The stress singularities at the free edge of an interface between adjacent layers in a laminated composite are studied. Each layer is assumed to be same orthotropic material with one principal axes being fiber direction. angle θ, however, which orientation, varies from layer. subjected uniform extension plane layers. At having angles (0/90), (θ/θ′), and family special combinations (θ/θ′) shown paper, singularity type k*rδ (δ<0), seems only possibility. For other orientations layers, it...

Abstract Hybrid‐stress eight‐node isoparametric multilayer plate elements are developed for the analysis of thin to thick fibre‐reinforced composite plates. Transverse shear deformation effects incorporated by allowing a linear through‐thickness displacement variation in‐plane displacements in each layer, with continuity enforced along interlayer surfaces. An alternative, kinematically constrained distribution is also studied, characterized laminate reference plane and non‐normal rotations....

Abstract The non‐linear response of soft hydrated tissues under physiologically relevant levels mechanical loading can be represented by a two‐phase continuum model based on the theory mixtures. governing equations for biphasic tissue, consisting an incompressible solid and incompressible, inviscid fluid, finite deformation are presented element formulation this highly problem is developed. phase assumed to hyperelastic, stress‐strain relations defined in terms free energy function. A...

Two quadrilateral-shaped multilayer plate bending/stretching elements based on the assumed-stress hybrid finite-element model are presented. These may be applied to analysis of fiber composite plates and shells composed an arbitrary number layers mate rial properties direction within each layer. Both incor porate effects transverse shear by including stresses τ xz yz , assuming independent rotations normals midsurface, so that midsurface in un deformed state need not normal after...

Abstract Formulation and applications of the hybrid‐stress finite element model to plane elasticity problems are examined. Conditions for invariance stiffness established two‐dimensional problems, results which easily extended three‐dimensional cases. Next, functional a 3‐D continuum is manipulated into more convenient form in location optimal stress/strain sampling points can be identified. To illustrate these concepts, 4‐ 8‐node isoparametric elements invariant correct rank developed...

A simple axisymmetric finite element model of a human spine segment containing two adjacent vertebrae and the intervening intervertebral disk was constructed. The incorporated four substructures: one to represent each vertebral bodies, annulus fibrosus, nucleus pulposus. semi-analytic technique used maintain computational economies two-dimensional analysis when nonaxisymmetric loads were imposed on model. material represented as layered fiber-reinforced composite. This paper describes...

Abstract Eight‐node hybrid‐stress elements are developed for the analysis of plates ranging from arbitrarily thin to moderately thick. The displacement behaviour is characterized by a transverse and independent cross‐section rotations, which interpolated using 8‐node Serendipity shape functions. All components stress included; alternative differe in form inplane distribution stresses. Elements sought whic stiffiness invariant correct rank, show on signs deterioration thin‐plate limit. A...

Abstract Two 20‐node quadratic displacement three‐dimensional isoparametric elements are developed based on the hybrid‐stress model. The differ in stress interpolation used. In one case, polynomials selected to correspond approximately strain obtained from field, and a 57β field results. other element, complete cubic used which forced satisfy equilibrium equations compatibility equations, 69β Both possess correct rank, but only element is invariant. Results using these two elements,...

Structured Abstract Authors – Nickel J, Spilker R, Iwasaki L, Gonzalez Y, McCall WD, Ohrbach Beatty MW, Marx D Objectives To determine the combined effects 1) of stress‐field aspect ratio and velocity compressive strain 2) joint load, on temporomandibular (TMJ) disc mechanics. Setting Sample Population Fifty‐two subjects (30 ♀; 22 ♂) participated in TMJ load experiments. Material Methods In absence human tissue, pig discs were used to variables surface plowing forces, build a biphasic finite...

This chapter addresses computationally demanding numerical formulations in the biomechanics of soft tissues. The theory mixtures can be used to represent hydrated tissues human musculoskeletal system as a two-phase continuum consisting an incompressible solid phase (collagen and proteoglycan) fluid (interstitial water). We first consider finite deformation which is represented hyperelastic. A element formulation governing nonlinear biphasic equations presented based on mixed-penalty approach...

We have developed an approximate method for simulating the three-dimensional contact of soft biphasic tissues in diarthrodial joints under physiological loading. Input to includes: (i) kinematic information describing vitro joint articulation, measured while cartilage is deformed loads, (ii) geometric properties relaxed (undeformed) layers, obtained analyses this study via stereophotogrammetry, and (iii) material parameters constitutive relations used represent cartilage. Solid models tissue...

Abstract A hybrid‐stress eight‐node isoparametric element is developed for the analysis of thin or thick multilayer fiber‐reinforced composite plates. Transverse shear deformation effects are included by allowing individual layer cross‐section warping laminates, alternatively, laminate non‐normal rotations to moderately laminates. All stress components and interpolated independently within each layer. Interlayer surface traction continuity appropriate upper/lower traction‐free conditions...

Abstract Two alternative numerical methods are presented, based on the assumed‐stress hybrid finite element model and initial‐stress approach, for elastic–plastic small‐deflection analysis of structures under static loading. The use approach results in a set simultaneous linear algebraic incremental equations to be solved at each loading step, with elastic stiffness matrix remaining unchanged throughout process effects plasticity included as equivalent loads. derivation these differs...

Abstract A hybrid‐stress formulation of isoparametric elements for the analysis thin multilayer laminated composite plates is presented. The element displacement behaviour characterized by laminate reference surface inplane and transverse displacements non‐normal cross‐section rotations; as a result, simple C o interpolation rotation can be used, number degrees‐of‐freedom independent layers. All components stress are included related to set parameters, which Attention restricted here...

Abstract Two alternative hybrid‐stress based three‐dimensional elements are presented. These intended for use in the analysis of thick plates which through‐thickness variation displacement and stress may be high order, a single element is to used through thickness plate. For both elements, assumption allows cubic inplane displacements, quadratic transverse displacement. The differ used. In first element, z variations components chosen consistent with strain distribution calculated from...

Abstract Solution of biomechanics problems involving three‐dimensional (3‐D) behaviour soft tissue on geometries representative such in vivo will require the use numerical methods. Toward this end, a pair tetrahedral finite elements has been developed. The equations which are used to model for both those commonly known as linear biphasic equations. This assumes that hydrated is mixture two incompressible, immiscible phases, and employs theory derive governing its mechanical behaviour....

Abstract Hydrated soft tissues of the human musculoskeletal system, such as articular cartilage in diarthrodial joints or annulus fibrosis inter vertebral disk, are accurately represented by a biphasic continuum model consisting an incompressible solid phase (collagen and proteoglycan) incompressible, inviscid fluid (interstitial fluid) derive from theory mixtures. These exhibit viscoelastic‐type response which is caused diffusive drag it flows past phase. In this study automated, adaptive,...