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Pedro Ponte Castañeda

Professor and Graduate Group Chair

Phone: 215.898.5046
Email: ponte@seas.upenn.edu
Office: 235 Towne Building


EDUCATION:

Ph.D. Applied Mathematics, Harvard University, 1986.
M.S. Engineering Sciences, Harvard University, 1983.
B.S. Mechanical Engineering, Lehigh University, 1982.
B.A. Mathematics, Lehigh University, 1982.


RECENT COURSES TAUGHT:

MEAM 321:  Vibrations of Mechanical Systems 
MEAM 454: Mechanics of Materials
MEAM 530/630:  Continuum Mechanics 
MEAM 635: Composite Materials


CURRENT RESEARCH PROJECTS:

Nonlinear Composite Materials

The tremendously successful studies of the effective or average properties of composite materials have mostly dealt so far with linear constitutive behaviors. However, more often than not nonlinear effects are critical in the understanding of the effective properties of real engineering materials. This project addresses nonlinear constitutive and kinematical effects as observed in low-temperature plasticity and high-temperature creep of metals, as well as in the large deformation of polymers. For details, refer to the recent review article by Ponte Castañeda and Suquet (1998) "Nonlinear Composites." Advances in Applied Mechanics 34, 171-302. Project funded by NSF and ONR.
 
 

Figure 1. Yield surfaces for fiber-reinforced composites as functions of the fiber-to-matrix flow stress ratio. Comparison of predictions of variational procedure of Ponte Castañeda (1991) (continuous lines) with FFT numerical simulations of Moulinec and Suquet (1995) (points). In this figure, S33 denotes the macroscopic stress in the direction of the fibers and S11 the corresponding shear stress  transverse to the fibers. The fiber volume fractions is 50%. Reprinted from P. Ponte Castañeda and M. Zaidman  (1996) "On the finite deformation of nonlinear composite materials. Part I. Instantaneous effective potentials." International Journal of Solids and Structures 33, 1271-1286.
 

Figure 2. Maps of accumulated plastic strain in the transverse plane according to the numerical simulations for the fiber-reinforced composites of Figure 1. (a) Pure shear transverse to the fibers; (b) and (c) Combined in-plane shear and axial stress; (d) Pure uniaxial stress along the fibers. (Note that state (b) corresponds to the stress at vertex of the yield surface in Figure 1.) Reprinted from Moulinec and Suquet  (1995) "An FFT-based numerical method for computing mechanical properties of composite materials from images of their microstructure." In Microstructure-Property Interactions in Composite Materials (R. Pyrz, ed.) Kluwer, Dordrecht, The Netherlands, pp. 235-246.

Microstructure Evolution and Localization in Manufacturing Processes

Shear localization in metals plays an important role in restricting the potential applications of several manufacturing processes, such as hot forging and extrusion. This difficulty is compounded by the presence of microstructural defects that may enhance, or delay the onset of localization during processing. This project is concerned with the theoretical development of constitutive models for porous materials, accounting for the evolution of the microstructure, that will be useful in assessing the effect of porosity on localization.  For more details, refer to Ponte Castañeda and Zaidman (1994) and Kailasam and Ponte Castañeda (1998) (see below for full references). Project funded by NSF and AFOSR.
 
Figure 3. Porosity evolution in uniaxial compaction of a porous metal. Comparison of the predictions (continuous line) of the anisotropic model of Ponte Castañeda and Zaidman (1994) with the experimental results (dark circles) of Haghi (1992; Ph.D. Thesis, Mechanical Engineering, M.I.T) and the predictions of the Gurson model (dotted line). Note that the anisotropic model, which captures the development of anisotropy due to the change in shape of the pores, is in much better agreement with the experimental results than the isotropic model of Gurson. Reprinted from M. Kailasam (1998; Ph.D. Thesis, Mechanical Engineering and Applied Mechanics, University of Pennsylvania.)
 
 

Figure 4. Axisymmetric extrusion of porous metal. (a) Contour maps of anisotropy (i.e., pore shape); (b) Contour maps of distribution of the anisotropy axes (i.e., orientation of the pores). Reprinted from M. Kailasam (1998; Ph.D. Thesis, Mechanical Engineering and Applied Mechanics, University of Pennsylvania.)

