Modeling nanoindentation using the Material Point Method

Hammerquist, Chad C.; Nairn, John A.

doi:10.1557/jmr.2018.75

Cited by 9 publications

(4 citation statements)

References 37 publications

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“…To avoid artifacts, the anvil had to be thick enough to avoid reflected waves during the simulation (for 7

\upmu

s). This was achieved by using larger particles in the anvil remote from the impact site using a Tartan grid 25 . The sphere and impact site were discretized with a regular grid having 224 particles across the sphere's diameter (20 million particles).…”

Section: Discussion With Examplesmentioning

confidence: 99%

“…After damage initiation, each time step is associated with an effective strain increment d𝜺 = (d𝜀 n , d𝛾 xy , d𝛾 xz ) and it's associated ||T (trial) ||. When Φ(T (trial) , c) ≤ 0, the update is elastic, but the new general methods must calculate elastic changes in 𝛿 n and 𝛿 s using Equation (25). When Φ(T (trial) , c) > 0, general damage mechanics modeling divides each step into three sub-steps:…”

Section: Methodsmentioning

confidence: 99%

“…This was achieved by using larger particles in the anvil remote from the impact using a Tartan grid. 25 The sphere and impact site were discretized with a regular grid having 224 particles across the sphere's diameter (20 million particles). Figure 8 compares damage state 4 μs into the impact event for pressure-independent and pressure-dependent material properties.…”

Section: 4mentioning

confidence: 99%

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Generalization of anisotropic damage mechanics modeling in the material point method

Nairn

2022

Numerical Meth Engineering

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Anisotropic damage mechanics is derived by redefining its fourth‐ranked damage tensor, bold-sans-serifD$$ \mathbf{\mathsf{D}} $$, not by its effect on stiffness reduction, but as a tensor that partitions total strain into bulk material strain and an cracking strain associated with crack‐opening displacement. This recharacterization of bold-sans-serifD$$ \mathbf{\mathsf{D}} $$ is irrelevant for 1D modeling, but significantly clarifies 3D algorithms. The new 3D derivation starts with three damage parameters associated with three independent strength models for three components of crack traction. By postulating a traction failure surface dependent on current damage state and requiring that all traction components simultaneously decay to zero at failure, the three damage parameters naturally couple to a single parameter. Many prior methods assume evolving strength depends only on damage. In real materials, strength often depends on other variables such as temperature, pressure, strain rate, and so forth. This article proposes a new general theory that extends prior methods to properly account for such external variables. The general damage mechanics methods must account for extra variables during damage initiation, damage evolution, and elastic loading and unloading. Several examples focus on the new concepts for coupling damage parameters and for using general methods to model materials with pressure‐dependent strength properties.

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“…To avoid artifacts, the anvil had to be thick enough to avoid reflected waves during the simulation (for 7

\upmu

Section: Discussion With Examplesmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: 4mentioning

confidence: 99%

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Generalization of anisotropic damage mechanics modeling in the material point method

Nairn

2022

Numerical Meth Engineering

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“…The CPDI improves the numerical accuracy of the MPM and prevents the occurrence of the nonphysical numerical fractures in the MPM, which is possible under the large extension condition. Given these advantages, the CPDI has been applied in the MPM simulations of, among others: nanoindentation, chemical/mechanical coupling of a silicon anode, the impact of thin‐walled structures as well as being enhanced to model fracture or fluid‐driven fracture . The CPDI has also been used in simulations of geotechnical problems, such as modeling pile penetration, pile installation, soil liquefaction, and the coupled analysis of saturated porous media …”

Section: Introductionmentioning

confidence: 99%

A convected particle least square interpolation material point method

Tran

Sołowski

Berzins

et al. 2019

Numerical Meth Engineering

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Summary Applying the convected particle domain interpolation (CPDI) to the material point method has many advantages over the original material point method, including significantly improved accuracy. However, in the large deformation regime, the CPDI still may not retain the expected convergence rate. The paper proposes an enhanced CPDI formulation based on least square reconstruction technique. The convected particle least square interpolation (CPLS) material point method assumes the velocity field inside the material point domain as nonconstant. This velocity field in the material point domain is mapped to the background grid nodes with a moving least squares reconstruction. In this paper, we apply the improved moving least squares method to avoid the instability of the conventional moving least squares method due to a singular matrix. The proposed algorithm can improve convergence rate, as illustrated by numerical examples using the method of manufactured solutions.

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