Numerical implementation of inelastic time-dependent and time-independent, finite-strain constitutive equations in structural mechanics
A number of complex issues are resolved in a way that allows the incorporation of finite strain, inelastic material behavior into the piecewise numerical construction of solutions in solid mechanics. Without recourse to extensive continuum mechanics preliminaries, an elementary time independent plasticity model, an elementary time dependent creep model, and a viscoelastic model are introduced as examples of constitutive equations which are routinely used in engineering calculations. The constitutive equations are all suitable for problems involving large deformations and finite strains. The plasticity and creep models are in rate form and use the symmetric part of the velocity gradient or the stretching to compute the co-rotational time derivative of the Cauchy stress. The viscoelastic model computes the current value of the Cauchy stress from a hereditary integral of a materially invariant form of the stretching history. The current configuration is selected for evaluation of equilibrium as opposed to either the reference configuration or the last established equilibrium configuration. The process of strain incrementation is examined in some depth. The stretching, evaluated at the mid-interval and multiplied by the time step, is identified as the appropriate finite strain increment to use with the selected forms of the constitutive equations. Discussed is the conversion of rotation rates based on the spin into incremental orthogonal rotations. These rotations are used to update stresses and state variables due to rigid body rotation during the load increment. Comments and references to the literature are directed at numerical integration of the constitutive equations with an emphasis on doing this accurately, if not exactly, for any time step and stretching. This material taken collectively provides an approach to numerical implementation which is marked by its simplicity.
- Research Organization:
- Sandia National Labs., Albuquerque, NM (USA)
- DOE Contract Number:
- AC04-76DP00789
- OSTI ID:
- 5969667
- Report Number(s):
- SAND-81-2192C; CONF-810896-1; ON: DE82004131
- Country of Publication:
- United States
- Language:
- English
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