Viscoplastic Polycrystals

The computation of the effective or average mechanical response of polycrystalline aggregates is a classical problem dating back to the early work of Taylor. Recently, we have been extending the "variational" and "second-order" homogenization procedures to generate estimates for the effective behavior of viscoplastic polycrystals. Preliminary results for a model two-dimensional  nonlinear polycrystal are very encouraging, especially for low symmetry, high-anisotropy crystal systems (e.g., HCP materials). For more details, refer to deBotton and Ponte Castañeda (1995), Ponte Castañeda and Nebozhyn (1997) (see below for full references). Project funded by NSF.
 
 
 

Fig. 5. Effective flow stress of model two-dimensional polycrystal as function of grain anisotropy for a value of the strain-rate sensitivity parameter equal to 0.1. Comparison of "variational" and "second-order" estimates with Taylor and Sachs bounds and predictions based on other schemes. Note that the classical incremental and secant schemes violate the recently established upper bound of Kohn and Little (1998; to appear in SIAM Journal on Applied Mathematics), while the "variational" and "second-order" estimates satisfy the bound. Reprinted from Bornert and Ponte Castañeda (1998).

SELECTED PUBLICATIONS:

(For a complete list of publications please visit the Full Publications site.)

P. Ponte Castañeda. "The overall constitutive behavior of nonlinearly elastic composites." Proceedings of the Royal Society of London A 422 (1989): 147-171.

P. Ponte Castañeda. "The effective mechanical properties of nonlinear isotropic composites." Journal of the Mechanics and Physics of Solids 39 (1991): 45-71.

K. Bose and P. Ponte Castañeda. "Stable crack growth under mixed-mode conditions." Journal of the Mechanics and Physics of Solids 40 (1992): 1053-1105.

P. Ponte Castañeda. "A new variational principle and its application to nonlinear heterogeneous systems." SIAM Journal on Applied Mathematics 52 (1992): 1321-1341.

G. Li and P. Ponte Castañeda. "Variational estimates for the elastoplastic response of particle-reinforced metal-matrix composites." Applied Mechanics Reviews 47 (1994): S77-94.

P. Ponte Castañeda and M. Zaidman. "Constitutive models for porous materials with evolving microstructures." Journal of the Mechanics and Physics of Solids 42 (1994): 1459-1497.

G. deBotton and P. Ponte Castañeda. "Variational estimates for the creep behavior of polycrystals." Proceedings of the Royal Society of London A 448 (1995): 121-142.

P. Ponte Castañeda and J. R. Willis. "The effect of spatial distribution on the effective behavior of composite materials and cracked media." Journal of the Mechanics and Physics of Solids 43 (1995): 1919-1951.

P. Ponte Castañeda. "Exact second-order estimates for the effective mechanical properties of nonlinear composites." Journal of the Mechanics and Physics of Solids 44 (1996): 827-862.

P. Ponte Castañeda and P. Suquet. "Nonlinear composites." Advances in Applied Mechanics 34 (1998): 171-302.

K. Bose, P. A. Mataga and P. Ponte Castañeda. "Stable crack growth along a brittle/ductile interface. interface - II. Small scale yielding solutions and interfacial toughness predictions." International Journal of Solids and Structures 36 (1999): 1-34.

P. Ponte Castañeda and P. Suquet. "Nonlinear composites and Microstructure Evolution." In Mechanics for a New Millennium (Proceedings of the 20th International Congress of Theoretical and Applied Mechanics, 27 Aug - 2 Sept 2000, Chicago), edited by. H. Aref and J. W. Phillips, 253-274. Dordrecht: Kluwer Academic Publishers, 2001.

P. Ponte Castañeda. "Second-order homogenization estimates for nonlinear composites incorporating field fluctuations. I. Theory and II. Applications" Journal of the Mechanics and Physics of Solids 50 (2002): 737-782.

J. P. Briggs and P. Ponte Castañeda. "Variational estimates for the effective response of SMA-actuated fiber composites." Journal of Applied Mechanics 69 (2002): 470-480.

P. Ponte Castañeda. "On the homogenized behavior of reinforced and other Bingham composites." Philosophical Transactions of the Royal Society of London A  361 (2003): 947-964.

