Physics

Geology

Yield (engineering)

Finite element method

Pure mathematics

Equivalence (formal languages)

Mathematics

Structural engineering

Statistical physics

Engineering

Paleontology

Artificial intelligence

Constitutive equation

Metallurgy

Materials science

Programming language

Work hardening

Stress path

Path (computing)

Context (archaeology)

Computer science

Yield surface

Applied mathematics

Plasticity

Microstructure

Thermodynamics

Proceedings of the National Academy of Sciences

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.

Deep learning predicts path-dependent plasticity