The paper presents a method for the stability analysis of simple one-dimensional structures whose... more The paper presents a method for the stability analysis of simple one-dimensional structures whose strain energy functionals are nonsmooth (due to the polygonal form of the stress-strain diagram) and nonconvex (due to the dissipative characteristics resulting in irreversibility). The analysis is based on the substationarity law of the increment of a modified total nonsmooth nonconvex potential containing equally stored, absorbed or released fractions of energy. The stability problems analyzed include those of the stability of a perfectly rigid-plastic cantilever; a perfectly rigid-locking cantilever; an elastic, perfectly plastic cantilever; an elastic, perfectly plastic, locking cantilever; an elastic-plastic hardening imperfect cantilever; a polygonally inelastic cantilever; a nonlinearly inelastic cantilever; and of a sawtooth-form material behavior.
The goal of this study was to document the effect of aging, sex and disc level on time-dependent ... more The goal of this study was to document the effect of aging, sex and disc level on time-dependent in vivo tensile deformability of human lumbar-lumbosacral motion segments and discs in pure centric tension, when the contracting effect of muscles can be neglected. Elongations of segments L3-L4, L4-L5 and L5-S1 were measured during the usual suspension hydrotraction therapy of patients, by using a subaqual ultrasound measuring method reported in (Kurutz et al., 2002a, 2003). Patients were suspended cervically in lukewarm water for 20 min, loaded by 20-20 N lead weights on ankles. The mean initial elastic elongations (strains) of segments or discs were about 0.8 mm (10%) for patients under 40 years; 0.5 mm (6%) between 40-60 years; and 0.2 mm (3%) over 60 years. The mean final viscoelastic elongations were 1.5 mm (18%) under 40 years; 1.2 mm (15%) between 40-60 years; and 0.6 mm (7%) over 60 years. In the beginning/end of the treatment, patients of extended segments were on average 6/8 years younger than those with unextended ones. Based on the in vivo measured elongations, initial tensile stiffness was obtained in terms of aging, sex and disc level. For the above age-classes, the approximate mean tensile stiffness of less/more degenerated lumbar FSUs or discs were about 600/800, 800/1000 and 1800/2800 N/mm, respectively. A new terminology, the so-called age-sensitivity has been introduced as a value of 0.01-0.04 mm/year elongation capacity decrease per a year of aging, after the age of 35. No significant difference was found between sexes regarding age-dependence in tension.
In vivo creep of human lumbar motion segments and discs subject to pure centric tension is presen... more In vivo creep of human lumbar motion segments and discs subject to pure centric tension is presented, in terms of aging, sex and disc level. Time-related elongations of segments L3-4, L4-5 and L5-S1 were measured during the usual 20 min long traction hydrotherapy of patients, by using a computerized subaqual ultrasound measuring method [Kurutz et al., 2002a. Orvosi Hetilap 143 (13), 673-684; Kurutz et al., 2003. Journal of Bioengineering and Biomechanics 5 (1), 67-92]. Elongation of segments was considered as a change of the distance between two adjacent spinous processes. Based on these experiments, in vivo creep of human lumbar FSUs was investigated in centric tension, in terms of sex, age and disc level. Three-parameter rheological models were used to determine viscoelastic tensile moduli of human lumbar FSUs and discs. From three time-related measured elongation values, in vivo damping constants with creep functions were calculated for each segment, in terms of sex, aging and disc level. It has been demonstrated that initial elastic elongations decrease, concerning stiffness increase with aging. Similarly, tensile creep elongations decrease, damping properties increase with aging. Former observations concerning the difference in deformation propagation of men and women in time, have been verified by means of creep analysis: although males have higher initial elastic deformability, due to a smaller damping of females, the deformation propagation of women overtakes men in creep process. This tendency is more significant with aging. Increasing damping was observed in distal direction, both for males and females.
The elements of a body whose stresses or strains or their combinations are governed by prescribed... more The elements of a body whose stresses or strains or their combinations are governed by prescribed conditions are termed conditional joints. During a loading process, new contacts develop (locking of gaps) or existing connections become ineffective (plastification), causing physical nonlinearity of the body. This ideal elastic-plastic and locking behavior of materials can be described by “polygonal” constitutive laws and related nondifferentiable strain and complementary energy functional. Using convex analysis and the notion of subdifferential, constitutive laws of nondifferentiable but convex energy functionals with corresponding variational principles can be discussed generally. This paper combines conditional joints and the subdifferential connection of mathematics, including elastic, plastic, hardening, locking, and contact behavior of materials.
