A review on the research of mechanical problems with different moduli in tension and compression

Abstract

Most materials exhibit different tensile and compressive strains given the same stress applied in tension or compression. These materials are known as bimodular materials. An important model of bimodular materials is the criterion of positive-negative signs of principal stress proposed by Ambartsumyan. This model is mainly applicable to isotropic materials and deals with the principal stress state in a point. However, due to the inherent complexity of the constitutive relation, FEM based on iterative strategy and analytical methods based on a simplified mechanical model are required. In this paper, we review the basic assumptions of this model and its development, several innovative computational methods, and some important engineering applications. We also discuss the sequent key problems in this field.

A practical method for simultaneous determination of Poisson’s ratio and Young’s modulus of elasticity of thin films

“…Most materials may exhibit different tensile and compressive strains given the same stress applied in tension or compression. These materials are known as bimodular materials [47]. However, in membrane problems, the flexural rigidity of flexible thin films is usually neglected; only stretching effect of the membrane is considered.…”

Large-deflection axisymmetric deformation of circular clamped plates with different moduli in tension and compression

“…In other words, except in particularly simple problems it is not easy to estimate a priori the stress state in a point in the deformed body. In some complex problems, we have to resort to FEM based on an iterative strategy [12][13][14]. Generally, many researchers adopted directly iterative methods based on an incrementally evolving stiffness, including an improved algorithm in which the shear stress and shear strain are set to zero to formulate the elastic matrix [15][16][17], an improved algorithm keeping Poisson's ratio constant while modifying the elastic matrix [18,19], the initial stress technique [20], the smoothing function technique [21], a new and simple analytical-iterative method for statically indeterminate structures [22] and an iterative process applying the principle of strain invariant [23].…”

The Influence of Boundary Conditions on Modulus Measurement in Uniaxial Compression Tests

“…Especially, the compression test is easier for metallic glass to produce the plasticity than tensile test [2][3][4][5]. In addition, compression tests are necessary for characterizing the mechanical behavior of anisotropic materials and bimodular materials [6][7][8], such as highly textured materials that deform by twinning as two separate crystals share some of the same crystal lattice points in a symmetrical manner [9].…”