Modelling the constitutive behaviour of thin metal sheet using strain gradient theory

The classical local continuum theory is not well adapted to represent the size effects in metal forming processes because there is no dependence on length or size intrinsic parameters. To simulate the material behaviour for sheet metal forming of very thin components the strain gradient plasticity theory is applied. A length intrinsic parameter associated to the gradient of the effective plastic strain is used. The gradient is computed at each integration point through the thickness using a interpolation matrix that only depends on the co-ordinates of the integration points. The effective plastic strain is obtained by solving a consistent iterative scheme. The flow chart of the algorithm in a finite element framework is presented so that two numerical examples of sheet metal forming.