Finite deformation coupled thermomechanical problems and ‘generalized standard materials’

Abstract

Technological forming processes of thermo-elastoviscoplastic solids are numerically simulated via ÿnite elements based on an appropriate theoretical framework. Departing from the local balance laws of linear momentum and internal energy, the constitutive behaviour is introduced via the concept of 'generalized standard materials (gsm)', 1-3 where a thermodynamic potential and a dissipation potential are the only two scalar quantities needed. They are expressed in invariants of symmetric mixed-variant tensors, respectively. Then the dissipation term evolves from the thermodynamic potential in a very natural way as well as the evolution equations for the internal variables emanate from the dissipation potential. An Eulerian setting is used.The numerical solution (of the non-linear coupled thermomechanical problem) is carried out via 'displacement and assumed enhanced displacement-gradient'-based ÿnite ring-elements 4 in an 'isentropic' mechanical phase and via 'temperature'-based ÿnite ring-elements in an isogeometrical thermal phase and a global Newton-Raphson iterative method in both phases, respectively. The coupled consistent tangent moduli are carefully derived. Numerical results of the thermally triggered necking of a circular bar and of the impact of a copper rod on a rigid wall are given. ? 1998 John Wiley & Sons, Ltd.

An improved ?assumed enhanced displacement gradient? ring-element for finite deformation axisymmetric and torsional problems

“…The numerical simulation (via a Newmark method, for details see Reference [8]) stops automatically, when the current length of the central ÿbre (x 1 = 0, rotational axis) re-increases: for the q1=e7-model i.e. at t = 77:0 s, for the q1=e7m-model i.e.…”

On strong discontinuities in anelastic solids. A finite element approach taking a frame indifferent gradient of the discontinuous displacements

“…g denotes the co-variant ‡ metric tensor of the current conÿguration and the accumulated plastic strain = n i=1 i (or Odquist parameter). From w we get the stresses, which are thermodynamically conjugate to 1 2 g; 1 2 c p−1 and , respectively (see Reference [12])…”

“…From (78) we get the mixed ÿnite element equations for iteration (k) in a speciÿc increment : The element tangent sti ness matrices k ij (i = u; c; j = u; a) consist of two parts, the geometric part k g ij and the material part k m ij , respectively: The matrices b g 1 ; B 4 × 4 ; b; b g 2 ; a g 1 ; a; a g 2 ; c g ; c are all explicitly given in Appendix A.1, jc see for instance Reference [12].…”

An invariant-based anisotropic material model for short fiber-reinforced thermoplastics: Coupled thermo-plastic formulation

“…In the related literature, from the numerical standpoint, a significant number of studies have been devoted to the theoretical formulation and numerical treatment of anisotropic plastic models [14,27,28,26,35,33,41] and thermo-mechanical formulations [11,23,24,38,40]. In this setting, Reese and coauthors developed several few models for the large deformation that accounted for anisotropic inelastic behavior based upon a structural tensorial representation, see [30,42] and the references therein given.…”