The paper presents a method for the stability analysis of simple one-dimensional structures whose... more The paper presents a method for the stability analysis of simple one-dimensional structures whose strain energy functionals are nonsmooth (due to the polygonal form of the stress-strain diagram) and nonconvex (due to the dissipative characteristics resulting in irreversibility). The analysis is based on the substationarity law of the increment of a modified total nonsmooth nonconvex potential containing equally stored, absorbed or released fractions of energy. The stability problems analyzed include those of the stability of a perfectly rigid-plastic cantilever; a perfectly rigid-locking cantilever; an elastic, perfectly plastic cantilever; an elastic, perfectly plastic, locking cantilever; an elastic-plastic hardening imperfect cantilever; a polygonally inelastic cantilever; a nonlinearly inelastic cantilever; and of a sawtooth-form material behavior.
The goal of this study was to document the effect of aging, sex and disc level on time-dependent ... more The goal of this study was to document the effect of aging, sex and disc level on time-dependent in vivo tensile deformability of human lumbar-lumbosacral motion segments and discs in pure centric tension, when the contracting effect of muscles can be neglected. Elongations of segments L3-L4, L4-L5 and L5-S1 were measured during the usual suspension hydrotraction therapy of patients, by using a subaqual ultrasound measuring method reported in (Kurutz et al., 2002a, 2003). Patients were suspended cervically in lukewarm water for 20 min, loaded by 20-20 N lead weights on ankles. The mean initial elastic elongations (strains) of segments or discs were about 0.8 mm (10%) for patients under 40 years; 0.5 mm (6%) between 40-60 years; and 0.2 mm (3%) over 60 years. The mean final viscoelastic elongations were 1.5 mm (18%) under 40 years; 1.2 mm (15%) between 40-60 years; and 0.6 mm (7%) over 60 years. In the beginning/end of the treatment, patients of extended segments were on average 6/8 years younger than those with unextended ones. Based on the in vivo measured elongations, initial tensile stiffness was obtained in terms of aging, sex and disc level. For the above age-classes, the approximate mean tensile stiffness of less/more degenerated lumbar FSUs or discs were about 600/800, 800/1000 and 1800/2800 N/mm, respectively. A new terminology, the so-called age-sensitivity has been introduced as a value of 0.01-0.04 mm/year elongation capacity decrease per a year of aging, after the age of 35. No significant difference was found between sexes regarding age-dependence in tension.
In vivo creep of human lumbar motion segments and discs subject to pure centric tension is presen... more In vivo creep of human lumbar motion segments and discs subject to pure centric tension is presented, in terms of aging, sex and disc level. Time-related elongations of segments L3-4, L4-5 and L5-S1 were measured during the usual 20 min long traction hydrotherapy of patients, by using a computerized subaqual ultrasound measuring method [Kurutz et al., 2002a. Orvosi Hetilap 143 (13), 673-684; Kurutz et al., 2003. Journal of Bioengineering and Biomechanics 5 (1), 67-92]. Elongation of segments was considered as a change of the distance between two adjacent spinous processes. Based on these experiments, in vivo creep of human lumbar FSUs was investigated in centric tension, in terms of sex, age and disc level. Three-parameter rheological models were used to determine viscoelastic tensile moduli of human lumbar FSUs and discs. From three time-related measured elongation values, in vivo damping constants with creep functions were calculated for each segment, in terms of sex, aging and disc level. It has been demonstrated that initial elastic elongations decrease, concerning stiffness increase with aging. Similarly, tensile creep elongations decrease, damping properties increase with aging. Former observations concerning the difference in deformation propagation of men and women in time, have been verified by means of creep analysis: although males have higher initial elastic deformability, due to a smaller damping of females, the deformation propagation of women overtakes men in creep process. This tendency is more significant with aging. Increasing damping was observed in distal direction, both for males and females.
The elements of a body whose stresses or strains or their combinations are governed by prescribed... more The elements of a body whose stresses or strains or their combinations are governed by prescribed conditions are termed conditional joints. During a loading process, new contacts develop (locking of gaps) or existing connections become ineffective (plastification), causing physical nonlinearity of the body. This ideal elastic-plastic and locking behavior of materials can be described by “polygonal” constitutive laws and related nondifferentiable strain and complementary energy functional. Using convex analysis and the notion of subdifferential, constitutive laws of nondifferentiable but convex energy functionals with corresponding variational principles can be discussed generally. This paper combines conditional joints and the subdifferential connection of mathematics, including elastic, plastic, hardening, locking, and contact behavior of materials.
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Papers by Marta Kurutz