Large Strain Analysis and Stresses in Linear Materials

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Abstract
A method is presented to determine stresses and strains in a greatly deformed body subjected to a state of plane stress when the modulus of elasticity of the material used is approximately constant within the range of natural strains being considered. To demonstrate the method, a birefringent disk is subjected to a series of large diametral compressive loads, and the principal stresses and strains are computed across the horizontal diameter by means of photoelasticity, grids, and thickness measurements. Natural strains and true stresses are used in the analysis. With this type of description, the mechanical properties of the material are linear to a strain of 0.15 with a deviation of less than 5% from linearity in Young's modulus at a strain level of 0.18. Birefringence is linear to beyond 0.15 strain. Results are given in dimensionless form. Equilibrium checks are satisfactory for all levels of load applied.

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