This paper addresses the critical role of fiber-matrix invariant coupling in accurately predicting the loss of stability, characterized by a non-monotonic relationship between the inflation-extension response of a thin-walled biological tube, often referred to as limit-point instability. Such deformations frequently occur in arteries and veins and are particularly relevant to cardiovascular mechanics, especially in aneurysm formation. Prior research used the chain extensibility parameter to establish the configuration-dependent stability thresholds for Gent materials (e.g., J(m) < 18.2 for thin-walled isotropic membranes and J(m) = 0.1 for anisotropic tubes under uniform inflation). These thresholds are not universal and arise under specific assumptions, such as incompressibility, thin-wall kinematics, and closed-end inflation. This work aims to evaluate further how these configuration-specific thresholds shift when fiber-matrix invariant coupling is incorporated. The strain energy density is formulated as a function of the invariants I-1 (matrix) and I4 (fiber), incorporating nonlinear coupling exponents (alpha,beta). The onset of instability is heavily influenced by the fiber orientations, invariant coupling exponents, and the associated threshold values of the chain extensibility parameter. The impact of these critical parameters on the mechanical response of a pressurized finitely extensible biological tube is illustrated by comparing anisotropic modes to isotropic modes, with and without fiber-matrix coupling effects. The modeling results are validated against pressurized porcine artery sample datasets.

Dielectric elastomer (DE) membranes with compliant electrodes exhibit two primary instabilities: wrinkling due to in-plane compressive stress relaxation, and electromechanical instability associated with rapid thinning before dielectric breakdown. Existing instability models for DE membranes commonly assume mechanically passive electrodes, neglecting their stiffness. In contrast, several experimental studies indicate that compliant electrodes exhibit finite stiffness. In this work, an experimentally validated analytical framework is developed for DE membranes that explicitly captures the nonlinear hyperelastic behavior of mechanically active compliant electrodes within an energy-based classical continuum formulation, with stability analyzed using a Hessian-based criterion. The model incorporates electromechanical coupling under unequal biaxial pre-stretch, inducing anisotropy in the membrane response. Tension-field theory is extended to account for mechanically active electrodes, allowing prediction of taut and wrinkled states together with their stability limits and critical electric fields. The results indicate that electrode stiffness influences stability in a pre-stretch-dependent manner. For a fixed pre-stretch configuration, increasing electrode thickness generally enlarges the admissible taut region and increases the critical electric field, whereas the effect of electrode stiffness depends on the degree of pre-stretch anisotropy. Unequal biaxial pre-stretch reduces the size of the taut domain and lowers the critical electric field relative to the equi-biaxial case, while also inducing a pronounced deviation of the taut region in stretch space. These results highlight the key role of electrode mechanics and the need to explicitly incorporate them in the modeling and design of DE systems for controlled electromechanical response and stability.

This study aims to model and predict the morpho-elastic behavior and failures of bamboo material characterized by intricate growth and inherent anisotropy. An experimentally validated continuum physics-based deformation model is developed using a growth-elastic decomposition framework and is evaluated against uniaxial and biaxial tension-compression data from the literature, achieving prediction errors below 3% and 5%, respectively. The model also utilizes an octahedral shear stress-based failure criterion to accurately predict the uniaxial and biaxial failure stresses of bamboo and construct the associated biaxial failure envelopes. Later, parametric studies are conducted to evaluate the impact of growth and anisotropy on the morphoelastic response and failures of bamboo. The results show that changes in growth, fiber orientation, biaxiality ratio and anisotropic stiffening alter the mechanical behavior of bamboo.

This article proposes a second-order constitutive approximation for electroelastic materials using the Biot strain measure. The deformation gradient tensor and the electric field vector, both expressed in terms of the undeformed reference configuration, are used to express the strain energy density. From this expansion, the Cauchy stress tensor is obtained by retaining terms up to second order in the gradient of the strain energy function, which introduces the electromechanical coupling contributions. As a result, the constitutive relation contains the usual mechanical response together with additional terms arising from the electric field. In the absence of the electric field, the formulation is consistent with material frame indifference and reduces to the conventional second-order elasticity model.

