# Initial-Boundary Value Problems and Solution Procedures

• Konstantin Naumenko
• Holm Altenbach
Chapter
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 112)

## Abstract

The objective of Chap. 2 is to introduce the governing mechanical equations to describe inelastic behavior in three-dimensional solids and to discuss numerical solution procedures. The set of equations includes material independent equations, constitutive and evolution equations, as well as the initial and boundary conditions. The formulated initial-boundary value problem (IBVP) can be solved by numerical methods. Explicit and implicit time integration methods were introduced in Chap. 1 for bars. In Chap. 2 they are generalized to analyze three-dimensional solids. Applying time-step procedures, linearized boundary value problems should be solved within time and/or iteration steps. The attention will be given to the variational formulations and the use of direct variational methods.

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