## 1 Introduction  
Skin wrinkles, particularly on the face, are a key sign of aging and play an important role in the expanding fields of skincare, cosmetics, facial recognition, and dermatological treatments [1]. Moreover, wrinkles adversely affect facial recognition accuracy while playing a significant role in facial modeling and machine learning applications [2, 3]. The image enhancement and denoising approach has driven the development of related fields such as facial modeling and wrinkle recognition [4]. Human skin develops two primary types of wrinkles: static wrinkles and dynamic wrinkles [5]. Static wrinkles result from age-related tissue volume loss, whereas dynamic wrinkles can form at any age due to the contraction of underlying skeletal muscles during facial expressions. Despite their differences, both types show similar wrinkling mechanisms. [PERSON] et al. [6] observed striking similarities in the facial wrinkle patterns of mothers and daughters when smiling or expressing anger. Wrinkles are an inherent feature of skin morphology, closely influenced by mechanical interactions with their surrounding environment [7]. To better understand wrinkle formation, it is essential to analyze the mechanical behavior of in vivo skin, as wrinkle development is strongly linked to deformation caused by repeated facial movements of both skin and muscles [6, 8]. Both experimental and numerical methods are widely used to study skin wrinkles. Human skin typically consists of three layers: the epidermis, dermis, and hypodermis [9]. Skin exhibits nonlinear mechanical behavior across its stratified structure. Hyperelastic and viscoelastic constitutive models are employed to characterize this nonlinear mechanical behavior of biomaterials [10; 11]. To investigate the formation of compressed skin folds, early studies employed a three-layer finite element (FE) model [12; 13; 14]. Recognizing the biomechanical contributions of sublayers, [PERSON] et al. [15] introduced a six-layer computational model to explore the relationship between aging and dynamic surface wrinkling. In their subsequent studies, they examined the potential mechanisms of three wrinkle formations [5]. Researchers extended earlier frameworks by developing enhanced FE models that integrated additional skin structural details. To investigate the effect of collagen fibers within the dermis, a multiscale four-layered 2D FE model was developed [16]. Considering the detailed geometry of a human finger, [PERSON] et al. [17] utilized a multi-layered 3D FE simulation model to characterize wrinkling behavior in terms of wavelength, amplitude, and critical wrinkling stress/strain. [PERSON] et al. [18] incorporated realistic microscale topography into a multi-layered 3D model to examine its impact on the mechanical and tribological properties of human skin. To deepen our understanding of wrinkle formation with aging, [PERSON] et al. [19] developed a four-layer skin model characterized by polygonal microrelief structures. Despite significant progress in modeling skin wrinkling, existing studies primarily focus on the structural composition of the skin itself while often overlooking the crucial role of underlying muscles. Dynamic wrinkles are directly induced by repeated muscle activity, and neglecting this factor limits the accuracy of simulations in capturing realistic wrinkle formation processes. There has been notable advancement in experiments aimed at understanding the underlying mechanisms of wrinkle formation [20]. [PERSON] et al. [13] utilized an experimental setup, including a charged-coupled device (CCD) laser displacement sensor and a micro-translation stage, to investigate wrinkling on the solar forearm. To quantify the wrinkles on the knee and crow's feet, [PERSON] et al. [21] employed an optical 3D capturing device and R-parameter. New optical methods are increasingly being adopted to study the formation of skin wrinkles.