Selected Topics of Inelasticity Theory

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It is the superior goal of the lecture to foster the understanding of general inelastic material behaviour with regard to the theoretical modelling and the numerical treatment based on selected model problems. Thereby, both purely phenomenological and micromechanically motivated approaches to inelastic material responses are considered. This comprises different kinds of solid inelasticity ranging from large strain viscoelasticity of polymeric materials via superplastic metal alloys to plastic strain localisation in granular matter such as soils.

Lecture-related exercises help to understand the partly abstract and theoretical course content. The numerical implementation of the governing equations for selected dissipative problems will be discussed and exercised employing easy-to-understand finite element software tools.

Course Content

• Introduction to general inelastic material behaviour
• Phenomenological classification of material responses
• Kinematics of finite inelastic deformations
• Multiplicative geometric concept in natural basis and spectral representation
• Constitutive modelling with internal state variables
• Derivation and evaluation of the dissipation inequality
• Formulation of thermodynamical consistent inelastic evolution equations
• Stress computation and numerical treatment of evolution equations

References (selection)

Fundamentals of Mechanics and Tensor Calculus

• B. Markert, lecture notes, Engineering Mechanics I, Vector calculus
• B. Markert, lecture notes, Engineering Mechanics II, Tensor calculus

Fundamentals of Continuum Mechanics and Materials Theory

• J.C. Simo, T.J.R. Hughes, Computational Inelasticity, Springer, 1998.
• G.A. Holzapfel, Nonlinear Solid Mechanics: A Continuum Approach for Engineering,
• John Wiley & Sons, 2000.
• P. Haupt, Continuum Mechanics and Theory of Materials, Springer, 2000.
• B. Markert, A Biphasic Continuum Approach for Viscoelastic High-Porosity Foams: Comprehensive Theory, Numerics, and Application. Arch Computat Methods Eng 15, 371–446 (2008).

More literature will be mentioned throughout lectures and exercises.