TY - JOUR
T1 - Modelling of strain softening materials based on equivalent damage force
AU - Vignjevic, Rade
AU - Djordjevic, Nenad
AU - Vuyst, Tom De
AU - Gemkow, Simone
N1 - © 2018 Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
PY - 2018/6/15
Y1 - 2018/6/15
N2 - The main aim of the work presented in this paper was treatment of damage and deformation localisation observed in the finite element method (FEM) analysis of strain softening materials combined with local constitutive models where damage is represented using continuum damage mechanics (CDM). The CDM/FEM approach typically suffers from a number of shortcomings, including mathematical (change of the type of partial differential equations leading to ill-posed boundary value problem), numerical (pronounced mesh dependency) and physical (infinitely small softening zone with the zero dissipated energy). The approach proposed here is still based on the local constitutive model including damage, but introduces an alternative representation of damage effects in the system of linear momentum balance equations. The damage effects are included through equivalent damage force (EDF), which contributes to the right-hand side of the momentum balance equations. The main advantages of this approach are that the problem remains well posed, as the type of partial differential equations remains unchanged when the material enters softening; numerical stability is preserved without a need for regularisation measures; and significantly reduced mesh dependency. In addition, the EDF approach can be used in combination with existing local CDM damage models and does not violate symmetry of the material stiffness tensor. The EDF approach is applicable to modelling of strain softening typically observed in damaged quasi brittle materials such as fibre reinforced composites and concrete. The EDF model was implemented in the in-house developed coupled FEM-SPH code, where an explicit FEM code is coupled with a stable Total-Lagrange form of SPH. Its performance is demonstrated in the analysis of a dynamic one dimensional (1D) stress wave propagation problem, which was analytically solved by Bazant and Belytschko in 1985. For a range of loading rates that correspond to the material softening regime, the numerical results shown nonlocal character with a finite size of the damaged zone, controlled with the damage characteristic length, which can be experimentally determined and is an input parameter independent of the discretisation density.
AB - The main aim of the work presented in this paper was treatment of damage and deformation localisation observed in the finite element method (FEM) analysis of strain softening materials combined with local constitutive models where damage is represented using continuum damage mechanics (CDM). The CDM/FEM approach typically suffers from a number of shortcomings, including mathematical (change of the type of partial differential equations leading to ill-posed boundary value problem), numerical (pronounced mesh dependency) and physical (infinitely small softening zone with the zero dissipated energy). The approach proposed here is still based on the local constitutive model including damage, but introduces an alternative representation of damage effects in the system of linear momentum balance equations. The damage effects are included through equivalent damage force (EDF), which contributes to the right-hand side of the momentum balance equations. The main advantages of this approach are that the problem remains well posed, as the type of partial differential equations remains unchanged when the material enters softening; numerical stability is preserved without a need for regularisation measures; and significantly reduced mesh dependency. In addition, the EDF approach can be used in combination with existing local CDM damage models and does not violate symmetry of the material stiffness tensor. The EDF approach is applicable to modelling of strain softening typically observed in damaged quasi brittle materials such as fibre reinforced composites and concrete. The EDF model was implemented in the in-house developed coupled FEM-SPH code, where an explicit FEM code is coupled with a stable Total-Lagrange form of SPH. Its performance is demonstrated in the analysis of a dynamic one dimensional (1D) stress wave propagation problem, which was analytically solved by Bazant and Belytschko in 1985. For a range of loading rates that correspond to the material softening regime, the numerical results shown nonlocal character with a finite size of the damaged zone, controlled with the damage characteristic length, which can be experimentally determined and is an input parameter independent of the discretisation density.
KW - Composite materials
KW - Damage localisation
KW - FEM
KW - Quasi brittle materials
KW - Strain softening instability
UR - http://www.scopus.com/inward/record.url?scp=85043368524&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2018.01.049
DO - 10.1016/j.cma.2018.01.049
M3 - Article
AN - SCOPUS:85043368524
SN - 0045-7825
VL - 335
SP - 52
EP - 68
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
ER -