This study examines how fiber-matrix invariant coupling influences the prediction of limit-point instability. Such behavior commonly occurs in heart and bladder and is closely linked to cardiovascular mechanics, particularly the formation of aortic aneurysms. Prior studies have utilized a well-known limiting chain-extensibility parameter to establish configuration-dependent stability thresholds for Gent materials (e.g., J_m < 18.2 for isotropic tubes and J_m = 0.1 for anisotropic tubes), but no corresponding thresholds exist for finitely extensible spherical shells. Certain assumptions, such as incompressibility, thin-wall kinematics, and closed-end inflation, give rise to these stability criteria, which are not universal. This work primarily aims to identify configuration-dependent stability thresholds for isotropic and anisotropic biological spheres under inflation and to assess how these configuration-dependent thresholds shift when fiber-matrix invariant coupling is incorporated. The strain energy density is formulated as a function of the invariants I_1 (matrix) and I_4 (fiber), incorporating nonlinear coupling exponents ( α , β ). The formulation yields a closed-form pressure-stretch relation that generalizes existing uncoupled models and enables systematic identification of instability thresholds. The onset of instability is heavily influenced by the fiber orientations, invariant coupling exponents, and the associated threshold values of the chain extensibility parameter. By comparing isotropic and anisotropic modes with and without fiber-matrix coupling, the impact of these essential characteristics on the inflation mechanics of finitely extensible biological spherical shell is investigated. Test data from a pressurized monkey bladder is used to compare the model predictions.

Collagen and/or elastin fibers are key load-bearing constituents of biological tissues. To realistically model the Poynting effect in biological tissues, which refers to the expansion or contraction of a material in directions perpendicular to an applied twist or shear, fiber dispersion cannot be neglected. The purpose of this work is to examine the often-ignored mechanics of fiber dispersion in accurately predicting the torque and axial stress responses of soft tissues under torsion, with particular emphasis on the Poynting effect. To model the critical role of fiber dispersion, a well-established generalized structural tensor framework is employed. Unlike the conventional quadratic term (I-4(& lowast;) -1)(2), which causes unphysical instabilities associated with negative instantaneous stiffness under specific deformation regions of tissues, an amended form of strain energy density with a nonlinear term I-4(& lowast;-m)-1, m > 0, is formulated. The impact of fiber dispersion on torque and axial stress is illustrated for white rabbit papillary muscle samples by comparing anisotropic modes to isotropic modes, with and without fiber-dispersion effects.

The Poynting and Swift-type responses are commonly used to describe axial deformation under torsion in soft tissues, although the mechanism governing the transition between these responses remains unclear. This work develops an analytical model to investigate the transition from Swift-type to Poynting-type response in torsion of soft tissues, incorporating the effect of fiber dispersion. The torsional response is represented by linear (L), quadratic (Q), and higher-order (H) nonlinear contributions associated with fiber anisotropy, matrix deformation, and nonlinear stiffening. A dimensionless transition parameter, Π=L/Q, is derived to identify the relative dominance of Swift-type and Poynting-type mechanisms, with the corresponding critical twist defined as τc=Π. The results indicate that fiber dispersion plays an important role in determining the critical transition point, as it alters the ratio of anisotropic to isotropic responses. The theoretical predictions show good agreement with experimental data reported for the rabbit papillary muscle under torsion.

Nonlinear vibration and sound radiation characteristics of viscoelastic variable stiffness laminated composite (VVSLC) plates subjected to harmonic force are presented. The fibre path within each lamina varies linearly along x direction. The lamina is assumed to exhibit viscoelastic behaviour. The viscoelastic constitutive relation in the time domain is transformed to incremental algebraic form. The displacement field is described using the first-order shear deformation theory, and the nonlinear equation of motion is obtained using principle of virtual work. The periodic solution in time domain is obtained using shooting technique coupled with Newmark's direct time integration and Newton-Raphson method. The unstable portion of frequency response curves is traced using the arc-length continuation. The acoustic pressure is obtained using time domain Rayleigh integral. A detailed parametric study is carried out to analyse the effects of variation in fibre angle at centre and edges of lamina and boundary conditions on the response. Also, the sound pressure level perceived by the human ear (dBA) is investigated. Finally, a comparative analysis between a purely elastic and a viscoelastic plate is also presented. It is observed that the fibre angle, boundary conditions and the inherent material damping have a significant effect on the nonlinear vibro-acoustic response of VVSLC.

