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[{"id":"1","value":"Non-local effects by homogenization or 3D–1D dimension reduction in elastic materials reinforced by stiff fibers.We first consider an elastic thin heterogeneous cylinder of radius of order ε: the interior of the cylinder is occupied by a stiff material (fiber) that is surrounded by a soft material (matrix). By assuming that the elasticity tensor of the fiber does not scale with ε and that of the matrix scales with ε2, we prove that the one dimensional model is a nonlocal system.We then consider a reference configuration domain filled out by periodically distributed rods similar to those described above. We prove that the homogenized model is a second order nonlocal problem.In particular, we show that the homogenization problem is directly connected to the 3D–1D dimensional reduction problem."}]

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[{"id":"1","value":"non-local effect by homogen or 3d–1d dimens reduct in elast materi reinforc by stiff fiber.we first consid an elast thin heterogen cylind of radius of order ε: the interior of the cylind is occupi by a stiff materi (fiber) that is surround by a soft materi (matrix). by assum that the elast tensor of the fiber doe not scale with ε and that of the matrix scale with ε2, we prove that the one dimension model is a nonloc system.we then consid a refer configur domain fill out by period distribut rod similar to those describ abov. we prove that the homogen model is a second order nonloc problem.in particular, we show that the homogen problem is direct connect to the 3d–1d dimension reduct problem."}]

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[{"id":"1","value":"le déplac chimiqu de carbon en phas gazeux et en fonction de la concentr dan dix-neuf solv dan le but de sépar le différent term de const dus aux interact"}]

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[{"id":"1","value":"Non-local effects by homogenization or 3D–1D dimension reduction in elastic materials reinforced by stiff fibers.We first consider an elastic thin heterogeneous cylinder of radius of order ε: the interior of the cylinder is occupied by a stiff material (fiber) that is surrounded by a soft material (matrix). By assuming that the elasticity tensor of the fiber does not scale with ε and that of the matrix scales with ε2, we prove that the one dimensional model is a nonlocal system.We then consider a reference configuration domain filled out by periodically distributed rods similar to those described above. We prove that the homogenized model is a second order nonlocal problem.In particular, we show that the homogenization problem is directly connected to the 3D–1D dimensional reduction problem."}]

HTTP 200
[{"id":"1","value":"non - local effect by homogenization or 3d–1d dimension reduction in elastic material reinforce by stiff fiber . we first consider an elastic thin heterogeneous cylinder of radius of order ε : the interior of the cylinder be occupy by a stiff material ( fiber ) that be surround by a soft material ( matrix ) . by assume that the elasticity tensor of the fiber do not scale with ε and that of the matrix scale with ε2 , we prove that the one dimensional model be a nonlocal system . we then consider a reference configuration domain fill out by periodically distribute rod similar to those describe above . we prove that the homogenized model be a second order nonlocal problem . in particular , we show that the homogenization problem be directly connect to the 3d–1d dimensional reduction problem ."}]

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[{"id":"1","value":"le déplacement chimique des carbone en phase gazeux et en fonction de le concentration dans dix-neuf solvant dans le but de séparer le différent terme de constante devoir aux interaction"}]

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[{"id":"1","value":"Non-local effects by homogenization or 3D–1D dimension reduction in elastic materials reinforced by stiff fibers.We first consider an elastic thin heterogeneous cylinder of radius of order ε: the interior of the cylinder is occupied by a stiff material (fiber) that is surrounded by a soft material (matrix). By assuming that the elasticity tensor of the fiber does not scale with ε and that of the matrix scales with ε2, we prove that the one dimensional model is a nonlocal system.We then consider a reference configuration domain filled out by periodically distributed rods similar to those described above. We prove that the homogenized model is a second order nonlocal problem.In particular, we show that the homogenization problem is directly connected to the 3D–1D dimensional reduction problem."}]

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HTTP 200
[{"id":"1","value":"Non-MX_local_effects by MX_homogenization or 3D–1D MX_dimension_reduction in MX_elastic_materials reinforced by stiff MX_fibers .We first consider an elastic thin heterogeneous MX_cylinder of MX_radius of MX_order ε: the interior of the MX_cylinder is occupied by a stiff MX_material (MX_fiber ) that is surrounded by a MX_soft_material (matrix). By assuming that the MX_elasticity tensor of the MX_fiber does not MX_scale with ε and that of the matrix MX_scales with ε2, we prove that the MX_one_dimensional_model is a nonlocal MX_system .We then consider a MX_reference MX_configuration domain MX_filled out by periodically distributed rods similar to those described above. We prove that the homogenized MX_model is a MX_second_order nonlocal MX_problem .In particular, we MX_show that the MX_homogenization MX_problem is directly MX_connected to the 3D–1D dimensional MX_reduction MX_problem ."}]
