Publicado 6 números por año
ISSN Imprimir: 1543-1649
ISSN En Línea: 1940-4352
Indexed in
THERMODYNAMICALLY CONSISTENT HOMOGENIZATION IN FINITE STRAIN THERMOPLASTICITY
SINOPSIS
The present research aims to develop a thermodynamically consistent framework for the application in the homogenization of finite strain thermoplasticity. The focus is set on the metallic materials, but the framework can be applied to other classes of materials as well. The cornerstone of the current research is the amount already existing results developed for the multiscale thermoelasticity. The essential part of the procedure is enforcement of consistency between thermodynamical quantities at macroscale and microscale levels. As will be demonstrated in the paper, such a consistency places additional constraints that are usually not accounted for in the literature. The developed procedure is implemented into the finite element framework, and performance is illustrated on two examples, one mechanically driven and the other thermally driven.
-
Argyris, J. and Doltsinis, J.S., On the Natural Formulation and Analysis of Large Deformation Coupled Thermomechanical Problems, Comput. Methods Appl. Mech. Eng., vol. 25, no. 2, pp. 195-253, 1981.
-
Armero, F. and Simo, J., A Priori Stability Estimates and Unconditonally Stable Product Formula Algorithms for Nonlinear Coupled Thermoplasticity, Int. J. Plasticity, vol. 9, pp. 749-782, 1993.
-
Bartels, A., Bartel, T., Canadija, M., and Mosler, J., On the Thermomechanical Coupling in Dissipative Materials: A Variational Approach for Generalized Standard Materials, J. Mech. Phys. Solids, vol. 82, pp. 218-234, 2015.
-
Berthelsen, R., Denzer, R., Oppermann, P., and Menzel, A., Computational Homogenisation for Thermoviscoplasticity: Application to Thermally Sprayed Coatings, Comput. Mech., vol. 60, no. 5, pp. 739-766, 2017.
-
(Canadija, M. and Brnic, J., Associative Coupled Thermoplasticity at Finite Strain with Temperature-Dependent Material Parameters, Int. J. Plasticity, vol. 20, pp. 1851-1874, 2004.
-
Canadija, M. and Mosler, J., On the Thermomechanical Coupling in Finite Strain Plasticity Theory with Non-Linear Kinematic Hardening by Means of Incremental Energy Minimization, Int. J. Solids Struct., vol. 48, nos. 7-8, pp. 1120-1129, 2011.
-
Canadija, M. and Mosler, J., A Variational Formulation for Thermomechanically Coupled Low Cycle Fatigue at Finite Strains, Int. J. Solids Struct., vol. 100, pp. 388-398, 2016.
-
Celigoj, C., Thermomechanical Homogenization Analysis of Axisymmetric Inelastic Solids at Finite Strains based on an Incremental Minimization Principle, Int. J. Num. Methods Eng., vol. 71, no. 1, pp. 102-126, 2007.
-
Chatzigeorgiou, G., Charalambakis, N., Chemisky, Y., and Meraghni, F., Periodic Homogenization for Fully Coupled Thermome-chanical Modeling of Dissipative Generalized Standard Materials, Int. J. Plasticity, vol. 81, pp. 18-39,2016.
-
Coleman, B.D. and Owen, D.R., On the Thermodynamics of Elastic-Plastic Materials with Temperature-Dependent Moduli and Yield Stresses, Arch. Rational Mech. Anal., vol. 70, no. 4, pp. 339-354, 1979.
-
de Souza Neto, E., Blanco, P., Sanchez, P. J., and Feijoo, R., An RVE-Based Multiscale Theory of Solids with Micro-Scale Inertia and Body Force Effects, Mech. Mater., vol. 80, pp. 136-144, 2015.
-
Fleischhauer, R., Bozic, M., and Kaliske, M., A Novel Approach to Computational Homogenization and Its Application to Fully Coupled Two-Scale Thermomechanics, Comput. Mech, vol. 58, no. 5, pp. 769-796, 2016.
-
Lehmann, T., General Frame for the Definition of Constitutive Laws for Large Non-Isothermic Elastic-Plastic and Elastic-Visco-Plastic Deformations, in Constitutive Law in Thermoplasticity, New York: Springer, pp. 379-463, 1984.
-
Lehmann, T. and Blix, U., On the Coupled Thermo-Mechanical Process in the Necking Problem, Int. J. Plasticity, vol. 1, no. 2, pp. 175-188, 1985.