In finite electro-elastic deformation, a commonly used electrical energy term is typically inconsistent with the general theory of nonlinear electroelasticity. Such formulations may violate the basic fundamental theoretical requirements, leading to an asymmetric total Cauchy stress tensor. This article proposes an appropriate correction by augmenting the total electro-elastic energy with an additional field-dependent term. The definition of an electrical displacement vector in the reference configuration forms the basis for this additional term. The proposed correction confirms that the total Cauchy stress tensor is symmetric by clarifying the role of the remnant polarization and material symmetry in soft electroactive materials.

This article addresses the problem of an isotropic, nonlinear elastic, incompressible magneto-active solid cube undergoing homogeneous deformation due to shear and triaxial extension, with no normal tractions applied. The novel material-dependent relations are established for this deformation, valid for all incompressible magneto-active solids. The considered cube generally undergoes dimensional changes due to shear deformation and the Poynting effect with no magnetic fields. The purpose of this study is to examine the impact of magnetic fields on these dimensional changes, developing the constitutive equations for nonlinear magneto-active solids. Expressions for the dimensional changes are derived as functions of shear and triaxial extension, accounting for different orientations of the magnetic field vectors relative to the shearing direction. Existing universal relations with no magnetic field validate the developed relations.

Stress-strain coaxiality is a key determinant in generating universal relations for materials. These relationships have been studied extensively in isotropic materials but remain underexplored in fiber-reinforced materials with different material symmetries. The present study aims to examine the role of fiber orientations and invariant coupling in the stress-strain coaxiality of transversely isotropic fiber-reinforced elastomers (FREs) under simple shear, uniaxial tension, and nonequibiaxial stretch. The strain energy density as a function of the invariants I-1 (matrix) and I4 (fiber) is adopted with nonlinear coupling exponents (alpha,beta). Illustrations are presented on how different invariant coupling terms affect the stress-strain coaxiality-driven universal relations for the transversely isotropic material class. Variations in axial vector terms are reported for different stretches, fiber orientations, and the degree of nonlinearity in the coupling terms with their coupling exponents. Such variations are compared across three distinct deformation modes: simple shear, uniaxial tension, and nonequibiaxial stretch. In all three modes, the inclusion of the I-1-I-4 invariant coupling term significantly altered the stress-strain coaxiality relations for theta=45deg, 60deg, and 75deg. These results provide significant evidence of the importance of fiber-matrix coupling terms in the constitutive properties of FRE materials.

Accurate failure prediction methods are crucial in evaluating the biological tissues prone to failure. These methods have been extensively studied in isotropic modes but remain underexplored in fiber-reinforced biological tissues with varying anisotropies and fiber-matrix coupling effects. This study aims to model the critical role of fiber orientations and invariant coupling in accurately predicting the uniaxial and biaxial failure stresses of biological tissues. The strain energy density is modeled as a function of the invariants I-1 (matrix) and I-4 (fiber), incorporating nonlinear coupling exponents (alpha,beta). The impact of invariant coupling and fiber orientations on failure behavior is illustrated for anisotropic tissues by comparing anisotropic modes, with and without fiber-matrix coupling effects, to isotropic modes. Variations in failure envelopes are also analyzed for different fiber orientations and degrees of nonlinearity in the coupling terms across uniaxial and non-equibiaxial stretches. Fiber-matrix coupling alters failure envelopes from theta=0 degrees to 90 degrees, emphasizing its role in tissue modeling. The impact of nonlinear coupling on the ratio of octahedral shear to octahedral normal stresses further underscores its significance in tissue engineering.

