<P> where F (\ displaystyle (\ boldsymbol (F))) is the deformation gradient and J = det F (\ displaystyle J = \ det (\ boldsymbol (F))) is the Jacobian determinant . </P> <P> In terms of components with respect to an orthonormal basis, the first Piola--Kirchhoff stress is given by </P> <Dl> <Dd> P i L = J σ i k F L k − 1 = J σ i k ∂ X L ∂ x k (\ displaystyle P_ (iL) = J ~ \ sigma _ (ik) ~ F_ (Lk) ^ (- 1) = J ~ \ sigma _ (ik) ~ (\ cfrac (\ partial X_ (L)) (\ partial x_ (k))) ~ \, \!) </Dd> </Dl> <Dd> P i L = J σ i k F L k − 1 = J σ i k ∂ X L ∂ x k (\ displaystyle P_ (iL) = J ~ \ sigma _ (ik) ~ F_ (Lk) ^ (- 1) = J ~ \ sigma _ (ik) ~ (\ cfrac (\ partial X_ (L)) (\ partial x_ (k))) ~ \, \!) </Dd>

Define stress and strain and state their units