Commit 48751791 by Jeremy BLEYER

### Few typos

parent 2c6c68e3
 ... ... @@ -15,8 +15,11 @@ Introduction In this first numerical tour, we will show how to compute a small strain solution for a 2D isotropic linear elastic medium, either in plane stress or in plane strain, in a tradtional displacement-based finite element formulation. The corresponding file can be obtained from :download:2D_elasticity.py. Extension to 3D is straightforward and an example can be found in the :ref:ModalAnalysis example. file can be obtained from :download:2D_elasticity.py. .. seealso:: Extension to 3D is straightforward and an example can be found in the :ref:ModalAnalysis example. We consider here the case of a cantilever beam modeled as a 2D medium of dimensions :math:L\times H. Geometrical parameters and mesh density are first defined ... ...
 ... ... @@ -8,7 +8,7 @@ "\n", "## Introduction\n", "\n", "In this tour will show how to perform periodic homogenization of linear elastic materials. The considered 2D plane strain problem deals with a skewed unit cell of dimensions $1\\times \\sqrt{3}/2$ consisting of circular inclusions (numbered $1$) of radius $R$ with elastic properties $(E_r, \\nu_r)$ and embedded in a matrix material (numbered $0$) of properties $(E_m, \\nu_m)$ following an hexagonal pattern. A classical result of homogenization theory ensures that the resulting overall behavior will be isotropic, a property that will be numerically verified later." "This tour will show how to perform periodic homogenization of linear elastic materials. The considered 2D plane strain problem deals with a skewed unit cell of dimensions $1\\times \\sqrt{3}/2$ consisting of circular inclusions (numbered $1$) of radius $R$ with elastic properties $(E_r, \\nu_r)$ and embedded in a matrix material (numbered $0$) of properties $(E_m, \\nu_m)$ following an hexagonal pattern. A classical result of homogenization theory ensures that the resulting overall behavior will be isotropic, a property that will be numerically verified later." ] }, { ... ... @@ -30,7 +30,7 @@ { "data": { "text/plain": [ "" "" ] }, "execution_count": 1, ... ... @@ -41,7 +41,7 @@ "data": { "image/png": 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"text/plain": [ "" "" ] }, "metadata": {}, ... ... @@ -233,9 +233,12 @@ "Solving Exx case...\n", "Solving Eyy case...\n", "Solving Exy case...\n", "[[65267. 17338. 