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meshfree failure algorithm to simulate plugging failure formed by
crack propagation during high-speed impact and contact. To do so,
we have to address a number of technical issues: (1) Physically, the
plugging fracture induced by high-speed impact is initiated by
two-body or multi-body contacts. Although, the impact/contact
algorithm has been well developed in finite element method, thereare still many pragmatic issues for the meshfree contact impact
algorithm and its actual implementation. In this work, based on
general philosophy of master/slave slide interface algorithm from
finite element method, a master/slave contact algorithm is devel-
oped to fit to meshfree computations. (2) During high-speed im-
pact, a large amount of heat will generated nearby the failure
area by plastic work accompanied by heat conduction; the ther-
mal–mechanical coupling will cause thermal softening and mate-
rial instability, which manifests as micro void formation and
coalescence, subsequent macro material damage and fracture. To
model such complex constitutive behaviors, we adopt the John-
son–Cook model in constitutive modeling, and use a modified for-
ward Euler one step time integration in constitutive update based
on a tangent modulus method by Peirce et al. [25]. Although the
Johnson–Cook model is a thermal-related model, the heat conduc-
tion process is considered by many researchers. In this work, fully
coupled thermal–mechanical equations of motion are considered
with heat conduction, large scale yielding, and finite deformation.
To ensure the numerical stability, an operator splitting algorithmis
adopted to update thermal–mechanical constitutive and to inte-
grate the weak form of heat conduction equation.
The paper is organized into six sections: in Section 2, we shall
present a complete meshfree Galerkin weak formulation, its inter-
polation and constitutive update; in Section 3, we shall discuss the
meshfree impact/contact algorithm, and in Section 4, we shall out-
line a meshfree crack growth algorithm. The results of the plugging
fracture simulation are presented in Section 5, and a few remarks
are made in Section 6.The high-speed impact process will produce enormous plastic
deformation, and in turn the material plastic flow will generate a
large amount of heat at some local area. In some spatial points,
the temperature can sharply increase up close to melting temper-
ature. For instance, this may happen at the tip of Adiabatic Shear
Band in less than 200 ls [36,37]. Therefore the effects of ther-
mal–mechanical coupling and heat conduction cannot be ne-
glected in high-speed impact simulations. In this work, a fully
coupled thermal–mechanical impact problem with inelastic dam-
age evolution is considered.
By the virtual power principle, the weak formulation of balance
of the linear momentum can be written as:
where P denotes the nominal stress, which is the transpose of the
first Piola–Kirchhoff stress, and it can be related to the Kirchhoff
stress as s = PFT
; and CT
0 denotes the traction boundary where the
traction force T is prescribed. The above weak form formulation is
obtained by integration by parts of the balance equation of linear
momentums.
Considering the heat generation and conduction process, the
strong form of energy equation can be written as:
where T is the temperature, v denotes the fraction of plastic work
converting to heat, rX is the gradient operator in reference config-
uration, Cp is specific heat. For isotropic heat conduction, the heat
conductivity tensor K ¼ jI, where j is the conductivity coefficient.
dp
is the plastic rate of deformation.