TY - JOUR
T1 - Strain gradient elasto-plasticity model: 3D isogeometric implementation and applications to cellular structures
AU - Khakalo, Sergei
AU - Laukkanen, Anssi
N1 - Funding Information:
The authors would like to acknowledge the financial support of Business Finland in the form of a research project ISA VTT Dnro 7980/31/2018. The authors are grateful to Dr. Viacheslav Balobanov from VTT Technical Research Centre of Finland, Dr. Aleksandr Morozov from Technical University of Berlin, and MSc Kseniia Khakalo from Top Data Science Oy for fruitful discussions and useful comments.
Funding Information:
The authors would like to acknowledge the financial support of Business Finland in the form of a research project ISA VTT Dnro 7980/31/2018 . The authors are grateful to Dr. Viacheslav Balobanov from VTT Technical Research Centre of Finland , Dr. Aleksandr Morozov from Technical University of Berlin, and MSc Kseniia Khakalo from Top Data Science Oy for fruitful discussions and useful comments.
Publisher Copyright:
© 2021 The Author(s)
PY - 2022/1/1
Y1 - 2022/1/1
N2 - In the present work, we combine Mindlin's strain gradient elasticity theory and Gudmundson–Gurtin–Anand strain gradient plasticity theory to form a unified framework. The gradient plasticity model is enriched by including the gradient of elastic strains into the expression of the internal virtual work and free energy. This augments the modelling capabilities by incorporating elasticity-related length scales along with plasticity-related energetic and dissipative ones. The strong form governing equations are derived via the principle of virtual work addressing a complete set of boundary conditions. The fourth-order boundary value problem of the gradient elasto-plasticity model is then formulated in a variational form within an H
2 Sobolev space setting. Conforming Galerkin discretizations for numerical results are obtained utilizing an isogeometric approach with NURBS basis functions of degree p≥2 providing C
p−1-continuity. The implementation follows a viscoplastic constitutive framework and adopts the backward Euler time integration scheme. A set of benchmark examples is considered to illustrate convergence properties and to accomplish parameter studies. It is shown that the elastic length scale parameter controls the slope of the elastic part and causes an additional hardening in the plastic part of the material response curves. Finally, an illustrative example is considered in order to demonstrate the applicability of both the continuum model and the numerical method in capturing the size-dependent torsion response of cellular structures.
AB - In the present work, we combine Mindlin's strain gradient elasticity theory and Gudmundson–Gurtin–Anand strain gradient plasticity theory to form a unified framework. The gradient plasticity model is enriched by including the gradient of elastic strains into the expression of the internal virtual work and free energy. This augments the modelling capabilities by incorporating elasticity-related length scales along with plasticity-related energetic and dissipative ones. The strong form governing equations are derived via the principle of virtual work addressing a complete set of boundary conditions. The fourth-order boundary value problem of the gradient elasto-plasticity model is then formulated in a variational form within an H
2 Sobolev space setting. Conforming Galerkin discretizations for numerical results are obtained utilizing an isogeometric approach with NURBS basis functions of degree p≥2 providing C
p−1-continuity. The implementation follows a viscoplastic constitutive framework and adopts the backward Euler time integration scheme. A set of benchmark examples is considered to illustrate convergence properties and to accomplish parameter studies. It is shown that the elastic length scale parameter controls the slope of the elastic part and causes an additional hardening in the plastic part of the material response curves. Finally, an illustrative example is considered in order to demonstrate the applicability of both the continuum model and the numerical method in capturing the size-dependent torsion response of cellular structures.
UR - http://www.scopus.com/inward/record.url?scp=85118835419&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2021.114225
DO - 10.1016/j.cma.2021.114225
M3 - Article
SN - 0045-7825
VL - 388
SP - 1
EP - 35
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
M1 - 114225
ER -