International Journal of Engineering Science 129 (2018) 1–20 Contents lists available at ScienceDirect International Journal of Engineering Science journal homepage: www.elsevier.com/locate/ijengsci Analysis of small temperature oscillation in a deformable solid matrix containing a spherical cavity ﬁlled with a compressible liquid – Analytical solutions for damage initiation induced by pore pressure variation Heraldo S. Da Costa Mattos ∗ , Luciana P. Teixeira, Maria Laura Martins-Costa Laboratory of Theoretical and Applied Mechanics, Graduate Program in Mechanical Engineering, Department of Mechanical Engineering, Universidade Federal Fluminense, Rua Passo da Pátria 156, 24210-240 Niterói, RJ, Brazil a r t i c l e i n f o Article history: Received 17 March 2017 Revised 27 September 2017 Accepted 5 February 2018 Keywords: Temperature variation Liquid-ﬁlled cavity Liquid compressibility Brittle-Elastic matrix behavior Elasto-plastic matrix behavior Damage initiation a b s t r a c t This paper analyzes the possibility of damage initiation induced by a very small tempera- ture variation near a liquid-ﬁlled spherical cavity inside a deformable solid matrix. Experi- ments conﬁrm that small temperature variations in a (compressible) liquid-ﬁlled cavity can induce high pressure peaks, depending on the initial temperature and pressures. The main motivation of the study is to verify the possibility of damage initiation induced by a very small temperature variation in a saturated liquid-ﬁlled porous medium with ultra-low per- meability. Depending on the interaction between micro-cracks and pores, this damage may signiﬁcantly affect the permeability conditions. The study of a single water-ﬁlled pore in an inﬁnite matrix is quite a convenient preliminary step, since the stress ﬁeld in the solid matrix is independent of its constitutive behavior (a statically determinate problem) what allows simplifying the complex coupled non-linear analysis. An abstract thermodynamic framework is used to present constitutive theories for generalized compressible Newtonian ﬂuids and for elastic and elasto-plastic solid matrix behaviors. Both theories encompass a wide variety of constitutive models for solids and ﬂuids found in the literature and can be applied in many engineering problems involving liquid-ﬁlled porous media. Using an ade- quate equation of state for the thermodynamic pressure proposed for liquid water at high pressures, it is possible to predict analytically if a very small liquid temperature variation (maximum of 5 K) can induce the matrix failure. Two examples of matrix behaviors are analyzed: brittle-elastic and elasto-plastic. Adequate failure criteria are used in each case to predict analytically the critical pressure required for the damage initiation. Once this pressure is determined, the temperature variation necessary to the damage initiation can also be obtained using the state law proposed for the thermodynamic pressure. © 2018 Elsevier Ltd. All rights reserved. 1. Introduction Along the past few years, many studies have been performed about the inﬂuence of temperature gradients in the fracture and permeability of liquid-ﬁlled porous media. Most of them are concerned with the modeling of the fracture propagation ∗ Corresponding author. E-mail address: heraldo@mec.uff.br (H.S. Da Costa Mattos). https://doi.org/10.1016/j.ijengsci.2018.02.014 0020-7225/© 2018 Elsevier Ltd. All rights reserved.