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.

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

A mixed finite-element analysis is presented for static behavior of rectangular plates laminated of composite materials having finite transverse shear moduli and different elastic properties depending upon whether the fiber-direction strains are tensile or compressive. As a benchmark to assess the validity and accuracy of the finite-element analysis, a closed-form solution is given for a two-layer, cross-ply plate having all edges simply supported without in-plane restraint and subjected to sinusoidally distributed normal pressure. Numerical results obtained by the two methods are compared and found to agree quite well.

Bending of Thick Rectangular Plates Laminated of Bimodulus Composite Materials

Free flexural vibration behavior of bimodular material angle-ply laminated composite plates

https://web.iitd.ac.in/~bppatel/publicatios/Thermo-flexural%20analysis%20of%20thick%20laminates%20of%20bimodulus.pdf

Thermo-flexural analysis of thick laminates of bimodulus composite materials

/pdf/application-of-the-kirchhoff-hypothesis-to-bending-thin-1gpid1jaf3.pdf

W.C. Chao

Papers

Nonlinear Bending of Bimodular-Material Plates.