From Event: SPIE Optical Engineering + Applications, 2017
Thermally induced stress is readily calculated for linear elastic material properties using Hooke’s law in which, for situations where expansion is constrained, stress is proportional to the product of the material elastic modulus and its thermal strain. When material behavior is nonlinear, one needs to make use of nonlinear theory. However, we can avoid that complexity in some situations. For situations in which both elastic modulus and coefficient of thermal expansion vary with temperature, solutions can be formulated using secant properties. A theoretical approach is thus presented to calculate stresses for nonlinear, neo-Hookean, materials. This is important for high acuity optical systems undergoing large temperature extremes.
John W. Pepi, "Linear analysis using secants for materials with temperature dependent nonlinear elastic modulus and thermal expansion properties," Proc. SPIE 10371, Optomechanical Engineering 2017, 1037108 (Presented at SPIE Optical Engineering + Applications: August 09, 2017; Published: 23 August 2017); https://doi.org/10.1117/12.2274817.
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