A general framework for the numerical solution of problems in finite elasto-plasticity

Papadopoulos, Panayiotis; Lu, Jia

Affiliations

¹Department of Mechanical Engineering, University of California, Berkeley, CA 94720-1740, USA

Abstract

This article discusses a general framework for the analysis of initial/boundary-value problems of rate-independent finite elasto-plasticity based on the theory of Green and Naghdi. A constitutive model is developed within the context of the above theory employing generalized measures of Lagrangian strain and work-conjugate measures of stress. Computational implications of the proposed formulation are discussed in conjunction with an implicit time integrator for the differential/algebraic equations of plastic flow. Representative numerical simulations demonstrate the applicability and predictive capacity of the model in the presence of large plastic deformations.

Links

DOI: 10.1016/S0045-7825(98)80101-1

WoS: 000074756200001

History

Received: 1996-06-17

Revised: 1996-12-17

Accepted: 1997-05-25

Cited By (15)

Year	Entry
2006	Bevill G, Eswaran SK, Gupta A, Papadopoulos P, Keaveny TM. Influence of bone volume fraction and architecture on computed large-deformation failure mechanisms in human trabecular bone. Bone. December 2006;39(6):1218-1225.
2009	Bevill G, Keaveny TM. Trabecular bone strength predictions using finite element analysis of micro-scale images at limited spatial resolution. Bone. April 2009;44(4):579-584.
2015	Wang J, Zhou B, Liu XS, Fields AJ, Sanyal A, Shi X, Adams M, Keaveny TM, Guo XE. Trabecular plates and rods determine elastic modulus and yield strength of human trabecular bone. Bone. March 2015;72:71-80.
2020	Sadoughi S, vom Scheidt A, Nawathe S, Zhu S, Moini A, Keaveny TM. Effect of variations in tissue-level ductility on human vertebral strength. Bone. August 2020;137:115445.
2007	Bevill G, Easley SK, Keaveny TM. Side-artifact errors in yield strength and elastic modulus for human trabecular bone and their dependence on bone volume fraction and anatomic site. J Biomech. 2007;40(15):3381-3388.
2009	Bevill G, Farhamand F, Keaveny TM. Heterogeneity of yield strain in low-density versus high-density human trabecular bone. J Biomech. September 18, 2009;42(13):2165-2170.
2013	Nawathe S, Juillard F, Keaveny TM. Theoretical bounds for the influence of tissue-level ductility on the apparent-level strength of human trabecular bone. J Biomech. April 26, 2013;46(7):1293-1299.
2015	Nawathe S, Yang H, Fields AJ, Bouxsein ML, Keaveny TM. Theoretical effects of fully ductile versus fully brittle behaviors of bone tissue on the strength of the human proximal femur and vertebral body. J Biomech. May 1, 2015;48(7):1264-1269.
2014	Nawathe S, Akhlaghpour H, Bouxsein ML, Keaveny TM. Microstructural failure mechanisms in the human proximal femur for sideways fall loading. J Bone Miner Res. February 2014;29(2):507-515.
2016	Wang J. Plate-Rod Microstructural Modeling for Accurate and Fast Assessment of Bone Strength [PhD thesis]. Columbia University; 2016.
2014	Gross T. Development and Application of 3d CT Image-Based Micro and Macro Finite Element Models for Human Bones and Orthopedic Implant Systems [PhD thesis]. Vienna University of Technology; 2014.
2008	Bevill GR. Micromechanical Modeling of Failure in Trabecular Bone [PhD thesis]. Berkeley, CA: Berkeley, University of California; 2008.
2010	Fields AJ. Trabecular Microarchitecture, Endplate Failure, and the Biomechanics of Human Vertebral Fractures [PhD thesis]. Berkeley, CA: Berkeley, University of California; 2010.
2014	Nawathe S. Micromechanics of the Human Proximal Femur: Role of Microstructure and Tissue-Level Ductility on Femoral Strength [PhD thesis]. Berkeley, CA: Berkeley, University of California; 2014.
2019	Sadoughi S. Micromechanics of Human Bone: Role of Architecture and Tissue Material Properties [PhD thesis]. Berkeley, CA: Berkeley, University of California; 2019.