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Comparison of the geometrically nonlinear and linear theories of martensitic transformation

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Abstract

Over the last few years, a continuum model based on finite or nonlinear thermoelasticity has been developed and successfully used to study crystalline solids that undergo a martensitic phase transformation. A geometrically linear version of this model was developed independently and has been widely used in the materials science literature. This paper presents the two theories and evaluates them by comparing and contrasting the results in various problems. It is established that in analyzing particular microstructures, the linear theory does not offer significant simplifications and misses important details. However, in more general situations where the particular microstructure is unknown and may involve stress, the linear theory can address certain problems which are currently beyond the capabilities of the nonlinear theory. Such analysis can yield valuable qualitative information. Finally, an example where the two theories differ dramatically is presented.

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  1. Cóurant Institute of Mathematical Sciences, 251 Mercer Street, 10012, New York, NY, USA

    K. Bhattacharya

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Bhattacharya, K. Comparison of the geometrically nonlinear and linear theories of martensitic transformation. Continuum Mech. Thermodyn 5, 205–242 (1993). https://doi.org/10.1007/BF01126525

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