(2007) A mathematical representation of the multiaxial Bauschinger effect Materials at High Temperatures: Vol 24, No 1, pp 1-26

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A mathematical representation of the multiaxial Bauschinger effect

A review of some plasticity and viscoplasticity constitutive theories

Multiaxial fatigue: An overview and some approximation models for life estimation

Ratchetting: Recent progresses in phenomenon observation, constitutive modeling and application

Plasticity theory aims at describing the yield loci and work hardening of a material under general deformation states. Most of its complexity arises from the nontrivial dependence of the yield loci on the complete strain history of a material and its microstructure. This motivated 3 ingenious simplifications that underpinned a century of developments in this field: 1) yield criteria describing yield loci location; 2) associative or nonassociative flow rules defining the direction of plastic flow; and 3) effective stress-strain laws consistent with the plastic work equivalence principle. However, 2 key complications arise from these simplifications. First, finding equations that describe these 3 assumptions for materials with complex microstructures is not trivial. Second, yield surface evolution needs to be traced iteratively, i.e., through a return mapping algorithm. Here, we show that these assumptions are not needed in the context of sequence learning when using recurrent neural networks, diverting the above-mentioned complications. This work offers an alternative to currently established plasticity formulations by providing the foundations for finding history- and microstructure-dependent constitutive models through deep learning.

https://www.pnas.org/content/pnas/116/52/26414.full.pdf

Deep learning predicts path-dependent plasticity.

It is proved that if two structures differing only in their initial internal stresses are subject to the same loading history, the distributions of internal stress will approach one another in regi...

C. O. Frederick

Papers

A mathematical representation of the multiaxial Bauschinger effect

Convergent internal stresses and steady cyclic states of stress