A dual-parametric finite element method is introduced in this paper for the computation of singular minimizers in the two dimensional cavitation problem in nonlinear elasticity. The method overcomes the difficulties, such as the mesh entanglement and material interpenetration, generally encountered in the finite element approximation of problems with extremely large expansionary deformation. Nu...

[A] matrix with constants describing the anisotropy of the material [B] strain matrix [BL] linear strain matrix [BNL] nonlinear strain matrix c speed of sound d rate of deformation tensor dp plastic rate of deformation D elastic constitutive tensor [D] matrix of the elastic constitutive tensor [DT] matrix form of the constitutive tensor ds lengths of the vector dx dS lengths of the vector dX dv...

Many materials exhibit a highly nonlinear elastic behavior, such as textiles or finger flesh. An efficient way of enforcing the nonlinearity of these materials is through strain-limiting constraints, which is often the model of choice in computer graphics. Strain-limiting allows to model highly non-linear stiff materials by eliminating degrees of freedom from the computations and by enforcing a...

In achieving accurate results, current nonlinear elastic recovery applications of finite element (FE) analysis have become more complicated for sheet metal springback prediction. In this paper, an artificial neural network (ANN) was used to mimic the nonlinear elastic recovery and provides a generalized solution in the FE analysis. The nonlinear elastic recovery was processed through back-propa...

One of the most promising materials in nanotechnology such as sensors, actuators and resonators is annular Boron Nitride sheets (ABNSs) due to excelled electro-thermo-mechanical properties. In this study, however, differential quadrature method (DQM) and nonlocal piezoelasticity theory are used to investigate the nonlinear vibration response of embedded single-layered annular Boron Nitride shee...

Biological materials such as, for instance, the human skin, brain tissue, papillary muscles, and arteries are often characterized as nonlinear elastic materials. Various attempts at characterizing a strain-energy density function for such materials have been made.1-4 In normal physiological functioning, as well as in inadvertent circumstances such as injuries, these materials are subject to fin...

An analytical solution for nonlinear vibration of an initially stressed beam with elastic end restraints resting on a nonlinear elastic foundation is obtained. As a first step in solving nonlinear vibration equation, the linear vibration mode functions for a beam with elastic end restraints resting on a linear elastic foundation are obtained. Then, the nonlinear vibration equation is solved by ...

Fire damage to concrete causes contact-type defects that degrade its durability through impaired mechanical properties. Various nondestructive tests are used to evaluate defects induced by fire damage. Recently, nonlinear ultrasonic methods such as the nonlinear resonance vibration method and nonlinear modulation method have been introduced. These nonlinear methods are more sensitive to fire-in...

This is the second of two papers describing a procedure for the three-dimensional nonlinear time-history analysis of steelframed buildings. An overview of the procedure and the theory for the panel zone element and the plastic hinge beam element are presented in part I. In this paper, the theory for an efficient new element for modeling beams and columns in steel frames called the elastofiber e...

An experimental observation of a new nonlinear-modulation effect for longitudinal elastic waves is reported. The phenomenon is a direct elastic wave analogy with the so-called Luxemburg-Gorky (L-G) effect known over 60 years for radio waves propagating in the ionosphere. The effect consists of the appearance of modulation of a weaker initially non-modulated wave propagating in a nonlinear mediu...