MechSys: Tensors::TijTensor Class Reference


Public Member Functions
	TijTensor (REAL TsMin)
	TijTensor class.
void	Derivs (const Tensor2 &Sig, REAL &tn, REAL &ts, REAL Is[3], REAL &sqrt_rz, Tensor2 &Tau, Tensor2 &inv_Tau, Tensor2 &a, Tensor2 &t, Tensor2 &dtn_ds, Tensor2 &dts_ds, Tensor2 &dts_dt)
	Derivatives and tij tensor related quantities {{{.
Private Attributes
REAL	_ts_min
	Mininum allowed value for ts (derivatives related).
Static Private Attributes
static REAL	ZERO = 1.0e-10

Detailed Description

Constructor & Destructor Documentation

Tensors::TijTensor::TijTensor ( REAL TsMin ) [inline]

Parameters:

TsMin

Minimum allowed value for ts (derivatives related)

Definition at line 55 of file tijtensor.h.

Member Function Documentation

void Tensors::TijTensor::Derivs	(	const Tensor2 &	Sig,
		REAL &	tn,
		REAL &	ts,
		REAL	Is[3],
		REAL &	sqrt_rz,
		Tensor2 &	Tau,
		Tensor2 &	inv_Tau,
		Tensor2 &	a,
		Tensor2 &	t,
		Tensor2 &	dtn_ds,
		Tensor2 &	dts_ds,
		Tensor2 &	dts_dt
	)			`[inline]`

Derivatives and tij tensor related quantities {{{.

Parameters:

	Sig	In: Stress tensor $\TeSe{\sigma}$
	tn	Out: Mean stress invariant $t_N \gets 3\frac{I_3}{I2}$
	ts	Out: Deviatoric stress invariant $t_S \gets \frac{\sqrt{I_1I_2I_3-9I_3^2}}{I_2}$
	Is[3]	Out: Characterist invariants of stress (Sig)
	sqrt_rz	Out: Sqrt of I3/I2 $\sqrt{\frac{I_3}{I_2}}$
	Tau	Out: Tensor Sqrt of Sig $\TeSe{\tau} \gets \sqrt{\TeSe{\sigma}}$
	inv_Tau	Out: Inverse of tensor Tau $\TeSe{\tau}^{-1}$
	a	Out: "normal-to-SMP" tensor == Derivative of tn w.r.t tij tensor $\TeSe{a} \gets \sqrt{\frac{I_3}{I_2}}\TeSe{\tau}^{-1} \equiv \pderiv{t_N}{\TeSe{t}}$
	t	Out: Modified tij tensor $\TeSe{t} \gets \TeSe{a}\bullet\TeSe{\sigma}$
	dtn_ds	Out: Derivative of tn w.r.t Sig $\pderiv{t_N}{\TeSe{\sigma}} \gets \frac{-\tn}{I_2}(I_1\TeSe{I}-\TeSe{\sigma}) + \frac{3}{I_2}(\TeSe{\sigma}\bullet\TeSe{\sigma}-I_1\TeSe{\sigma}+I_2\TeSe{I})$
	dts_ds	Out: Derivative of ts w.r.t Sig $\pderiv{t_S}{\TeSe{\sigma}} \gets \frac{t_N}{6t_S}\TeSe{I}+\frac{t_N(6t_N-I_1)}{6t_S I_2}(I_1\TeSe{I}-\TeSe{\sigma}) + \frac{I_1-6t_N}{2t_S I_2} (\TeSe{\sigma}\bullet\TeSe{\sigma}-I_1\TeSe{\sigma}+I_2\TeSe{I})$
	dts_dt	Out: Derivative of ts w.r.t tij tensor $\pderiv{t_S}{\TeSe{t}} \gets \frac{\TeSe{t}-t_N\TeSe{a}}{t_S}$ }}}