Viscoelastic Modeling for Structural Analysis

Materials such as polymers, soils and concrete often change shape over time under a constant load, and viscoelasticity theory provides a mechanical way to describe this time-dependent response. Aimed mainly at students of civil and mechanical engineering, this book focuses on linear viscoelastic behavior under small disturbances. It starts with the basic one-dimensional creep and relaxation experiments, then introduces linearity and the absence of aging one at a time, showing how each leads to a constitutive law written with Boltzmann integral operators and Riemann convolution products.

The author then applies these ideas to simple quasi-static loading cases, showing how ignoring time-dependent effects during design can lead to serious and even disastrous outcomes. Extending the analysis to three dimensions, the book writes the linear viscoelastic constitutive equation in compact tensor notation while accounting for material symmetries. It then examines quasi-static linear viscoelastic problems, comparing them with their elastic counterparts to highlight where the two agree and where they diverge.

Throughout, worked case studies stress that a clear physical understanding of a problem should come before its mathematical treatment.