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This chapter provides a succinct introduction to the historical and conceptual foundations of nonlinear elasticity. We begin with presenting the evolution of nonlinear elasticity from its linear counterpart, and its extension to modern applications with modelling the mechanical behaviour of rubber and biological soft tissues. We then recall essential mechanical, algebra, and calculus concepts required for understanding the theory, including stress-strain relationships, tensor algebra, and differential operators. We present typical stress-strain curves for metals, soft tissues, and rubber-like materials (including a tabletop experiment) to illustrate the versatility of nonlinear elasticity. This foundational knowledge sets the stage for exploring the mechanical behaviour of rubber-like materials and biological tissues in the subsequent chapters.

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Introduction

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  • 发表日期：

    2025年

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  • Michel Destrade,
  • Giuseppe Zurlo

摘要

This chapter provides a succinct introduction to the historical and conceptual foundations of nonlinear elasticity. We begin with presenting the evolution of nonlinear elasticity from its linear counterpart, and its extension to modern applications with modelling the mechanical behaviour of rubber and biological soft tissues. We then recall essential mechanical, algebra, and calculus concepts required for understanding the theory, including stress-strain relationships, tensor algebra, and differential operators. We present typical stress-strain curves for metals, soft tissues, and rubber-like materials (including a tabletop experiment) to illustrate the versatility of nonlinear elasticity. This foundational knowledge sets the stage for exploring the mechanical behaviour of rubber-like materials and biological tissues in the subsequent chapters.