Computational Inelasticity (J.C. Simo, T.J.R. Hughes)

Computational inelasticity is a field of computational mechanics that deals with the numerical simulation of materials that undergo large deformations and/or exhibit plastic behavior. It is a subfield of computational solid mechanics and has applications in various engineering and scientific fields such as aerospace, civil, mechanical, and materials engineering.

The behavior of materials that undergo large deformations cannot be accurately described by linear elasticity theory. Therefore, inelasticity theories have been developed to describe the behavior of these materials. These theories are based on the concept of a plastic flow rule, which relates the increment of plastic strain to the increment of stress.

Computational inelasticity involves the numerical solution of the inelasticity equations using finite element methods. The finite element method involves discretizing the material into small elements and solving the equations of motion for each element. The solution is then combined to obtain the overall behavior of the material.

One of the challenges in computational inelasticity is the accurate modeling of the material behavior. Material models are used to describe the behavior of the material under different loading conditions. These models can be simple or complex, depending on the level of accuracy required.

Another challenge is the numerical stability of the solution. Inelasticity problems can be highly nonlinear and require advanced numerical techniques to ensure convergence and stability of the solution.

Despite these challenges, computational inelasticity has been successful in simulating the behavior of materials such as metals, polymers, and composites. It has been used to study a wide range of problems such as impact, fatigue, and fracture. The field continues to evolve with the development of new material models and numerical techniques.