Demand Response is a strategy to address imbalances between power generation and consumption in energy systems. This is achieved by offering incentives for adjusting energy demand based on the current state of the power grid. The consumer-centric approach gives the end-user the freedom to participate in programs or make load decisions. Originally conceived and extensively studied within the electricity sector, it can also be applied to other energy domains or cross-sector scenarios. The integration of renewable energy resources, together with an evolving consumption landscape, positions Demand Response as a cornerstone of the energy transition. To provide an overview of its diversity and multitude of aspects, a structured approach is essential. This work introduces a novel structural model to holistically address key aspects of Demand Response. It further explores the organization of these aspects within the Smart Grid Architecture Model (SGAM), a widely recognized structural framework in smart grids. The SGAM employs a multi-layered methodology that encompasses the technical, logical, and business perspectives of smart grids. This work contends that the SGAM framework lacks a sufficient societal and human dimension in its approach to Demand Response. The adoption of Demand Response is frequently driven by societal objectives rather than solely by business interests. Furthermore, modeling consumers based only on business aspects is insufficient for capturing the complexity of human behavior in private contexts, particularly in residential energy demand. This necessitates insights from psychological and social disciplines. The central role of human factors in Demand Response is addressed through the introduction of a new layer in the SGAM framework, termed the \textit{Society Layer}. SGAM-S, the enhanced SGAM model incorporating this new layer, provides a comprehensive perspective on use cases, standards, and other critical aspects of Demand Response.