TY - JOUR
T1 - Interfacial stabilization at finite strains for weak and strong discontinuities in multi-constituent materials
AU - Chen, Pinlei
AU - Truster, Timothy J.
AU - Masud, Arif
N1 - Funding Information:
This work was partially supported by grants from the National Science Foundation NSF DMS 16-20231 and from the Air Force Research Laboratory FA8650-13-C-5009 . This support is gratefully acknowledged. Appendix In order to achieve quadratic convergence with the Newton–Raphson method for the nonlinear equation (85) , we need consistent linearization of the term which is related to the damage part. (89) ∂ ∂ T Δ γ n = ∂ Δ γ ∂ T ⊗ n + γ ∂ n ∂ T = ∂ Δ γ ∂ T i n j + Δ γ ∂ n i ∂ T j . According to Sections 5.1.1 and 5.2.1 , the return mapping algorithms and the corresponding expression for the damage consistency parameter Δ γ and the unit normal n are different for different loading scenarios. Therefore, we first consider the case of damage in tension. Note that compression damage case follows a similar pattern. For the case of damage in tension, from the expressions in Box II , the yield function f and the damage consistency parameter Δ γ are expressed in (67) and (68) , Eq. (89) becomes: (90) ∂ ∂ T Δ γ n = 1 r P − H c I − P c − Q n ‖ T ‖ I − n ⊗ n . For compression friction case, the yield function and the damage consistency parameter are expressed in (77) and (79) . Thus (89) becomes: (91) ∂ ∂ T Δ γ n = 1 r p I + μ f ‖ T N ‖ ‖ T T ‖ I − n T ⊗ n T I − N ⊗ N + 1 r p μ f n T ⊗ N . Appendix B
Publisher Copyright:
© 2017 Elsevier B.V.
PY - 2018/1/1
Y1 - 2018/1/1
N2 - A stabilized interface formulation is developed for debonding at finite strains across general bimaterial interfaces by embedding stabilized Discontinuous Galerkin (DG) ideas in the Continuous Galerkin method. Introducing an interfacial gap function that evolves subject to constraints imposed by opening and/or sliding interfaces, the proposed Variational Multiscale DG (VMDG) method seamlessly tracks interface debonding by treating damage and friction in a unified way. An internal variable formalism together with the notion of irreversibility of damage results in a set of evolution equations for the gap function. Evolution of the debonding surfaces requires interfacial stabilization that is developed based on residual-based stabilization concepts. Tension debonding, compression damage, and frictional sliding are accommodated, and return mapping algorithms in the presence of evolving strong discontinuities are developed. A significant contribution of the paper is the consistently derived method to model the Lagrange multiplier field via interfacial flux and jump terms and variational embedding of various nonlinear interfacial debonding models at the interfacial boundaries. This derivation variationally embeds the interfacial kinematic models that are crucial to capturing the physical and mathematical properties involving large stains and damage. A set of representative test cases highlights the salient features of the proposed VMDG method and confirm its robustness and range of applicability.
AB - A stabilized interface formulation is developed for debonding at finite strains across general bimaterial interfaces by embedding stabilized Discontinuous Galerkin (DG) ideas in the Continuous Galerkin method. Introducing an interfacial gap function that evolves subject to constraints imposed by opening and/or sliding interfaces, the proposed Variational Multiscale DG (VMDG) method seamlessly tracks interface debonding by treating damage and friction in a unified way. An internal variable formalism together with the notion of irreversibility of damage results in a set of evolution equations for the gap function. Evolution of the debonding surfaces requires interfacial stabilization that is developed based on residual-based stabilization concepts. Tension debonding, compression damage, and frictional sliding are accommodated, and return mapping algorithms in the presence of evolving strong discontinuities are developed. A significant contribution of the paper is the consistently derived method to model the Lagrange multiplier field via interfacial flux and jump terms and variational embedding of various nonlinear interfacial debonding models at the interfacial boundaries. This derivation variationally embeds the interfacial kinematic models that are crucial to capturing the physical and mathematical properties involving large stains and damage. A set of representative test cases highlights the salient features of the proposed VMDG method and confirm its robustness and range of applicability.
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U2 - 10.1016/j.cma.2017.06.020
DO - 10.1016/j.cma.2017.06.020
M3 - Article
AN - SCOPUS:85032173754
SN - 0374-2830
VL - 328
SP - 717
EP - 751
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
ER -