# American Institute of Mathematical Sciences

September  2014, 19(7): 2169-2187. doi: 10.3934/dcdsb.2014.19.2169

## Strain gradient theory of porous solids with initial stresses and initial heat flux

 1 Department of Mathematics, "Al.I. Cuza" University, and Octav Mayer Institute of Mathematics (Romanian Academy), 700508, Iaşi, Romania

Received  March 2013 Revised  May 2013 Published  August 2014

In this paper we present a strain gradient theory of thermoelastic porous solids with initial stresses and initial heat flux. First, we establish the equations governing the infinitesimal deformations superposed on large deformations. Then, we derive a linear theory of prestressed porous bodies with initial heat flux. The theory is capable to describe the deformation of chiral materials. A reciprocity relation and a uniqueness result with no definiteness assumption on the elastic constitutive coefficients are presented.
Citation: Dorin Ieşan. Strain gradient theory of porous solids with initial stresses and initial heat flux. Discrete & Continuous Dynamical Systems - B, 2014, 19 (7) : 2169-2187. doi: 10.3934/dcdsb.2014.19.2169
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##### References:
 [1] Patricia Gaitan, Hiroshi Isozaki, Olivier Poisson, Samuli Siltanen, Janne Tamminen. Probing for inclusions in heat conductive bodies. Inverse Problems & Imaging, 2012, 6 (3) : 423-446. doi: 10.3934/ipi.2012.6.423 [2] Stan Chiriţă. Spatial behavior in the vibrating thermoviscoelastic porous materials. Discrete & Continuous Dynamical Systems - B, 2014, 19 (7) : 2027-2038. doi: 10.3934/dcdsb.2014.19.2027 [3] Zhiqiang Yang, Junzhi Cui, Qiang Ma. The second-order two-scale computation for integrated heat transfer problem with conduction, convection and radiation in periodic porous materials. Discrete & Continuous Dynamical Systems - B, 2014, 19 (3) : 827-848. doi: 10.3934/dcdsb.2014.19.827 [4] Tomás Caraballo, José Real, I. D. Chueshov. Pullback attractors for stochastic heat equations in materials with memory. Discrete & Continuous Dynamical Systems - B, 2008, 9 (3&4, May) : 525-539. doi: 10.3934/dcdsb.2008.9.525 [5] Mircea Bîrsan, Holm Altenbach. On the Cosserat model for thin rods made of thermoelastic materials with voids. Discrete & Continuous Dynamical Systems - S, 2013, 6 (6) : 1473-1485. doi: 10.3934/dcdss.2013.6.1473 [6] Tomás Caraballo, I. D. Chueshov, Pedro Marín-Rubio, José Real. Existence and asymptotic behaviour for stochastic heat equations with multiplicative noise in materials with memory. Discrete & Continuous Dynamical Systems - A, 2007, 18 (2&3) : 253-270. doi: 10.3934/dcds.2007.18.253 [7] Toyohiko Aiki, Kota Kumazaki. Uniqueness of solutions to a mathematical model describing moisture transport in concrete materials. Networks & Heterogeneous Media, 2014, 9 (4) : 683-707. doi: 10.3934/nhm.2014.9.683 [8] Paolo Paoletti. Acceleration waves in complex materials. Discrete & Continuous Dynamical Systems - B, 2012, 17 (2) : 637-659. doi: 10.3934/dcdsb.2012.17.637 [9] Edward Della Torre, Lawrence H. Bennett. Analysis and simulations of magnetic materials. Conference Publications, 2005, 2005 (Special) : 854-861. doi: 10.3934/proc.2005.2005.854 [10] John Murrough Golden. Constructing free energies for materials with memory. Evolution Equations & Control Theory, 2014, 3 (3) : 447-483. doi: 10.3934/eect.2014.3.447 [11] Luca Deseri, Massiliano Zingales, Pietro Pollaci. The state of fractional hereditary materials (FHM). Discrete & Continuous Dynamical Systems - B, 2014, 19 (7) : 2065-2089. doi: 10.3934/dcdsb.2014.19.2065 [12] Mariano Giaquinta, Paolo Maria Mariano, Giuseppe Modica. A variational problem in the mechanics of complex materials. Discrete & Continuous Dynamical Systems - A, 2010, 28 (2) : 519-537. doi: 10.3934/dcds.2010.28.519 [13] Merab Svanadze. On the theory of viscoelasticity for materials with double porosity. Discrete & Continuous Dynamical Systems - B, 2014, 19 (7) : 2335-2352. doi: 10.3934/dcdsb.2014.19.2335 [14] Alexander Plakhov, Vera Roshchina. Fractal bodies invisible in 2 and 3 directions. Discrete & Continuous Dynamical Systems - A, 2013, 33 (4) : 1615-1631. doi: 10.3934/dcds.2013.33.1615 [15] Joris Vankerschaver, Eva Kanso, Jerrold E. Marsden. The geometry and dynamics of interacting rigid bodies and point vortices. Journal of Geometric Mechanics, 2009, 1 (2) : 223-266. doi: 10.3934/jgm.2009.1.223 [16] Liran Rotem. Banach limit in convexity and geometric means for convex bodies. Electronic Research Announcements, 2016, 23: 41-51. doi: 10.3934/era.2016.23.005 [17] Angelo Alberti, Claudio Vidal. Singularities in the gravitational attraction problem due to massive bodies. Discrete & Continuous Dynamical Systems - A, 2010, 26 (3) : 805-822. doi: 10.3934/dcds.2010.26.805 [18] K. A. Ariyawansa, Leonid Berlyand, Alexander Panchenko. A network model of geometrically constrained deformations of granular materials. Networks & Heterogeneous Media, 2008, 3 (1) : 125-148. doi: 10.3934/nhm.2008.3.125 [19] David G. Ebin. Global solutions of the equations of elastodynamics for incompressible materials. Electronic Research Announcements, 1996, 2: 50-59. [20] Giuseppina Autuori, Patrizia Pucci. Entire solutions of nonlocal elasticity models for composite materials. Discrete & Continuous Dynamical Systems - S, 2018, 11 (3) : 357-377. doi: 10.3934/dcdss.2018020

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