The Eshelby tensor E has vanishing divergence in a homogeneous elastic material, whereas the invariance of the crack tip J integral suggests, in accord with known solutions, that the product rE will have a finite limit at the tip. Here r is distance from the tip. These considerations are shown to lead to two general integrals of the equations governing singular crack tip deformation fields. Som...

In this paper, a new formulation based on Artificial Neural Networks (ANN) is presented for backcalculation of pavement layer moduli. In structural analysis of flexible pavements, the procedures as Layered Elastic Theory, Equivalent Layer Thickness (ELT), and Finite Elements Method (FEM) generally have complex formulations and give approximate results. Therefore, it is extremely difficult to pe...

We investigate short wavelength buckling of a thin elastic rod embedded in an elastic gelatin biopolymer network. Using a combination of micro-mechanical testing, microscopic imaging, as well as theory, we show that the buckling penetration depth can be tuned by varying the mechanical properties of the rod and the rod–gel interface. Prior models have predicted a decay length that is dependent o...

In quasi-static tests, flexible polyurethane foam undergoing large compressive loading and unloading deformation exhibits highly nonlinear and viscoelastic behavior. In particular, the response in the first cycle is significantly different from the response in subsequent cycles. In addition, the stresses in the loading paths are higher than those in unloading paths. It is assumed that this quas...

An extremum principle is presented covering problems in solid mechanics equilibrium analysis for piecewise linear softening materials. Problems formulated according to this principle are expressed in a mixed “stress and deformation” form. The mechanics interpretation is limited according to linear deformation kinematics. More specialized models, such as an exfremumprinciple in mixed form for li...

Developed in the late 1980s, Nonlinear Resonant Ultrasound Spectroscopy (NRUS) has been widely employed in the field of material characterization. Most of the studies assume the measured amplitude to be proportional to the strain amplitude which drives nonlinear phenomena. In 1D resonant bar experiments, the configuration for which NRUS was initially developed, this assumption holds. However, i...

We present a constitutive model capturing some of the experimentally observed features of soft biological tissues: nonlinear viscoelasticity, nonlinear elastic anisotropy, and nonlinear viscous anisotropy. For this model we derive the equation governing rectilinear shear motion in the plane of the fiber reinforcement; it is a nonlinear partial differential equation for the shear strain. Special...

Nonlinear properties of lead zirconate-titanate ~PZT! piezoceramics are investigated using ultrasonic second harmonic generation technique. When a sinusoidal ultrasonic wave of frequency v0 is sent into a nonlinear material, the second harmonic wave with frequency 2v0 is generated. Through measuring the absolute amplitude of the fundamental (v0) and of the second harmonic (2v0) waves, the ultra...

In bioengineering applications problems of flow interacting with elastic solid are very common. We formulate the problem of interaction for an incompressible fluid and an incompressible elastic material in a fully coupled arbitrary Lagrangian-Eulerian formulation. The mathematical description and the numerical schemes are designed in such a way that more complicated constitutive relations (and ...

In this work, the effect of the concentration-dependent chemical-expansion coefficient, b, on the chemo-elastic field in lithium-ion cathode particles is examined. To accomplish this, an isotropic linear-elastic model is developed for a single idealistic particle subjected to potentiostatic-discharge and charge conditions. It is shown that b can be a key parameter in demarcating the chemo-stres...