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$$ \sigma = \sigma_y + H \epsilon^p $$

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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.

As metals deform plastically, dislocations tangle and multiply, making the material progressively harder to deform further. This phenomenon is known as work hardening or strain hardening. Engineers model this evolution using isotropic hardening (where the yield surface expands uniformly) or kinematic hardening (where the yield surface shifts in stress space to model effects like the Bauschinger effect). Practical Applications in Modern Engineering