I have the following expression to simplify

$$k\_1 c\_1^4 + k\_{12} c\_1^2c\_2^2 + k\_2 c\_2^4$$

using the conditions

$$
c\_1^2 = c\_{11}
$$
$$
c\_2^2 = c\_{22}
$$
$$
c\_1 c\_2 = c\_{12}
$$

and I would like to write the expression above as

$$k\_1 c\_{11}^2 + k\_{12} c\_{12} + k\_2 c\_{22}^2$$

How can I do it with Mathematica?