초록

필요한 내용

1. polymer의 점탄,점소성

2. mechanical 물성 예측 필요성

   1. 어려운 점?

3. Data-driven method의 적용 가능성

4. 현 연구에서의 approach

   1. This research aims to propose a machine learning (ML)-based constitutive model to predict elastoplastic behavior for J2-plasticity.
   2. ANN 적용
   3. Physics 도입
   4. 점탄성 점소성 거동
   5. 3D DP, kinematic hardening,
   6. perzyna flow rule과 dynamic yield function

5. 연구 단계

   1. 적용할 부분

      1. return mapping

   2. 2D J2에서의 사전 도입 테스트

      1. 데이터 구축 방법
      2. 인공신경망 훈련
         1. Physics 도입
      3. Abaqus UMAT 적용
         1. 시간 및 정확도 테스트

   3. 3D DP에서의 적용

      1. 계산 효율성 향상을 위한 input 축소

   4. 최종 결과

      1. 정확도 및 계산 시간 비교

         1. linear, nonlinear loading

한글 작성 초안

폴리머의 점소성 특성은 매우 복잡한 거동을 보이며 이를 예측하기 위해 정립된 많은 구성방정식들이 Newton Raphson iteration 기반의 return mapping을 사용함. 그러나 Newton-Raphson 기반의 iteration은 계산에 있어 상당한 계산 cost와 시간을 요구함. 이 점소성의 해석에 data driven method를 적용하면 iteration이 필요 없어 계산 cost 감소에도 기여할 수 있고, 더 나아가 기존의 구성방정식이 예측하지 못했던 부분을 보완할 수 있음. 이 연구에서는 physics informed artificial neural network을 이용한 polymer의 3D Drucker-Prager 점탄 점소성 구성 방정식을 제안함.

simple 2D J2 plasticity와 3D drucker prager viscoplasticity 시스템에 대해 적용하며 kinematic hardening과 dynamic yield surface가 고려됨. 인공신경망은 리턴 매핑 알고리즘에서의 trial stress로부터 corrected stress를 계산하는데 적용되며, hardening을 고려하기 위해 flow stress가 input으로 사용됨. The training dataset required for the ANN Model was numerically generated based on the conventional return mapping scheme in the principal stress space and backward calculation method was used to control the direction of the stress precisely.
physically inconsistent한 예측을 방지하기 위해 리턴 매핑 알고리즘에서의 physics를 이용한 physical constraint를 활용함. 3D drucker prager의 경우 효율적인 dataset 구축과 학습을 위해 data space의 축소와 복원이 고려되었음.

The viscoplastic properties of polymers exhibit very complex behavior and many of the constitutive equations established to predict them use a return mapping based on Newton Raphson iteration. However, the Newton-Raphson iteration requires significant computational cost and time. Applying a data-driven method to the analysis of viscoplasticity can contribute to reducing the computational cost by not using iteration, and furthermore, it can compensate for the parts that are difficult to predict with the existing constitutive equations. In this study, we propose a 3D Drucker-Prager viscoplastic constitutive equation for polymers based on a physics-informed artificial neural network.

Simple 2D J2 plasticity and 3D Drucker Prager viscoplasticity systems were considered, with kinematic hardening and a dynamic yield surface. Artificial neural network was applied to calculate the corrected stress from the trial stress in the return mapping algorithm, using the flow stress as input to account for the hardening. The training dataset required for the neural network model was numerically generated based on the conventional return mapping scheme and backward calculation method was used to control the direction and density of the stress precisely. To efficiently build the dataset and train the neural network, proper data space reduction and restoration methods were considered. We utilized physical constraints using physics in the return mapping algorithm to avoid physically inconsistent predictions. To compare the accuracy and computation time of the calculation with the conventional theoretical method, the trained neural network was applied to Abaqus User MATerial (UMAT) and its performance was verified. For this purpose, tests were made for 1 element with arbitrary linear and non-linear strain path, followed by part-level multi elements tests.