A Bond-Based Peridynamic Model with Matrix Plasticity for Impact Damage Analysis of Composite Materials

Abstract

The prediction of damage and failure to fiber-reinforced polymer composites in extreme environments, particularly when subjected to impact loading, is a crucial issue for the application and design of protective structures. In this paper, based on the prototype microelastic brittle (PMB) model and the LaRC05 composite materials failure model, we proposed a bond-based peridynamic (BB-PD) model with the introduction of plastic hardening of the resin matrix for fiber-reinforced polymer composites. The PD constitutive relationships of the matrix bond and interlayer bond under compressive loading are considered to include two stages of linear elasticity and plastic hardening, according to the stress–strain relationship of the resin matrix in the LaRC05 failure model. The proposed PD model is employed to simulate the damage behaviors of laminated composites subjected to impact loading. The corresponding ballistic impact tests of composite laminates were carried out to observe their damage behaviors. The PD prediction results are in good agreement with the ballistic experimental results, which can verify the correctness and accuracy of the PD model developed in this study in describing the impact damage behaviors of composite materials. In addition, the characteristics and degree of damage in composite laminates are analyzed and discussed based on this PD model. The difference in the impact resistance of composite laminates with different stacking sequences is also studied using the numerical simulation results.

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“…The motion state of material point x depends only on its initial state and interaction with all material points x′ within the horizon. In the BBPD, the interaction between x and all other material points in the domain Hx is called bond force 𝑓, which can be expressed as [34] 𝑓 = 𝑐𝑠𝜇 (𝑡, 𝜉) ∥ 𝜉 + 𝜂 ∥ (𝜉 + 𝜂)…”

“…where c is the PD micro-modulus; 𝜇 and s represent the damage function and bond stretch, respectively. The bond force 𝑓 is a function of the relative position vector 𝜉 in the reference configuration and the relative displacement vector 𝜂 in the current configuration [34]. As shown in Figure 5, they can be expressed as [35] 𝜉 = 𝑥′ − 𝑥…”

“…The force between two material points of matter in the equation of motion will disappear forever when damage occurs. In order to visualize the damage behavior of the material, the damage function 𝜇 is introduced [34]:…”

“…The damage range of the material point x can be quantified by the damage variable φ defined as the ratio of the number of damage bonds at the material point to the initial total number of PD bonds [34]:…”