Nonuniform Deformation of Sandstone Specimens

In order to explore the mechanical response mechanism of rock materials under cyclic loading, uniaxial constant amplitude cyclic loading tests for sandstone specimens were carried out. The images of specimen deformation during the tests were captured by charge-coupled device (CCD) cameras. Based on the digital image correlation method (DICM), the evolution laws of nonuniform deformation and displacements around localization bands during cyclic loading were investigated. The experimental results show that, during the cyclic loading process, the nonuniform deformation continually escalates with the number of cycles increasing and fluctuates with the cyclic loading stress condition; the nonuniform deformation lags behind the variation of loading stress; and the whole nonuniform deformation experiences a slow evolution stage and a fast evolution stage. At the loading stage or unloading stage, the nonuniform deformation of rock deteriorates with the number of cycles increasing under the same stress condition. In each loading cycle, the nonuniform deformation at the unloading stage is more than that at the loading stage under the same stress condition. The time of dislocation displacements and tension displacements meets hysteresis, compared with the time of stress change. In addition, the dislocation displacements and tension displacements around localization bands in general increase with the number of cycles increasing. The displacement evolution around localization bands has the same hysteresis and accumulation laws as that of nonuniform deformation.