On a kinematic compatibility equation related to elastic stress-free joints and crystal twins
✍ Scribed by Biao Ou
- Publisher
- Springer Netherlands
- Year
- 1996
- Tongue
- English
- Weight
- 768 KB
- Volume
- 45
- Category
- Article
- ISSN
- 0374-3535
No coin nor oath required. For personal study only.
✦ Synopsis
Consider the kinematic compatibility equation
Here Q and R are two 3 x 3 matrices representing two rotations, F is a 3 x 3 matrix with det(F) > 0, I is the 3 x 3 identity matrix, a and n are two vectors in the 3-dimensional Euclidean space/~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.