Solid Mechanics | 15. Need for stress-strain relation by Abraham | Learn Smarter
Students

Academic Programs

AI-powered learning for grades 8-12, aligned with major curricula

Professional

Professional Courses

Industry-relevant training in Business, Technology, and Design

Games

Interactive Games

Fun games to boost memory, math, typing, and English skills

15. Need for stress-strain relation

15. Need for stress-strain relation

The relationship between stress and strain is crucial for understanding material behavior under external loads. This chapter introduces the stress-strain relation and focuses on formulating the linear stress-strain relationship and its implications in solid mechanics. The importance of additional equations, known as constitutive relations, is emphasized to solve equilibrium equations for deformed bodies.

7 sections

Enroll to start learning

You've not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.

Sections

Navigate through the learning materials and practice exercises.

  1. 1
    Need For Stress-Strain Relation

    The section discusses the necessity of establishing a stress-strain...

  2. 2
    Linear Stress-Strain Relation

    This section discusses the linear relationship between stress and strain in...

  3. 2.1
    Taylor’s Expansion

    This section explores Taylor's expansion as a method to relate stress to...

  4. 2.2
    Independent Components In Tensor C

    This section discusses the independent components of the stiffness tensor C...

  5. 2.2.1
    Minor Symmetry

    This section discusses minor symmetry within the stiffness tensor in the...

  6. 2.2.2
    Major Symmetry

    This section discusses Major Symmetry in the stiffness tensor, explaining...

  7. 3
    Voigt Notation

    Voigt Notation simplifies the representation of stress and strain tensors in...

What we have learnt

  • The stress-strain relation is fundamental for predicting material deformation.
  • Lagrangian description is utilized to relate displacement, velocity, and acceleration.
  • The stiffness tensor has major and minor symmetries, reducing the number of independent material constants.

Key Concepts

-- StressStrain Relation
A mathematical formulation that describes the relationship between stress (internal forces) and strain (deformation) in materials.
-- Lagrangian Description
A method of describing motion where quantities are expressed in terms of the reference configuration of particles.
-- Stiffness Tensor
A fourth-order tensor that relates stress and strain using a linear approximation, incorporating material properties.
-- Linear StressStrain Relation
An approximation where stress is directly proportional to strain, valid for small deformations.

Additional Learning Materials

Supplementary resources to enhance your learning experience.