81.]\n", " [17338. 65451. 79.]\n", " [ 81. 79. 24009.]]\n" "[[65266.54 17337.7 81.36]\n", " [17337.72 65450.73 79.01]\n", " [ 81.36 79.01 24008.79]]\n", "[[65266.54 17337.69 81.35]\n", " [17337.69 65450.73 79. ]\n", " [ 81.35 79. 24008.79]]\n" ] } ], ... ... @@ -259,14 +262,16 @@ " Sigma[k] = assemble(sum([stress2Voigt(sigma(v, i, Eps))[k]*dx(i) for i in range(nphases)]))/vol\n", " Chom[j, :] = Sigma\n", "\n", "print(np.array_str(Chom, precision=0))" "print(np.array_str(Chom, precision=2))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It can first be verified that the obtained macroscopic stiffness is indeed symmetric and that the corresponding behaviour is quasi-isotropic (up to the finite element discretization error). Indeed, if $\\lambda^{hom} = \\mathbb{C}_{xxyy}$ and $\\mu^{hom} = \\mathbb{C}_{xyxy}$ we have that $\\mathbb{C}_{xxxx}\\approx\\mathbb{C}_{yyyy}\\approx \\mathbb{C}_{xxyy}+2\\mathbb{C}_{xyxy} = \\lambda^{hom}+2\\mu^{hom}$." "It can first be verified that the obtained macroscopic stiffness is indeed symmetric and that the corresponding behaviour is quasi-isotropic (up to the finite element discretization error). Indeed, if $\\lambda^{hom} = \\mathbb{C}_{xxyy}$ and $\\mu^{hom} = \\mathbb{C}_{xyxy}$ we have that $\\mathbb{C}_{xxxx}\\approx\\mathbb{C}_{yyyy}\\approx \\mathbb{C}_{xxyy}+2\\mathbb{C}_{xyxy} = \\lambda^{hom}+2\\mu^{hom}$.\n", "\n", "> **Note:** The macroscopic stiffness is not exactly symmetric because we computed it from the average stress which is not stricly verifying local equilibrium on the unit cell due to the FE discretization. A truly symmetric version can be obtained from the computation of the bilinear form for a pair of solutions to the elementary load cases." ] }, { ... ... @@ -324,7 +329,7 @@ { "data": { "text/plain": [ "" "" ] }, "execution_count": 8, ... ... @@ -333,9 +338,9 @@ }, { "data": { "image/png": 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9wrhohqontcxUICg7KdwXs9WBcbefBf8bIQs6OPKYs8MMQ2E+APz5r/1rIx/A\n2cDGlBwRHQC4JcfMfBvAxbHxBcFdAvDS2FjDvcUjzz6bzNHKLG1AEx7FhFxqKLQ0pvS3la+norMy\np5jFGowhOKEJqQyYrBIoKVNR9CWv61jlN7Kk3/Le0hzNOpco5adz18pIq1aDpSk7tbGOBBwAIzhg\ns+bqPoDbxblbkfwyRAIEkFTdg8x8Uw25QESXotl7pWX2EtFlIrpORNd/93d/d1Pv4czhkY89C+pR\nRzA92r4vUU+eRs3KlNtWmqtyXUValyELLqjnV2ZseR9jqJgoS7OqyGocVgQ4kjGR/8qgyUbv+cCR\nmLRZCwSCI7UpTUceC+/SPqy6HrbcplDOexDu9rNhXHMfCYe/cPCXGys+e9ikufrgEe/7EQAfLM5d\nFSIkolsAPgXgUT0gmrZXAeDw8HCFr4uhxBs+/BxQ+rIjYekIY7rURb5QyilLu/IAxVy0lNnhEPxw\nOvKqXhMAOK55SoiH4xza5yaTyfmo5tLYYt2DFRvHUgwyOM5bJfUEcgDF3nFV3aosX4IJihS9d3BF\nTzghs0Xv0Kln9d4BcWxXxl2ictNmaolQr5qfX7DDDO1OJGcdm1RytwCUimsV4ruolR2QKz1mvgHg\nYCqIYTgiODdNy6gqkIsgtwCoj+PiT+rLKOP7/J5VzF8JRowpu9H7y/FUiDaKik7y+1hODoRZFtgH\nBRj7somZKoStgx7EyT/XCjAsK7KXZGJdNF8W6Jc5c2luUCzo78KPmkNy4q4e/vzk888SNklyN9Eg\ntUhSTRDRRSg/Xjx3QEQvN+YpTWHDMfAHPvRceCGVB4sh8jn8DONb/rYQeR1+GmlcgzL0w/hwc2ts\no4QrPT8fN2yvhSEdRZ7XQukYFILTJjlpBZvvB1EtNSq9Vh84PUbSUqZIT4rmBdpslUirRGEFs4L5\n5bhnMoIrsDGSK8kspn3o4MJ+Q40doPbj3QTwvLrvIoCzl6Z9DyEEp0lnSMUYflKaSHL+iyKK51KN\nqZix0Q8n1QwjJEWiAHnsZyCtlrpL9aslypSRNZwYpZ+ulThMxLkrMJaB6Ry4spZWR1k1WY6RIpB3\nMNGmqz4X5vDhB0Mjzp/7up9b/U2fEWw6heSpmOt2A4HAnlLXrgC4huhHU9ABBzDzbSK6SUSX46lH\ninkMx8AbfzL44Sgm3bJTCswNgki+gzJOW3npPAD0BO646fynBWXVCtQrn5l6Bhd+uoToQ0t8MJUO\nku4R39wbOThfAAAgAElEQVSg7KhTD+Lc4SgVCENlQ7jM0W9G4r/Tvju1jNBJGOji+xTfXDsYQFmz\nSw0X1+KZcK4bUkBEwekKCCCWh0ldq6uVnWEA8VqN908nDg8P+fr16ye9jFOPL39/UHBN57wQnJCc\nL3irQS7kw1zNcS3SIq7HMjJylbWk+xVJpjGkjnUQooyOOqRAQ+I1x9WaKI0RZo/j43HX+ey5Mq6L\nCkvn0zniFIAQ4iPijNwccbpXrmuS0tfOdX0VaMhIEIxzXfhf6q+85QWcJRDRy8x8uGyc1a6eEQjB\nAbnpKAFH9Ag1q9Kc0tXRSopKKt2D4ZwWKLr6KM0XU0GoIBgAoX+cnHNhLSMbyGfI1qdTTSRBV13P\nBFw1EXJ5VozXSi79xmBejm1w3cc62FK9eaYQhcZQ+rWAG/xq3iWi89H/6JnSdb0Bjhz/tX+9NJAM\nAqtdPSMok32FfMaiq+m6CiqILy2ZsCqoUD7LlVFWHUjgeKIo0xIk83XM96bNXDnWSf46MFFiYr4p\n6DZNVbaLjkBnCm24V3LmBGm7QkWgZd1ruU1h6CtX586N1bQaAozkzgDe9BPPNb/IiZy4+K2ur5q0\ni4LQsvOM+hk6HWNZRYLUvBbzjgYg4nWmketFpJbVT3MqIdUyMZfr/Vt137kxSLCitbmNoFWsr6Hv\ne/Gt/8Xk2LMOI7kdx5ve91xOMgKlwlbKZSvubSpC/SPPEBQBjfyaOlBz15Kp5RjM700qkVYkZygz\ntPqMcqWZWqir5UuPuWxrw6jadORVEoNbLvAW2Yn6k58Si9gIwAhuOcwnt8P4ih97LvtvTNJFWBz7\nhSM/KKP8nKCKiqrAQpMgxc/WCBaUsYnkqysDE6WfTAcWWkpJ+tN5FdWl4ri6V4d2i4XpaPISxtR5\nc5qwSr+cmKQUCVD8b8l8Jcae6+sHyFtU8/+Nt/6FyTUZAkzJ7Si+8r3PZb4xraC0f00gvreElukq\nY1rmqB7L42ZuljaSTrbfQ/L9pTU22jTp/VN1EKKct9wPIq2bRwmMRRUiN1V1Tl0r+NBqr6TbpSfC\nW1IVUVU6FPlzhtVgSm6XUUimJum0VNiIj053Epe4QXZ5SuwoVUYxkitzpkBDVIUpIuqK+4GQk6eP\nx/6bjoECKupiV22KqaEDCACyQv5CbAJA6gA89jwh2q7R8bjlFywrIGbk8bf/jZ9e702cYZiS20F8\n5XulZAupvrRSYBGillLlg/jYxghLVSvowMSYTy8Lbox1EJZzqoJCfmdzu2Ft1fq01Sm/CxJJhNPY\np0G2I9Svw8VxP1p6LFMKOLT2kZVzrc1udGmYjGkFOPQYI7j1YEpuByEkJF1DuFB04Fx9iO8skQvC\nPTqDgVWCrlZeet5U0VAqPEksFkW0Sg6cR+UHZA4mq/a3pffHmP4vm3jIfZMgQ3Ia5iZrVt1QflbZ\ntbCAUnuFDadddg9F/xvQTiLWc865Q+d80zf3yW/88xNv0tCCkdyO4Q/+8HOJVKhHHWVsp