J Elast DOI 10.1007/s10659-016-9614-1 On the Nonlinear Theory of Thermoviscoelastic Materials with Voids D. Ie¸ san 1 Received: 21 June 2016 © Springer Science+Business Media Dordrecht 2016 Abstract This article is devoted to a theory of thermoviscoelastic materials with voids where the time derivative of the strain tensor and the time derivative of the gradient of the volume fraction are included in the set of independent constitutive variables. The equations of the nonlinear theory are considered. A stability result for bodies which are non-conductor of heat is presented. The stability is interpreted as continuous dependence of the processes upon initial state and supply terms. Keywords Thermoviscoelasticity · Materials with voids · Porous materials · Continuous dependence results Mathematics Subject Classification 74D05 · 74D10 · 74E20 · 74F05 · 74H25 1 Introduction There has been much recent interest in the study of porous bodies. For the history of the problem and the analysis of various results on the subject see Bowen [1], De Boer [2] and Coussy [3]. Nunziato and Cowin [4] established a theory of elastic materials with voids. The basis for the continuum theory employed is the concept of a distributed body proposed by Goodman and Cowin [5] for flows of granular materials in which the porous nature of the material is represented in terms of the volume fraction of the granules. The wave propagation in granular materials has been studied in various papers (see, e.g., [6]). Nunziato and Cowin [4] have presented an adaptation of the model introduced in [5] appropriate for porous solids where the skeletal material is elastic. Capriz and Podio-Guidugli [7] have studied the elastic materials with voids as materials with spherical structure. The theory of elastic materials with voids is one of the simple extensions of the classical theory of elasticity for the treatment of porous solids in which the matrix material is elastic and the interstices B D. Ie¸ san iesan@uaic.ro 1 “Al.I. Cuza” University of Ia¸ si, and “Octav Mayer” Institute of Mathematics, Romanian Academy, Bd. Carol I, nr. 8, 700506, Ia¸ si, Romania