Abstract
Consider the kinematic compatibility equation QFR = F(I + a ⊗ n).
Here Q and R are two 3×3 matrices representing two rotations, F is a 3×3 matrix with det (F) > 0, I is the 3×3 identity matrix, a and n are two vectors in the 3-dimensional Euclidean space R 3, and a ⊗ n is the direct product. Assume F and R are given, and we solve for Q, a, n. We will first present a new proof of a criterion, due to Professor Jerry Ericksen, to be met by F and R for the existence of non-trivial solutions. Then we will give sufficient and necessary conditions for F and R under which the equation has solutions of special properties that are related to compound twins and multiple twins in crystals.
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Ou, B. On a kinematic compatibility equation related to elastic stress-free joints and crystal twins. J Elasticity 45, 73–89 (1996). https://doi.org/10.1007/BF00042484
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DOI: https://doi.org/10.1007/BF00042484