Finite strain elastostatics is expressed for general anisotropic, piecewise linear stiffening materials, in the form of a constrained minimization problem. The corresponding boundary value problem statement is identified with the associated necessary conditions. Total strain is represented as a superposition of variationally independent constituent fields. Net stress-strain properties in the model are implicit in terms of the parameters that define the constituents. The model accommodates specification of load fields as functions of a process parameter.

1.
Bendso̸e
M. P.
,
Guedes
Jose M.
,
Plaxton
S.
, and
Taylor
J. E.
,
1996
, “
Optimization of Structure and Material Properties for Solids Composed of Softening Material
,”
International Journal of Solids &Structures
, Vol.
33
, pp.
1799
1813
.
2.
Clarke, F. H., 1983, Optimization and Nonsmooth Analysis, Wiley-Interscience, New York.
3.
Frisen
M.
,
Magi
M.
,
Sonnerup
L.
, and
Viidik
A.
,
1969
, “
Rheological Analysis of Soft Collagenous Tissue: Part I. Theoretical consideration
,”
Journal of Biomechanics
, Vol.
2
, pp.
13
20
.
4.
Gurtin, M. E., 1981, Topics in Finite Elasticity, Society for Industrial and Applied Mathematics, Philadelphia, PA.
5.
Kwan
J. K.
, and
Woo
S. L.-Y.
,
1989
, “
A Structural Model to Describe the Nonlinear Stress-Strain Behavior for Parallel Fibered Collageneous Tissues
,”
ASME Journal of Biomechanical Engineering
, Vol.
11
, pp.
361
363
.
6.
Prager, W., 1964, “On Elastic, Perfectly Locking Materials,” Proceedings, llth International Congress of Applied Mechanics, H. Gortler, ed., Munich, Springer-Verlag, Berlin.
7.
Reddy, J. N., 1984, Energy and Variational Methods in Applied Mechanics, John Wiley and Sons, New York.
8.
Taylor
J. E.
, and
Washabaugh
P. D.
,
1994
, “
Analysis and Design of Trussed Structures Made of Elastics/Stiffening Materials
,”
Structural Optimization
, Vol.
8
, pp.
1
8
.
9.
Taylor
J. E.
,
1994
, “
A Global Extremum Principle in Mixed Form for Equilibrium Analysis with Elastic/Stiffening Material: a Generalized Minimum Potential Energy Principle
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
61
, pp.
914
918
.
10.
Taylor
J. E.
,
1997
, “
Generalized Potential Formulations for Elastostatics of Constitutively Nonlinear Structures Under Generalized Loading
,”
International Journal of Mechanical Sciences
, Vol.
39
, No.
5
, pp.
537
548
.
This content is only available via PDF.
You do not currently have access to this content.