FE-Models of the Sheet Metal Forming Processes

[A] matrix with constants describing the anisotropy of the material [B] strain matrix [BL] linear strain matrix [BNL] nonlinear strain matrix c speed of sound d rate of deformation tensor dp plastic rate of deformation D elastic constitutive tensor [D] matrix of the elastic constitutive tensor [DT] matrix form of the constitutive tensor ds lengths of the vector dx dS lengths of the vector dX dv volume element in the current configuration dV volume element in the reference configuration E Young’s modulus E1, E2 principal values of Lagrangian strains E Green’s strain tensor Ė Green strain rate tensor f yield function f load {f ext} external force vector {f int} internal force vector F deformation gradient tensor [K] linear stiffness matrix [KG] geometric stiffness matrix [KM] material stiffness matrix [KS] initial stress stiffness matrix [KT] tangent matrix L lenght L velocity gradient tensor