User's manual for GAMNAS: Geometric and Material Nonlinear Analysis of Structures

GAMNAS (Geometric and Material Nonlinear Analysis of Structures) is a two dimensional finite-element stress analysis program. Options include linear, geometric nonlinear, material nonlinear, and combined geometric and material nonlinear analysis. The theory, organization, and use of GAMNAS are described. Required input data and results for several sample problems are included

Finite element analysis of compressible solids with nonlinear material properties

Finite-element computer program solves for nodal point displacements in an axisymmetric solid. The options in the program include plane stress analysis, axisymmetric solids analysis, nonlinear /plastic/ analysis, and equivalent stress and strain

Amplitude-equation formalism for four-wave-mixing geometry with transmission gratings

An amplitude equation is derived for a four-wave-mixing geometry with nearly counterpropagating, mutually incoherent, nondiffracting pump beams, spatially overlapping in a photorefractive material with a nonlocal response. This equation extends the earlier linear two-dimensional theory to the weakly nonlinear regime. The analysis also starts from a more complete equation for the photorefractive effect, which leads to the prediction of novel effects especially apparent in the nonlinear regime. Precise predictions for the spatiotemporal behavior of the grating amplitude in the nonlinear regime are presented. The range of validity of the amplitude equation is studied. The characteristics of the instability in the nonlinear regime are analyzed through a front-selection analysis

Arbitrary order 2D virtual elements for polygonal meshes: Part II, inelastic problem

The present paper is the second part of a twofold work, whose first part is reported in [3], concerning a newly developed Virtual Element Method (VEM) for 2D continuum problems. The first part of the work proposed a study for linear elastic problem. The aim of this part is to explore the features of the VEM formulation when material nonlinearity is considered, showing that the accuracy and easiness of implementation discovered in the analysis inherent to the first part of the work are still retained. Three different nonlinear constitutive laws are considered in the VEM formulation. In particular, the generalized viscoplastic model, the classical Mises plasticity with isotropic/kinematic hardening and a shape memory alloy (SMA) constitutive law are implemented. The versatility with respect to all the considered nonlinear material constitutive laws is demonstrated through several numerical examples, also remarking that the proposed 2D VEM formulation can be straightforwardly implemented as in a standard nonlinear structural finite element method (FEM) framework

Design sensitivity analysis of nonlinear structural response

A unified theory is described of design sensitivity analysis of linear and nonlinear structures for shape, nonshape and material selection problems. The concepts of reference volume and adjoint structure are used to develop the unified viewpoint. A general formula for design sensitivity analysis is derived. Simple analytical linear and nonlinear examples are used to interpret various terms of the formula and demonstrate its use

Trends of mechanical consequences and modeling of a fibrous membrane around femoral hip prostheses

In the present study, the effects of a fibrous membrane between cement and bone in a femoral total hip replacement were investigated. The study involved the problem of modeling this fibrous membrane in finite-element analyses, and its global consequences for the load-transfer mechanism and its resulting stress patterns. A finite-element model was developed, suitable to describe nonlinear contact conditions in combination with nonlinear material properties of the fibrous membrane. The fibrous tissue layer was described as a highly compliant material with little resistance against tension and shear. The analysis showed that the load transfer mechanism from stem to bone changes drastically when such a membrane is present. These effects are predominantly caused by tensile loosening and slip at the interface, and are enhanced by the nonlinear membrane characteristics.\ud \ud Using parametric analysis, it was shown that these effects on the load-transfer mechanism cannot be described satisfactorily with linear elastic models.\ud \ud Most importantly, the fibrous tissue interposition causes excessive stress concentrations in bone and cement, and relatively high relative displacements between these materials

Quantifying perception of nonlinear elastic tissue models using multidimensional scaling

Simplified soft tissue models used in surgical simulations cannot perfectly reproduce all material behaviors. In particular, many tissues exhibit the Poynting effect, which results in normal forces during shearing of tissue and is only observed in nonlinear elastic material models. In order to investigate and quantify the role of the Poynting effect on material discrimination, we performed a multidimensional scaling (MDS) study. Participants were presented with several pairs of shear and normal forces generated by a haptic device during interaction with virtual soft objects. Participants were asked to rate the similarity between the forces felt. The selection of the material parameters – and thus the magnitude of the shear\ud and normal forces – was based on a pre-study prior to the MDS experiment. It was observed that for nonlinear elastic tissue models exhibiting the Poynting effect, MDS analysis indicated that both shear and normal forces affect user perception

Noise Performance Comparison of 1.5 um Correlated Photon Pair Generation in Different Fibers

In this paper, the noise performances of 1.5 um correlated photon pair generations based on spontaneous four wave-mixing in three types of fibers, i.e., dispersion shifted fiber, highly nonlinear fiber, and highly nonlinear microstructure fiber are investigated experimentally. Result of the comparison shows that highly nonlinear microstructure fiber has the lowest Raman noise photon generation rate among the three types of fibers while correlated photon pair generation rate is the same. Theoretical analysis shows that the noise performance is determined by the nonlinear index and Raman response of the material in fiber core. The Raman response raises with increasing doping level, however, the nonlinear index is almost unchanged with it. As a result, highly nonlinear microstructure fiber with pure silica core has the best noise performance and has great potential in practical sources of correlated photon pairs and heralded single photons.Comment: 10 pages, 6 figure

Temperature dependent nonlinear metal matrix laminae behavior

An analytical method is described for computing the nonlinear thermal and mechanical response of laminated plates. The material model focuses upon the behavior of metal matrix materials by relating the nonlinear composite response to plasticity effects in the matrix. The foundation of the analysis is the unidirectional material model which is used to compute the instantaneous properties of the lamina based upon the properties of the fibers and matrix. The unidirectional model assumes that the fibers properties are constant with temperature and assumes that the matrix can be modelled as a temperature dependent, bilinear, kinematically hardening material. An incremental approach is used to compute average stresses in the fibers and matrix caused by arbitrary mechanical and thermal loads. The layer model is incorporated in an incremental laminated plate theory to compute the nonlinear response of laminated metal matrix composites of general orientation and stacking sequence. The report includes comparisons of the method with other analytical approaches and compares theoretical calculations with measured experimental material behavior. A section is included which describes the limitations of the material model