Continuum Mech. Thermodyn. https://doi.org/10.1007/s00161-019-00793-z ORIGINAL ARTICLE Marin Marin · Andreas Öchsner · Daniel Taus On structural stability for an elastic body with voids having dipolar structure Received: 8 May 2019 / Accepted: 21 May 2019 © Springer-Verlag GmbH Germany, part of Springer Nature 2019 Abstract In our study, we consider the linear mixed initial boundary value problem for a porous elastic body having a dipolar structure. The equations that describe the elastic dipolar deformations are coupled with the equations which describe the evolution of the voids by means of certain coefficients. Our main result proves the continuous dependence of solutions for the mixed problem with regard to the coefficients which perform this coupling. Using an adequate measure, we can evaluate the continuous dependence by means of some estimate regarding the gradient of deformations and the gradient of the function that describes the evolution of the voids. Keywords Dipolar bodies · Voids · Gradient of displacement · Continuous dependence · Structural stability · Coupling coefficients 1 Introduction We must outline that our bodies are included in the theory of elasticity for bodies with voids. As we know, Nunziato and Cowin, in the paper [1], have initiated the approach of bodies with vacuous pores (or voids). An essential element of this theory is the introduction of a new degree of freedom so that in the mechanical behavior of such kind of material the skeletal material is elastic and the pores are interstices. There are many modern applications of this theory, of which we just mention manufactured porous materials and geological materials like soils and rocks. In the linear case, this theory of bodies with pores was approached by Cowin and Nunziato in the study [2]. In this paper, the authors demonstrated a result of the uniqueness regarding the solution for the mixed problem and obtained a result of weak stability for the respective solutions; see also [3]. The equations of the thermoelasticity of bodies with pores were obtained by Iesan in work [4]. Other results regarding the contributions of voids of material in the theory of micropolar body with pores can be found in the papers [5–9]. In our study, we took into account the dipolar structure of the elastic body. Communicated by Andreas Öchsner. M. Marin (B ) Department of Mathematics and Computer Science, Transilvania University of Brasov, 500093 Brasov, Romania E-mail: m.marin@unitbv.ro A. Öchsner Faculty of Mechanical Engineering, Esslingen University of Applied Sciences, 73728 Esslingen, Germany D. Taus Department of Civil Engineering, Transilvania University of Brasov, 500093 Brasov, Romania