The fundamental equations of the theory of elasticity are:

In contrast, plasticity theory deals with materials that undergo permanent deformation without failing. Plastic deformation occurs when the material is subjected to a stress that exceeds its yield strength. The plastic behavior of materials is characterized by a non-linear stress-strain curve, which can be described by various mathematical models.

The theory of elasticity and plasticity is a fundamental concept in mechanics of materials, and it has numerous applications in various fields of engineering. The book "Theory of Elasticity and Plasticity" by Jane Helena is a comprehensive textbook that covers the fundamental principles of the theory. A free PDF updated version of the book is available online, which provides readers with a convenient and accessible resource for learning about the theory of elasticity and plasticity.

The book is available in PDF format, and can be downloaded for free from various online sources. The updated version of the book includes new chapters on non-linear elasticity, plasticity with damage, and multi-scale modeling.