Computational Homogenization of Materials with Microstructures Based on Incremental Variational Formulations

被引：0

作者：

Miehe, Christian ^{[1
]}

Lambrecht, Matthias ^{[1
]}

Schotte, Jan ^{[1
]}

机构：

[1] University of Stuttgart, Institute of Applied Mechanics (Civil Engineering), 70569 Stuttgart

来源：

Lecture Notes in Applied and Computational Mechanics | 2003年 / 12卷

关键词：

Computational homogenization - Constitutive materials - Convexification - Dissipative materials - Finite strain - Heterogeneous microstructure - Incremental variational formulations - Minimization problems;

D O I：

10.1007/978-3-540-36527-3_10

中图分类号：

学科分类号：

摘要：

The paper presents incremental minimization principles for the broad class of standard dissipative materials at finite strains. Starting with a minimization principle for the local constitutive material response we define a minimization problem for the incremental boundaryvalue problem of standard dissipative solids. The existence of this principle allows the determination of micro-structure developments in non-stable dissipative materials based on a convexification analysis. Finally, we propose a minimization principle for the boundary-value problem of homogenization in heterogeneous microstructures. © Springer-Verlag Berlin Heidelberg 2003.

引用

页码：111 / 122

页数：11

共 25 条

[1]

Ball J.M., Convexity Conditions and Existence Theorems in Nonlinear Elasticity, Archive of Rational Mechanics and Analysis, 63, pp. 337-403, (1977)

[2]

Biot M.A., Mechanics of Incremental Deformations, (1965)

[3]

Bronkhorst C.A., Kalidindi S.R., Anand, Polycrystalline Plasticity and the Evolution of Crystallographic Texture in f.c. c, Metals. Philosophical Transactions Royal Society London A, 341, pp. 443-477, (1992)

[4]

Carstensen C., Hackl K., Mielke A., Nonconvex potentials and microstructures in finite-strain plasticity. Royal Society London, Proc. Ser. A, 458, pp. 299-317, (2002)

[5]

Dacorogna B., Direct Methods in the Calculus of Variations, (1989)

[6]

Halphen B., Nguyen Q.S., Sur les Materiaux Standards Generalises, Journal de Mecanique, 40, pp. 39-63, (1975)

[7]

Hill R., On Constitutive Macro-Variables for Heterogeneous Solids at Finite Strain, Proceedings of the Royal Society London A, 326, pp. 131-147, (1972)

[8]

Kohn R.V., Strang G., Explicit Relaxation of a Variational Problem in Optimal Design, Bulletin of the American Mathematical Society, 9, pp. 211-214, (1983)

[9]

Martin J.B., Plasticity, Fundamentals and General Results, (1975)

[10]

Miehe C., Strain-Driven Homogenization ofInelastic Microstructures and Composites Based on an Incremental Variational Formulation, International Journal for Numerical Methods in Engineering, 55, pp. 1285-1322, (2002)

← 1 2 3 →