A thin dielectric elastomeric (DE) plate with thickness gradients deforms and wrinkles under applied voltages. Such wrinkling, with regular periodic patterns in thin functionally graded DEs, occurs to relax in-plane compressive stresses through out-of-plane deformations. These functionally graded DE-based soft actuators, primarily used in soft robotic applications, exhibit highly localized point loads compared to non-graded soft actuators. DE-based soft actuators frequently exhibit a variety of instabilities, which may adversely affect their functioning and trigger device failure. Conversely, fine-tuned wrinkles can be utilized proactively in specific applications, necessitating an intentional transformation with directional gradients and the truncation of biaxial deformations. This paper presents an experimentally verified continuum physics-based model under a special case for unequal-biaxial deformation in functionally graded DEs. The proposed model integrates classical tension field theory to predict thresholds in taut domains within the plane of principal stretches. The model solutions provide insight into the deviations of taut domains influenced by the graded parameter and the biaxiality ratio in unequal-biaxial deformations of wrinkle formations in this material class.

Modeling the response of biological tissues undergoing torsion is a topic of considerable current interest. Such deformations frequently occur in ligaments and tendons, particularly relevant to cardiac mechanics, especially in papillary muscle biomechanics. This work examines the classical torsion problem for an incompressible, fiber-reinforced anisotropic biological cylinder. The present work primarily aims to model the critical role fiber orientations and invariant coupling in accurately predicting the torque and axial stress response of tissue under torsion, emphasizing the Poynting effect. This Poynting effect describes the tendency of materials expand or contract perpendicularly to the direction of applied twist or shear. The strain energy density modeled as a function of the invariants I1 (matrix) and I4 (fiber), incorporating nonlinear coupling exponents (a, /i). The impact of invariant coupling and fiber orientations on torque and axial stress is illustrated for white rabbit papillary muscle samples by comparing anisotropic modes to isotropic modes, with and without fiber-matrix coupling effects. The modeling results are validated against existing experimental data.

A Mullins effect is a commonly observed phenomenon describing how biological tissues lose their elastic modulus encountering a certain level of deformation. Many biological tissues, including heart, skin, and blood vessels, exhibit this stress-softening phenomenon. The current study models and simulates such an effect using skin samples from male and female mice tested under higher cyclic loading conditions. The study employs a newly proposed energy density function and compares its performance against existing energy functions that fail to accurately predict the Mullins effect at higher loading cycles. The findings, supported by experimental data, demonstrate that the proposed energy function qualitatively captures the effect in the tested skin samples.

In light of recent and growing interest in soft electro-magneto-active materials, this letter addresses the problem of an isotropic, nonlinear elastic, incompressible electro-magneto-active solid cube undergoing homogeneous deformation due to shear and triaxial extension with no normal tractions applied. This cube generally undergoes dimensional changes due to shear deformation and the Poynting effect with no electromagnetic field. This short article is devoted to analytically examine the impact of electromagnetic fields on these dimensional changes, developing the constitutive equations for nonlinear electro-magneto-active solids. The purely geometric universal relations are established for the cube deformation, directly linking the shear, the electric field, the magnetic field, and the stretch. Such a direct linkage of kinematical quantities-based universal relations provides an essential feature of being easily tested experimentally. Existing universal relations with no electromagnetic field validate the developed relations.

Wrinkles, with regular periodic patterns in thin elastomeric membranes, occur to relax in-plane compressive stresses through out-of-plane deformations. Existing studies on such wrinkling have primarily ignored the thermo-electro-magnetostrictive unequal-biaxial taut states, focusing instead on the equal-biaxial deformations of thin membranes. Soft actuators made of electro-magneto-active (EMA) membranes, used mainly in soft robotics, often exhibit a variety of instabilities, which may adversely affect their performance and lead to actuator failure. Conversely, fine-tuned wrinkles in their regular periodic patterns can be used proactively in specific applications that necessitate an intentional loading transformation and dual responsiveness to electromagnetic fields. This paper theoretically develops a physics-based thermo-electro-magnetostrictive unequal-biaxial deformation model of thin EMA membranes, incorporating classical tension field theory to predict the thresholds on the taut domains in the plane of principal stretches. The model solution is then experimentally verified for a readily available thin membrane. In addition, the analytical findings tie an unanswered ideal remark on the deviations of taut states with the biaxiality ratio of the unequal-biaxially deformed wrinkle appearance in thin EMA-based smart membranes.