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.
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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.
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