Converting to Voigt’s notation

Many finite-element solvers store symmetric second-order tensors as 6-component vectors and symmetric fourth-order tensors as matrices (Voigt notation). tmech bridges full tensor notation and Voigt storage through the adaptor, which wraps a pre-allocated raw array and presents it as a tensor while transparently applying the solver’s Voigt layout.

The adaptor is parameterised by the value type, the spatial dimension, the tensor rank, and a layout policy. The bundled abq_exp policy implements the Abaqus UMAT/VUMAT convention (the trailing true selects the strain layout, where off-diagonal shear components carry the engineering factor of two):

#include <tmech/tmech.h>

// Raw arrays as they arrive from the solver.
double ptrC[36], ptrSig[6];
double ptrEps[6]{1, 1, 1, 1, 1, 0.5};

const double K{12000}, G{200};
tmech::eye<double, 3, 2> I;
const auto IIsym = (tmech::otimesu(I, I) + tmech::otimesl(I, I)) * 0.5;
const auto IIvol = tmech::otimes(I, I) / 3.0;
const auto IIdev = IIsym - IIvol;

// Wrap the raw arrays; the adaptor handles the Voigt layout.
tmech::adaptor<double, 3, 4, tmech::abq_exp<3>>        C(ptrC);
tmech::adaptor<double, 3, 2, tmech::abq_exp<3>>        sig(ptrSig);
tmech::adaptor<double, 3, 2, tmech::abq_exp<3, true>>  eps(ptrEps);

// Compute using ordinary tensor syntax; results are written back
// into the raw arrays in Voigt order.
C   = 3 * K * IIvol + 2 * G * IIdev;
sig = tmech::dcontract(C, eps);

Assigning to an adaptor writes the result back into the underlying array in the solver’s Voigt ordering, so ptrC and ptrSig above are ready to be returned to the solver. See the adaptor page and the complete UMAT/VUMAT programs under examples/adaptor/abaqus/ for full, compilable examples.