# CE 234 : Computational Inelasticity

## Expanded Course Description

This course will cover issues related to computational inelasticity
in a variety of settings. A brief overview of 1-D plasticity with hardening in the
small-deformation setting will be given. Proper algorithmic methods for approximating boundary
value problems utilizing this constitutive relation will then be considered. Particular attention
will be given to respecting the physical and theoretical properties of the continuum problem.
Loading/unloading conditions will be covered in detail, as will be thermodynamic considerations
as they pertain to algorithm design. Extensions of these methods to viscoplasticity will also be
considered using the Perzyna and Duvaut-Lions regularizations. The 3-D formulation of classical
rate-independent plasticity and viscoplasticity will also be covered. Included in this discussion
will be a thermodynamic framework for such problems that has direct bearing on computational issues.
Notations related to the maximum-dissipation hypothesis and stability will be presented. Based on
the theoretical , algorithms will be considered that respect the properties of the time continuous
equations. Closest-point projection and operator split methodologies will be examined. The
remainder of the course will utilize these computational methodologies in large deformation
inelasticity; both classical rate formulations and modern displacement based formulations will be
examined. For large deformation problems in rate form, particular emphasis will be given to the
development of algorithms that are incrementally objective. Displacement based formulations will
be addressed by exploiting their formal mathematical relation to classical small-deformation
plasticity in a setting that respects objectivity and thermodynamic properties of the continuum
relations. Modern multiplicative formulations of finite strain plasticity
will be studied in detail. Plasticity in coupled settings (i.e. thermoplasticity and plasticity of
porous media) and their integration agorithms will also be discussed, as it will be
damage theories and recent variational treatments involving relaxation,
time permitting and depending of class interests.

armero@CE.Berkeley.EDU

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