P. Ponte Castañeda, J. J. Telega and B. Gambin (Eds.) Nonlinear Homogenization and Applications to Composites, Polycrystals and Smart Materials. (NATO Science Series, II. Mathematics, Physics and Chemistry - Volume 170.) Dordrecht: Kluwer Academic Publishers (2004). (ISBN 1-4020-2622-6).


Y. Liu and P. Ponte Castañeda. "Homogenization estimates for the average behavior and field fluctuations in cubic and hexagonal viscoplastic polycrystals." Journal of the Mechanics and Physics of Solids  52 (2004): 1175-1211.


N. Aravas and P. Ponte Castañeda. "Numerical methods for porous metals with deformation-induced anisotropy." Computer Methods in Applied Mechanics and Engineering 193 (2004): 3767-3805.

R. Lebensohn, Y. Liu and P. Ponte Castañeda. "Macroscopic properties and field fluctuations in model power-law polycrystals: full-field solutions versus second-order estimates." Proceedings of the Royal Society of London A 460 (2004): 1381-1405.


R. Lebensohn, Y. Liu and P. Ponte Castañeda. "On the accuracy of the self-consistent approximation for polycrystals: comparison with numerical simulations." Acta Materialia  52 (2004): 5347-5361.


P. Ponte Castañeda. Heterogeneous materials. Lecture Notes, Department of Mechanics, Ecole Polytechnique (2005):191 pages (ISBN 2-7302-1267-1).


Y. Liu, P. Gilormini and P. Ponte Castañeda. "Second-order estimates for texture evolution in halite." Tectonophysics 406 (2005): 179-195.


O. Lopez-Pamies and P. Ponte Castañeda. "On the overall behavior, microstructure evolution and macroscopic stability in reinforced rubbers at large deformations: I - Theory." Journal of the Mechanics and Physics of Solids 54 (2006): 807-830.


O. Lopez-Pamies and P. Ponte Castañeda. "On the overall behavior, microstructure evolution and macroscopic stability in reinforced rubbers at large deformations: II - Application to cylindrical fibers." Journal of the Mechanics and Physics of Solids 54 (2006): 831-863.


O. Lopez-Pamies and P. Ponte Castañeda. "Homogenization-based constitutive models for porous elastomer and implications for macroscopic instabilities. I - Analysis." Journal of the Mechanics and Physics of Solids 55 (2007): 1677-1701.

O. Lopez-Pamies and P. Ponte Castañeda. "Homogenization-based constitutive models for porous elastomer and implications for macroscopic instabilities. II - Results." Journal of the Mechanics and Physics of Solids 55 (2007): 1702-1728.


M.I. Idiart and P. Ponte Castañeda. "Field statistics in nonlinear composites. Part I. Theory." Proceedings of the Royal Society of London A 463 (2007): 183-202.


M.I. Idiart and P. Ponte Castañeda. "Field statistics in nonlinear composites. Part II. Applications." Proceedings of the Royal Society of London A 463 (2007): 203-222.

M. Brun, O. Lopez-Pamies and P. Ponte Castañeda. "Homogenization estimates for fiber-reinforced elastomers with periodic microstructures." International Journal of Solids and Structures 44 (2007): 5953-5979.


J.-C. Michel, O. Lopez-Pamies, P. Ponte Castañeda, and N. Triantafyllidis. "Microscopic and macroscopic instabilities in finitely strained porous elastomers." Journal of the Mechanics and Physics of Solids 55 (2007): 900-938.

M.I. Idiart and P. Ponte Castañeda. "Variational bounds for nonlinear composites with anisotropic phases. I. General Results." Proceedings of the Royal Society of London A 463 (2007): 907-924.


M.I. Idiart and P. Ponte Castañeda. "Variational bounds for nonlinear composites with anisotropic phases. II. Crystalline materials." Proceedings of the Royal Society of London A 463 (2007): 925-943.


R. A. Lebensohn, C. N. Tome, P. Ponte Castañeda. "Self-consistent modeling of the mechanical behavior of viscoplastic polycrystals incorporating intragranular field fluctuations." Philosophical Magazine 87 (2007): 4287-4322.



Please direct inquiries to waddingt@seas.upenn.edu