Multiscale Modelling of Rubber-like and Soft Materials

This book provides a comprehensive introduction to the multiscale modeling of rubber-like and soft materials, linking microscopic mechanisms with macroscopic mechanical behavior. It presents a unified framework based on continuum mechanics, statistical mechanics, and microstructural modeling to understand and predict the complex response of the systems under scrutiny.

Rubber-like materials are essential in many technological applications, including tires, seals, vibration isolators, biomedical devices, and components for soft robotics. At the same time, biological soft materials such as tissues, spider silk, and protein-based structures display remarkable mechanical properties that often surpass those of many synthetic materials. These properties arise from sophisticated molecular architectures and hierarchical structures that span multiple physical scales. Understanding how these microscopic mechanisms influence macroscopic behavior is therefore crucial for both accurate modeling of existing materials and the design of new advanced materials.

The main objective of this book is to present a coherent theoretical framework capable of connecting material behavior across different scales. Classical nonlinear elasticity provides powerful tools to describe large deformations and nonlinear stress-strain relationships, but it often relies on phenomenological constitutive laws that are not directly linked to molecular structure. Conversely, statistical mechanics describes the physics of polymer chains and molecular networks but is not always easily translated into engineering-scale models. This book addresses this gap by integrating continuum mechanics with statistical and thermomechanical approaches within a multiscale modeling perspective.

The book first introduces the physical characteristics of rubber-like materials, including large reversible deformations and entropic elasticity. It connects nonlinear elasticity and experimental observations with thermodynamics and statistical mechanics. Single-chain models, molecular unfolding, and network homogenization provide a multiscale framework for interpreting macroscopic behavior, including damage, anisotropy, and residual deformation, with applications to elastomeric, biological, and bioinspired materials.

The book is intended for graduate students, but also researchers, and professionals in applied mathematics, continuum mechanics, materials science, mechanical engineering, and biomechanics interested in the modeling of rubber-like and soft materials.