-
Lemaitre, J. and Chaboche, J.L., Mechanics of Solid Materials, Cambridge: Cambridge University Press, 2000.
-
Miehe, C., Numerical Computation of Algorithmic (Consistent) Tangent Moduli in Large-Strain Computational Inelasticity, Comput. Methods Appl. Mech. Eng., vol. 134, nos. 3-4, pp. 223-240, 1996.
-
Miehe, C., Strain-Driven Homogenization of Inelastic Microstructures and Composites based on an Incremental Variational Formulation, Int. J. Numer. Methods Eng., vol. 55, no. 11, pp. 1285-1322,2002.
-
Miehe, C. and Koch, A., Computational Micro-to-Macro Transitions of Discretized Microstructures undergoing Small Strains, Arch. Appl. Mech, vol. 72, nos. 4-5, pp. 300-317, 2002.
-
Miehe, C., Schroder, J., and Schotte, J., Computational Homogenization Analysis in Finite Plasticity Simulation of Texture Development in Polycrystalline Materials, Comput. Methods Appl. Mech. Eng., vol. 171, nos. 3-4, pp. 387-418, 1999.
-
Mosler, J., Variationally Consistent Modeling of Finite Strain Plasticity Theory with Non-Linear Kinematic Hardening, Comput. Methods Appl. Mech. Eng., vol. 199, pp. 2753-2764, 2010.
-
Mosler, J. and Bruhns, O., Towards Variational Constitutive Updates for Non-Associative Plasticity Models at Finite Strain: Models based on a Volumetric-Deviatoric Split, Int. J. Solids Struct., vol. 46, pp. 1676-1685, 2009.
-
Mosler, J. and Bruhns, O., On the Implementation of Rate-Independent Standard Dissaptive Solids at Finite Strain-Variational Constitutive Updates, Comput. Methods Appl. Mech. Eng., vol. 199, pp. 417-429, 2010.
-
Munjas, N., Canadija, M., and Brnic, J., Thermo-Mechanical Multiscale Modeling in Plasticity of Metals Using Small Strain Theory, J. Mech, vol. 34, pp. 579-589, 2018.
-
Ozdemir, I., Brekelmans, W., and Geers, M., Computational Homogenization for Heat Conduction in Heterogeneous Solids, Int. J. Numer. Methods Eng., vol. 73, no. 2, pp. 185-204, 2008a.
-
Ozdemir, I., Brekelmans, W., and Geers, M.G., FE2 Computational Homogenization for the Thermo-Mechanical Analysis of Heterogeneous Solids, Comput. Methods Appl. Mech. Eng., vol. 198, nos. 3-4, pp. 602-613, 2008b.
-
Pina, J., Kouznetsova, V., and Geers, M., Thermo-Mechanical Analyses of Heterogeneous Materials with a Strongly Anisotropic Phase: the Case of Cast Iron, Int. J. Solids Struct., vol. 63, pp. 153-166, 2015.
-
Schmid, S., Schneider, D., Herrmann, C., Selzer, M., andNestler, B., A Multiscale Approach for Thermo-Mechanical Simulations of Loading Courses in Cast Iron Brake Discs, Int. J. Multiscale Comput. Eng., vol. 14, no. 1, pp. 25-43, 2016.
-
Sengupta, A., Papadopoulos, P., and Taylor, R.L., A Multiscale Finite Element Method for Modeling Fully Coupled Thermome-chanical Problems in Solids, Int. J. Numer. Methods Eng., vol. 91, no. 13, pp. 1386-1405, 2012.
-
Simo, J. and Miehe, C., Associative Coupled Thermoplasticity at Finite Strains: Formulation, Numerical Analysis and Implementation, Comput. Methods Appl. Mech. Eng., vol. 98, pp. 41-104, 1992.
-
Temizer, I. and Wriggers, P., On a Mass Conservation Criterion in Micro-to-Macro Transitions, J. Appl. Mech., vol. 75, no. 5, p. 054503, 2008.
-
Temizer, I. and Wriggers, P., Homogenization in Finite Thermoelasticity, J. Mech. Phys. Solids, vol. 59, no. 2, pp. 344-372,2011.
-
Zdebel, U. and Lehmann, T., Some Theoretical Considerations and Experimental Investigations on a Constitutive Law in Thermo-plasticity, Int. J. Plasticity, vol. 3, no. 4, pp. 369-389,1987.