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An embedded atom hyperelastic constitutive model and multiscale cohesive finite element method

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Abstract

Based on embedded atom method (EAM), an embedded atom hyperelastic (EAH) constitutive model is developed. The proposed EAH constitutive model provides a multiscale formalism to determine mesoscale or macroscale material behavior by atomistic information. By combining the EAH with cohesive zone model (CZM), a multiscale embedded atom cohesive finite element model (EA-cohesive FEM) is developed for simulating failure of materials at mesoscale and macroscale, e.g. fracture and crack propagation etc. Based on EAH, the EA-cohesive FEM applies the Cauchy-Born rule to calculate mesoscale or macroscale material response for bulk elements. Within the cohesive zone, a generalized Cauchy-Born rule is applied to find the effective normal and tangential traction-separation cohesive laws of EAH material. Since the EAM is a realistic semi-empirical interatomic potential formalism, the EAH constitutive model and the EA-cohesive FEM are physically meaningful when it is compared with experimental data. The proposed EA-cohesive FEM is validated by comparing the simulation results with the results of large scale molecular dynamics simulation. Simulation result of dynamic crack propagation is presented to demonstrate the capacity of EA-cohesive FEM in capturing the dynamic fracture.

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Authors and Affiliations

  1. Department of Civil Engineering, Tsinghua University, Beijing, 100084, China

    Minghua He

  2. Department of Civil and Environmental Engineering, University of California, Berkeley, CA, 94720, USA

    Shaofan Li

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  1. Minghua He
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  2. Shaofan Li
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Correspondence to Shaofan Li.

Additional information

National Natural Science Foundation of China (Grant 50878117; Key Project Grant 51038006); China Scholarship Council Project (M.H. HE-2009621076); NSF (Grant No. CMMI-0800744).

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He, M., Li, S. An embedded atom hyperelastic constitutive model and multiscale cohesive finite element method. Comput Mech 49, 337–355 (2012). https://doi.org/10.1007/s00466-011-0643-0

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  • DOI: https://doi.org/10.1007/s00466-011-0643-0

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