## 1 Introduction  
Materials science and engineering drive technological innovation across industries through advanced materials and applications [1]. Materials science market research focuses on material properties, structure, and applications, enabling efficient and durable products that enhance the quality of life. As industries innovate, demand for skilled materials scientists grows, stimulating economic development [1]. Companies investing in materials research gain competitiveness through innovation. Advanced materials use drives leadership in green materials, additive manufacturing, smart and functional materials, nanomaterials, and biomaterials. The driving factors of the materials science market can be summarized as:  
* Technological advancements: due to evolving needs in electronics, healthcare, aerospace, and automotive; they require high-performance materials to maintain competitiveness [1];
* Sustainability: environmental concerns drive the development of sustainable materials like biodegradable plastics, recyclables, and bio-based alternatives [2];
* Emerging technologies: new technologies require materials that enhance performance, accelerating market growth [1]. Tailor-made materials result from advances in structure-property theory, characterization, and control of advanced manufacturing (e.g., nanotechnology, molecular and surface engineering). While lab identification of suitable materials is often feasible, scaling up manufacturing remains a major challenge. Moreover, mathematical-statistical modelling improves efficiency in material and process design. Understanding the thermophysical behavior of solids is essential for engineering design, particularly under high temperatures, where phase stability is critical. However, studies on the mechanical performance of advanced structural materials remain limited. Furthermore, fatigue cracks have been a key factor in structural failures for two centuries [3]. The use of fracture mechanics has improved structural efficiency, avoiding premature decommissioning and reducing costs. However, aspects like crack closure remain poorly understood, primarily due to difficulties in evaluating their effect on the crack driving force [4]. Recently, there has been a notable increase in research on the interaction between mechanical and thermal effects in solid materials [5]; driven by the development of advanced materials (e.g., ceramics, composites), researchers now emphasize time, temperature, and scale phenomena, beyond purely mechanical aspects [6]. For metals and alloys, extensive studies have explored temperature-strain relationships based on thermodynamic laws [5], extending to concrete and mortar via analyses of Gruneisen parameters, heat diffusivity, and thermal expansion [7]. Improved measurement tools have advanced non-destructive structural testing by enabling surface heat emission analysis [8; 9]. In the elastic regime, challenges include incorporating principal stresses under thermal changes and using the linear stress tensor in 2D and 3D bodies [10; 11]. In inelastic analyses, attention centers on dissipation phenomena preceding failure [5]. Most theoretical models assume absolute zero temperature and a perfect and fixed crystalline arrangement of atoms, offering insights under low stress and temperature, but for engineering purposes, it is more relevant to investigate solids at ambient temperature under high external loads [12; 13; 14]. Thermomechanical interactions in solids are of growing interest due to their engineering relevance and insight into material thermophysical behavior. The theory of thermoelasticity combines principles of elasticity and heat conduction. It relates to how heat affects the deformation of an elastic medium and how deformation, in turn, influences the medium's thermal state. Thermal stress arises when the rate of change in heat sources or boundary conditions in a medium is compared with the medium's structural oscillation characteristics.