PSI - Issue 61

Sandipan Baruah et al. / Procedia Structural Integrity 61 (2024) 180–187 Baruah and Singh/ Structural Integrity Procedia 00 (2024) 000 – 000

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Nomenclature b body force vector strain-displacement matrix for quadratic shape functions ̅ strain-displacement matrix for linear shape functions C elastic modulus matrix D damage variable F yield function ext external load vector int internal load vector corresponding to displacement int ̅ G shear modulus Hardening modulus i iteration number stiffness matrix corresponding to displacement ̅ coupling stiffness matrix-1 ̅ coupling stiffness matrix-2 ̅ ̅ l length scale quadratic shape functions ̅ linear shape functions S derivative of yield function with respect to stress H

internal load vector corresponding to non-local equivalent plastic strain

stiffness matrix corresponding to non-local equivalent plastic strain

time

t

temperature

T u Z

displacement vector

elasto-plastic modulus matrix α , β damage parameters total strain vector plastic strain vector p e l q local equivalent plastic strain ̅ p l non-local equivalent plastic strain ̅ pm l ax maximum non-local equivalent plastic strain σ stress vector eq von-Mises equivalent stress y yield stress ∇ †‹˜‡”‰‡ ‡ ‘’‡”ƒ–‘” 1. Introduction

Metals and alloys subjected to monotonically increasing loads beyond their yield limits undergo strain hardening and consequent softening in elasto-plastic regime. Classical isotropic elasto-plasticity consists of various models to capture the stress-strain behaviour of metals under tensile or compressive loads. These include the Hollomon’s power law, Ramberg-Osgood equation, exponential hardening equation, etc. However, the major challenge in all such models is to satisfactorily capture the material softening, which is characterized by reduction of stresses at high strains before final failure. At elevated temperatures, a material shows varying amounts of softening, and the parameters of the standard elasto-plastic models often fail to account for it. In the last few decades, damage-based modelling has gained significant popularity among computational researchers for simulating material behaviour and to understand their failure mechanisms. A damage variable is