Anisotropic hyperelastic/plastic behavior on stress-constrained thin structures by iterating on the elastic Cauchy–Green tensor

January 2022

Thin-walled structures impose zero-stress constraints at free faces. These are in general nonlinear functions of strain and, in the elasto-plastic case, non-smooth. Under these circumstances, the conjugate strain components become constitutive unknowns. By iterating for the elastic Cauchy–Green tensor in the 6−dimensional space, we directly obtain a system that includes the zero-stress constraints. Coupling of the stress and strain constitutive unknowns is possible due to the use of a convenient equation arrangement. This contrasts with the standard decoupling schemes. Herein, we use the Kröner–Lee decomposition of the deformation gradient to obtain a differential–algebraic system which includes stress constraints in analogous form to additional yield conditions. The source is the right Cauchy–Green tensor. The main contribution is the development of a thin-walled implicit integrator for any hyperelastic case and any yield function. Integration is based on a backward-Euler method for the flow law complemented by the solution of a yield condition and the stress constraints. We make use of the elastic Mandel stress construction, which is power-consistent with the plastic strain rate. Two complete fully orthotropic worked examples are presented.

Authors in the community:

• 

  P

  Pedro Areias

  ist24806

• 

  P

  Pedro Alexandre Rodrigues Carvalho Rosa

  ist14190

  Affiliations and sources

  IST > LAETA

  Laboratório Associado de Energia, Transportes e Aeronáutica

  IST > IDMEC

  Instituto de Engenharia Mecânica

  IST > DEM

  Departamento de Engenharia Mecânica

Elsevier

https://www.sciencedirect.com/science/article/pii/S0263823121006212?via%3Dihub

Thin-Walled Structures

108512

170

10.1016/j.tws.2021.108512

materials-engineering - Materials engineering

Keywords

• Thin-walled structures
• Stress constraints
• Finite strain plasticity
• Mandel stress
• Dimensional reduction

eng - English