6bVfrXi\nsiYdKslPm4OFj45d47wipOT20uuSbGNFpHlAIr8eXlIuo1x+f5qHAUIxf7w/9QUugy5So+ram9eU\nJmvLDG0h7OPqsgoHYDzIYX64o8HM1R3CH3r3c7mp1+qk2zArVx1XmqiAIq9GACLN1cJYUMIvyf2o\n0koUAao9VqvnxCinLtcqKx3K7r8AqkaaKdWEBzJK3BxN3ZKMZGNqYMiP69kps3VoseTVHK/2uQa5\n9s3PwbA+jOR2BG/+oecG/1UWkYwv5ByF6Kr+AQZSHN2RqzV34Ysj8e0pwivHTImRjKziWpu7dxVI\nnEjKtmxVUrTIXIiuVKCNJGLv831XW2NkXO8pJQtPbVdS+vB0+smMQmrJwjsjuGPASG7X0CACt1AB\ngoKE0j2i3gpnf5a8W74WIvOYFF8aZdAgHTeCCRWBTilGAKPlXJNlG62ognqpUlRaZqTezSs9rqiC\nGMPYHq2GzcJIbgfwVe/K/5fXEc+sBrVRYwpunJfo6UhEtkSLnMaeVRFla45lSb+rIKuEGEvEKw51\nW6hWBcQIWmauRFV771KOnCg8gezX0DNlm9uU1//ut3xstYUYmjCS23J81buUmapVWKnUInSibpXn\nNqLIUvffBiHK/NUzgbZfT+XZteYJ97WjI02u0vMRq5IyypVdIiJ1rZinlQeX1KoyO6fqXFtqT/xw\nZVNMgSQHi29Oz/H3v/UjzecYVoeR3Bbjq//0c1nLIwnSMXIfW7LWxvx1UOSlFRahqWaqTiQofi/z\nnQmWBSxiQi8wBFQB5EpPro+ov7KyojYjY26LrINyEqPUqklMVjW3Vm7xt1eVDWGMehLlRfnMYUcu\nnUsnqo+ZjOA2BCO5XQLnZKeVWZmUm9JLhAiLlKymaiuCACsV9euC/ZE1Z88cI8gsIEJpfKbUhFwm\nnpcIpWyeCaRNqocTdWCgJK3yPbSWrzedBoBFr6KpGH6A6f1UDUeDkdyW4qv/dPTDlQpMdwUh9RqK\n/Hj4nX5QK7uWGszIRhKIVeAgCxBolGSrMeF3y1xrrb9W9V6SDd5SoMrHRssiqowqIRgj6qyxlKwC\novmeiDOfXTlv7x3+4WNXRu83rAcjuS3E1/zAc1kgoSyurwrt1c9U8XxrLkCNLeaqyrS4vm+U9BrI\nXGU6n02O9WumupIDaJqyo3M0Bma+Nj1VJLrBL1esvZEbp++VEq4WAZY+vn/0eLkNseE4MJLbMnzt\n9z+XkZRTEdAsqqlUnUbGG0qFVRwkpFj63lCTZL5dYP3M5E8rf4ox2VyM0DlEqa4s2tuMkBTHjrOd\nxIJCm7hnjUiubHCTyIlrsmodL5vTCG7zMJLbUpAH3ByJiJppHIy2z02RjDZlowt+Wu2NkEKm9rwi\nR2C5yekb70EW03pm9WYLBVjM0bxWbl9Yzlcps/BcvavXmNlatlpipqrUq6UId2BPqVMJI7ktwsHT\nzw1qrfCrpdfSdUT9RkFACaWPri/GKgyKKPxohZUdpxvG50mvNZEycjXHyCOmek4AYBo1uVdCFmQY\nCI/UDlt6/czBZ5dFXidUYEl0Oj9urDb1V574qaO8E8MSGMltCQ6eVgm/yWQbTtGYGkKuzDJ1x8jN\nwxKlP02Nr5J9y+dyPqYiQX2+BBXzMQZFRvVNTKjaKgEYalll2lFrsbbXS1M03c/5Hq3ZGkdIV+aS\nUq8WbnzbB8YWZzgmjOS2AId/8tnhQH+ZVF1pE8WXsBVUYEKm7sZcXc3zBamWJm62nSHLRCNrXfKX\nONS1Dg/S7ZvK6HLT1K3ewPQzqzVkpqWouvZ8RByWpIv948uyusEI7t7CSO6UQwiOGHA9p5/Kx6ZT\nOYqUj1J9aTN2zJ9XIvsul+SpiDcLFIypQ6/GAs2/Qi7VnEbZAl0CCyWJkuoKXLJx9abiqUL9tVD6\n66oKiBiEoGrM9LyGewMjuVOOIVct/4YQR7IrTMgUZCginrrgvlXSVUYwqzQSGSPzFf607LfcwCPP\nKyOpOmFYSFJ8Y4x87wYho4mggX6d8uegggVTeXmrOPpaZWHAoCZXUIiSSvKP/633Lx9sOBY2SnJE\ntE9EzxDRxfj7wsTYK0TERPR5IrpGRPtHmWeX8XXfF1VcWfCuRUkkvzLVI9sisLiPqSC9lj+vMWf5\nbLm/PC6VXjOfbQzJFA9EkvHJiE+vip5WBF4HFprjgMoPN4oiD67yzyFvW+6KxpieCf/rH/uzSx5i\n2AQ23Rn4RWZ+FACI6DqAFwA8OTL2FR5PHFpnnp3E1/+JZwG1MbomOnZRMMSqBkIwy9jJNxm5WVhu\nCBOHuR7NlA7SZBg3nUm3tay5SJrcDfdVQzzq1ugj//rlmqgf5gYDPGswkN6CUB3roARpshz5773q\n+sukIq4DmZVBDL3ZjY7Mkgu+ubID8P/27T/RXoBh49iYkiOiAwC35JiZbwO4eFLz7AKa3X2BPHIp\nXzoOJix5rk1bGTuxEcxUKVbTtNV+tdLpD3Uuzq2DEHq+tA4hiZLgtPlHADqurwODn04HB8qghD5Z\nfq5Tyi3en6u1qDRVvlvWcqmlOuN1I7j7i02aq/sAbhfnbkXSauECEV2KJukVZZKuO8/O4S3vfHbI\ncyt20UrBgpaJmfnWOf3I/a3+cFkQgnNS1QSTvUYxJp4sa2LlfGlO6utVlxDOn5XeV4sY9XteNWku\nFeqi/iyOlXjXmIfyIAUzGcGdADZprj645virUaWBiG4B+BSAR1edh4guA7gMAA899NCajz69eMs7\nn63OpY4hkfAqtVOmTUCNK80qH7/bK6RYiErL9klNEyGRTxZYEPJyao6JuTPyimapfn+1iizCrq33\nkfndOLVLqu7X0ZQ100laSLuBITdb5fVmKNSwLjap5G4BKAMEo4QlBBdf3wBwENXcSvMw81VmPmTm\nw9e+9rVHX/UpRVVaVZBHGufbrwUcv3XEHNUa10GM4hlNjF1jRVhyasTPV3YsaRGUTvlg7WdLkUt1\nrhWUILWmYm4Ate9Ov4+SUVcKlFCVQjLmav70d/z4ChMaNo1NktxNtMnoRnmOiA6I6OXG2NvrzLNr\n+MPf/TG4BcMtlF9N/GyRGFxfE2AiD6qvSV6dEJygFY3N5kPtL5vK6s/m1ceKQFPyLqG5VSGrQEsz\nYlqYsBmXOMQecVwr2sk11zlvo9BE3phzal8HI7iTw8ZIriShmBLykj5WfrebAJ5X1y4C+MQq8+wq\n3vqOjw01p8n/NvjTNEhIS/vpeIJgUJ7PiTPDRABCormMfIzuXScR2cqvJuMKIs3WyQPpkRTQF+Qm\nKSOZWhRiE8e/UoNQJqQct99ceV6NSEW1aBNdo9he+/c+8+/82PjkhnuOTaeQPEVEzwC4AeAAwFPq\n2hUA1xB9cUR0M/rVAOCRYuzUPDuHt77jY8FXpv1TC+QpJP3wpWGHoPSIwnkqeqvJd1LSNlh9PxMZ\naeZA5mPLvsyaZEjNpW93+XPTuZaPsHid0tKq44GQ0jUVWW0mNJdoRUiyz2lNL1kVqBjm1vWs0oaJ\nwPjMJSO4k8ZGSS6qMFFiLxXXniyOR9XZ1Dy7CCEq+eKm757OD9PjI3lRz9mu9ule5auSoEWzUW3h\nx0pBBAyvoY6bqSStHLyC9FIKSYOUiAEf/wonidHxQGw0nAu/G++tCD6k95nONd4LYa0Iawo0FMEQ\nOW8EdzpgZV0njD9y6aPZMXkGmDOSauXLrbS/QgFiPV/jy8zDONcPAYUyNaSqXfX5mDI/TRNxy6dX\nlpAlOAxlXWOlVOVb0E0BCEOFQ3XreiouM1kjyk1tmi2YDCeOTZurhjXwDd/x0fBF9oD+0iVzFIi2\nj1wIyk6U3EAe+ReZHWU+MV3GJcfLoMVJlvBbfNczvutkPW0FOvr8QsFVfeRGJ0Jm0nPXIm4lT7Pn\nFlGMRurHsrQSnTJS4jee/NHpmw33DabkTgjf8B0fjdUJ9bVmpQO3i/HdYkQJFd/hcv7wux3YaJml\nmXorr5MiwnicghFleog6pwMIVSpIqzOJlGo5Xk6EOtiQHTfWXz6n8b/ApBkbr8kYI7jTBSO5E4J0\nEHF9XopVRzs5C9tpknMLPW4wG0MrJkVgNFyrTU9O/rdmaZeGpH+MkERWalbM0yyyV+eydBWlHFM9\nbCK4YpyUl3WM0p5uFc2Pvq+py/ofRbv6qlQVwm9+pxHcaYOR3AngG789bhocv8ikCEoTiNM7cukv\n1xL1l9xHI11/624j+Ze4TECulFo5pyYoOeVQN/SkSFpjhOO4eKMYmmSWkFMdp6AEGn6z0fuWnVPn\nl21AI3jlHe9daZzh/sJI7j7jm/7ohytnfXL4S0NMUXYsai9e9+0C/JVR+tjUuWzYSBS0OZ2s3bfv\nSwNL1dOIdFKfy8TmfHohHdeEJnPpoMMo2tJ11QirNcHcDhjJ3Ud807dFgusZ8AxEkxUoTMkRpTaa\nqKvP5xZbCjqMdTMJYwamyCy+0p8GjO5Oz91g7mqTUkc7Zf48V22YO+tUos3S8j4gBBxKFlwlYLFO\n5LNJsupleh9kKu4Uw0juPqLZPUP5z+R8Vr5VpJQAQlxR6bVaK+m9WKcCBvq6Jkrl96vqUCUSSvV0\nElgou6OUhDW2nhRQ0AGKkgAdqr/alQIRafDIApbcztx4wxGvfNefWe3ZhhOBkdx9wje//QrID3Wk\nghQxFWVXEN5AepyrrAKB9ALBNfc2LccrZaRrWlmSeYGYyoJkXmfrak6aH1brKO8rkoWp0RNukKSN\n57iiiF8uHzNPbZXoquXCbQ+M5O4D/s3HrxSBg7putNV+HFAkqCHkV+zbUN1bqLyUdiIpJ8U9iZQm\noqRQ9avpUpGHV1U66GdQPgYYKh4AhC7Es3y8VEJkeXC6DnXUF6iZT58fGb8Mjc/DVNzph5HcfYSQ\njhO1xoPJmcAA+oaqU+OzOZvkhqW+p1aLojGyBAqyEkWpHpNapascuGx9I+vJAxCc+Rir5N4y767w\n9wGFwmp+OHqO9putVVt7nBHcdsBI7h7jW771Q5WiYiK4hc8CAuJjGwMtVJDCqy4iaR+HfEd5nSA8\nRGuRqqPSfa3KBIm+Fn6xdE391s0vs/QQ9ZdF+rpKb9FEy47TdSnlygIoySxl1RNuDUm2bGiKytbu\ngqykS973UdWg4b7DSO4e4lu/+aeGJF9RZh5Dom5MxBVIoCEjRc/hB4HohsFVJuryBTVUEI2YrojK\nLNWv6u7DSwIIaT79g/x13ipp8MdxIkOux+nSNKlnLR+7zF9YBR7yOVbNibv575qK2xYYyd0jfOs3\n/1R6TXORTfW4qZy3VtrH4E/LFUciSEUkrXKvpvgR4tEqb8Q/qNfFBUfIfdxScSXBTpnHLSJ0AOIu\nXSvyUPHQ0UHZUWWaJuU2zGUEt10wkrtHcKK6pOa0H/xv5HlQdsjVmyv8cMu6jdR1pjxuxXFjfKkk\nNXc6RWiuvrd8TorMFg76zCQuiDELOmhfoh8GpS0IPdXNMsu3Q+paWT1xXLQCMYZTDyO5e4DHvuEn\nASBvY47CFG2YscO4QZmlYw/AUWqqoa9rZGpLfyllrwdNJEphZT5Dh8k0FDFhGQA8cr9c4b8Lfe+W\nu89Sfpy6Nz1L0I10Mx5dZD5XY9AKE+W4+d2m4rYNRnIbxmN/5ANtx1Dr3IipKpvODL4sRZQ8kB5P\nmHxV/SoUAbZIZ0rpjKRfEDD0fNNpJCrXTtaSVTUUfrqq+B6An6kE6KJN1BCwWMMndxRUbk9LjttG\nGMltEI+99QPDgU73UNuuV2khUdUNgYY4tLyXuSLFoNbqb3VtkhbO9UbqRZhPq04V2Wx9t2mYJ/ut\nI6ZCSGPpI7L5jEzJ4Zg7ZXITB19cx+lwJSXXiJIeF5/9nh85/iSG+w4juXsECTaIOUo6qloSndyz\niJtBF0SXfakjKVb+MXH6l+qjG8zkMlhRzZ0mw2AuugaxjAkaMVtF2bUCCGpsMHMpRFZ1E1BNcJPP\nW5G5WikwjYmroIP533YCRnIbwtu+/s+BvM97w/U+/IgPrvDPOZ0SUib6tlosjZBjWdu67Ltf7q4V\nXuj58rnK9JG0QfWSbsO+G8a35p4ykbmxf0PaqYswGnRollvx9LNWgam47YWR3Abw+KPvGxRYrFYA\nEI7L6KiYpwvO25wDzW8oNVQboFRh2eV3UqGppFb9uwUeUWCcb4qT+ciOVN8azNMyjQVA+Ossduga\nGgrUgYWV/HE8csANn1s8NILbbhjJHROPf+37MvOSvJipeZJaUHntfJAs+TdGTYU0mfJKhjHyKCse\ngDx1g91AcFUDzFa+mzxLk93Is6tW5zRCkNl6lVobI9tGe6llvv8m0Y2aq8vPG8FtP4zkjoHHv/Z9\nw8HCh29Yr4hOfGqLyBpekR1FH5wyQamPcxBSj7ehOiKOUWSoyWTwf5GaD4PvTfnkdHulstdclj5S\nkpUbfHQaVfJvvLd8LZHVKslXntUVUdZZToKTTTllmok8wNGbWrBA6s7ASO6IePvX/HjWogjAYKZK\n3pv3QdExgxY+H6/8RHUhviKzqncaDcQl9azxm52RAHNWK1r2o2spLU2QqS+cL0zIEo3zVfJveQsj\nj6C20Gp3tMQEHvXHHQVsKm5XYCR3TFDfp59JMIO7NlPo82WCL7e+uTr6ScgUmpi+7ChGdDH4u7Ln\n6GcgP6/nLgMH+vmS8wbkyrJh5o6Zr9L/ThMjeWS+uPaNdaR4k/jsHzeC2xUYyR0Bb3/ze4G+Dz8K\n5Au1JoGH0mwVRDJobT8I5uFfJ6aGJMe7Iq1ASkUe3IRZp/u5tfq9NRFJrYrgFlHLVMyvP5aG768s\nrm+Wrq3a6VfmReGPW6lu1XAWsFGSI6J9InqGiC7G3xcmxh4Q0eU47kUi2lfXrhARE9HnieiavnbS\nePub3zvkvsV6VPHFAQgmKnP6SZDgxMIH39yiHYjIfWoMtxD/XjznedzMlfuSfw55gq66NvjqItnF\nTayrPDsaxmXnoVRb+R66nDyXma/SdSSte6/9vu5ZwUExr6m43cJs+ZC18CIzPwoARHQdwAsAniwH\nRfI7ZOar8fgigGsAHolDXuFTWkNDCz/i/EEIPgAA90DXBV8cAPRCIgw4B2IeAgvMiKNAPasoaCQd\nV6g0fewo3hOvdZQ1q0xUoRVXob7CnPLm4o82PQuCnPTPpYHqWSUSAU/Iq/JSY81j19Ou9kuL88sQ\ns9x/Kv/sDMfAxpQcER0AuCXHzHwbwMWR4fsA3qOOrwPYn1J+pwFPvPE9QO+BRZ8UHPVcm6FEgC/I\nsJn1P3wzsyjrpENeq0MGz0ipvHyo3ny6JEtgCVkViq/ymSmEQII8dFCHle8Qg8pL/eOyNJc4vtUR\neGrxVUR1GcGVeSnDy8+984dbNxi2GJs0V/cB3C7O3Yrkl4GZbwB4TJ06BHA7EiMAXCCiS9HsvXIa\nyO+JN74nP9H7gfA8p9SQygT1Pg8e+JAmUtWmRkjQoIRWUCnqOStVnkwSzvtCp1c+OB1YmFJ35Vqq\niG9OfL5rEGhD3aVqCuJ8zhH2XacR8DQU+6q1GcHtJjZprj64zmBmvqkOnwbwlDq+KoRHRLcAfArA\no/p+IroM4DIAPPTQQ0dZ78p44g3vBpwLBOXcQEzNyCclZScbsoQ0EjdEN8WmSkSH/DvXBxXIHSVz\ntox6MiFUTcQ5k5XZ8KsJJHghr/Xv9GzZhlDGcizPkutiBqsARrX+xhrIK1+drEH/9ZUmabZYVIGP\nyV5y+t5sQH1KYAS3u9gkyd0CUCqupcQXyerjzPwJOacUHZj5RgxSXCjOXwVwFQAODw/vWfzsif0f\nArxsYU9D/amjmuR8ZAV9rWegi+Zrp20zDo0htd8rlV1RU80BuaJLpFkRCsPPaCAshC0NvfjsGn41\n8uE6oIiIhvvhkXQ/xVgLSsUm1yOhgYdzzb0korIsc/jSQ44DJnzue5853hyGncAmSe4mGqQWTdMm\nYsDhJjO/pM4dAHhBAhhqntIUvud44qH/MBCWgAo7zfuB9Pbyj5KJhogrEAkyvnYAu2EurdzSOa9U\nWlR8vkjWTc9qBSc4JxbZkFqXd1XrzeYYxhDnpm96V1T89khVEWOOEDFr/Tn5z2LgMy++uCUE91t/\n8t2T1w0GjY2RXFRc6TimfbxUHN9SZuhBPL4Rjy9FNXcTwPPqvosAkso7MfjoQBKiWywA15InGBRZ\nynMLUdXsXDlWDpNZN5xnotrUEh6gxrnyvD7NscC+5Z8rxqWecAVZjkK3SyqTfJUSbNXC6nk/d9lI\nzLA5bDqF5CkiegbADQAHyP1sVxDSRK5GwnsZABQx3gTwCWa+TUQ3oxkLhLQSPc99wRNf+oPBvOyV\nR33RA+iBrmAqRyExWIgsBha0WgOQp4tEdSbHVWVD9NuNVUmEOYSwOJElx+NAMoooHTXN1HQNQ5R0\nzKem78/MT6Uayec+vGGCYc3sOJE59YDfC9c+9/0/NPpeDYajYqMkF1WZmKcvFdeeVK9vYsINrM3X\nk8ATX/qD4YUQV6pAcIVfDgB7APFbLYGERQ/MOtDCg2cF0fXRDJUgBnKCKzdxDjc1FinBB9/2zeUE\nN5i/WqFpv77u4Jsl8o40vJQbCTUhuqji/FRgAQhdVvaAz/7gf9x4iMGwGWxayW09nvjX/tQQ+aSc\njDKyA4D5HJh1gQzJhQCDoPeD4ovzsAQePIaxWvUxJ3OYGCEQ4AFCnlYSfGRKuaF24Jf+srFARphv\nUJhSliUEFVJVlnxoRUZGlWKirmmV98oP/UdLJjYYjg8jOYUnXvvvx1cxQqqJDqijo8BgznZA8KLr\n4ABlY6nvA9EJMWVjw3hRekFp5SYtxQqIqqqBRZrlz01RzrRmVD68ZtRT7nU5YWm1l+XctfyFjdQS\nwW++28jNcP9gJBfx9gefAmkS85xHVoHcfG2h90HZAXV6CTCUdIEqfx0ApE4lyseWXdYE14f1kTI9\ngwIbCM7PUBGNVnxDf7dhnqZ5WpIlMGxLKKkiQEaakiAsPr5P/9i7GhMbDPceRnKCvs8rGR0BfTif\nkR8wKLtZ/PjEjC2DBL0HKN5bkIeuX83OS/mrqkcN5+v0j7E60tZuXcTtgEBmBhfPDusciKoZUFD3\nVkTojNwMJw8jOQBv/5e/L7zQlQwtJaehKyCAIRihy7VmBcH1fTJ562gq0vO4Yc5mEdDWshr96kri\nKe/VycLVdJro+oHoymtpvIqu/pMPGLEZTg/OPMklgtNI5mgknfkCJMm+ouISualKBukvJwqPKHfq\nq5QQ6nvwnjJtCYmoOFZMaPWmm2O2HF2Vr07nohUEmMiuSggeCRq0qhKKIIcRm+G04kyTXEVwWpkB\n2RaCrM1WokyVVZAIbEwlSfe0oDJQErKC/vh7wlQE2mkfZcH+VCKvLv6vkoSVX09vYfjrHzFiM5x+\nnGmSywIIQixaqWUBBgpENytbe8T7StNWF+GX5WACqQLgyCJEbd/WTAUGOhqetYI/LlUglPNWfrv6\ndfQ/3igAAAlxSURBVLmOX3vWSM2wfTizJPf23/O9+Ymys0hllhYpI0I0zFHVxbR9Umkko7sdx2sp\nuFDaiDycd/k9YWPnoUmAkJ/r68DAYLLmeXZpk+bCBxieoVRdD/zqf2bEZthunFmSY9k2sJXKsQpa\n+XCN66kjMACezfJE4Ab8bCBGYg5dhacCIBGSRqLTQzLTszQ3ZX4g+AxVOyMjNsMu4UyS3OP/0p9I\nryuym1J0RGCO4+EGv5xzg8Kb5fMQM9gT0NEQbMhqTd1o0iwAeFUWJi2Uwnrk/tx0lS0EgSH9pJlq\noo5vPG+kZthdnDmS0wSnwd7nqk4n5GYEOKGqxOzUJV2C2FeurGfN8uWYQax7vsn5IlqqVZkU8hc+\ntaHjbktlAtd/xqoODGcDZ47kprr6VkTXghBYKuuKaSPSsUQrOaKidKuudKj7uA3ENhZRHfrMyRzR\nJzejOvAQj/+XnzdSM5xNnCmSe/w1/97SMU2ia6SWMFSktRVhjekltOjBDzQistrvhmC2hn1Ulfry\nALmhY2/KpwMGNaeCB1kumwP+p79q3T0MhjNDco9/wTvDCyfVDOriWARUm6ya6HRkVZd2oUF2QDBV\nHWJ01IPhALUJTTO6qqKvWetyN7RL8sVGNr/8143UDIYSZ4bkElSC70bm6ntgb284NxEJTabqzAUz\ntbXjVqHQwrmGaR39cf/j37QuugbDFM4EyT1+/nvCi7Gk3KLrx6hvTtRcK7AAhPOyabITNTYosmSa\nir9O/HexTjavK2X48hnRbP17f9uIzWBYFTtPcm87992gZF7GNA9yuaKT3nFAbbqWbY9SbznXVm3K\nlOVU7wpgr44ipEhrvMcthhSRUOUQIq9/9xffU91rMBhWw86T3EbQ6u9WBh+A6TrVmFOXmZ5jScFE\n+KVrtg+owbAJ7DTJve3cdwMA2POg5lqQtkqrmKxACkAkgpvPgXPngrnae+CBc+G694MfTtJJZEpd\niRBV5LV/+KPrvkWDwbAEO01ya8HHppe6GkGqIXS3EZUYzHfnoC84P1zTPjTn6iiuqiUVGLEZDPcW\nO0tyb9v7rvAiBhsyNad9cwLtl1OYypmjrgPuzoHzD+T39kVeHZCpxL/z8p9d/w0ZDIYjYSdJLhHc\nMrAfj7imIdFsLYMPQmKdC+aqpJF0HdLuXOeG1JJf+MfvX+ctGAyGDWEnSS6DUm0cI6pN/9xIu/Os\ncL8kOjFPZ7Nm3zha9Pjkpz907LdgMBiOjp0juce6dwAYIbISpbkKjFc/lHAOvFjk0dU4xyd/48Or\nzWEwGO45dorkhOBWRpk3V+TLLYuulvjkb35kvecbDIZ7jp0iOY2ptJHsmlZzhcm6tPIhmr+f/O3/\ndGPrNhgMm8VGSY6I9gFcAnADwAGAq8x8e92x68wjeMw9GSceSGlpflyJxtgpovuF/+tnV5/bYDCc\nCDat5F5k5kcBgIiuA3gBwJNHGLvOPJuHTvf4f37+vj3WYDBsHhsjOSI6AHBLjpn5NhFdXHfsOvMI\nPvPyTbyFvizesDwthBzh79z5K8veksFg2AFsUsntAyhNyltEdMDMN1Ydu+o8RHQZwGUAOI8vBABc\n8y8e7x0YDIadwxG3qmriwQ2NXWkeZr7KzIfMfPgHH/0KIziDwdDEJknuFoALxbkxwpoau848BoPB\nMIlNmqs30SCjhqk6OZaC03/VeQwGg2ESG1NyJQnFNJCX9DERXVg2dtk8BoPBsA42nULyFBE9gyG/\n7Sl17QqAawCurjB26prBYDCsDOJGe6Ftw+HhIV+/fv2kl2EwGO4jiOhlZj5cNm6TgQeDwWA4dTCS\nMxgMOw0jOYPBsNMwkjMYDDsNIzmDwbDTMJIzGAw7DSM5g8Gw0zCSMxgMOw0jOYPBsNMwkjMYDDsN\nIzmDwbDTMJIzGAw7DSM5g8Gw0zCSMxgMOw0jOYPBsNMwkjMYDDsNIzmDwbDTMJIzGAw7DSM5g8Gw\n0zCSMxgMOw0jOYPBsNMwkjMYDDsNIzmDwbDTMJIzGAw7DSM5g8Gw0zCSMxgMOw0jOYPBsNPYGMkR\n0T4RPUNEF+PvCxNjD4jochz3IhHtq2tXiIiJ6PNEdE1fMxgMhnUx2+BcLzLzowBARNcBvADgyXJQ\nJL9DZr4ajy8CuAbgkTjkFWamDa7LYDCcYWyE5IjoAMAtOWbm25G8WtgH8B4AV+PxdQD7RHSBmW+v\n8czLAC7Hw1eJ6NfXX/mZwr8K4F+c9CJOMezzWY7T9hm9fpVBm1Jy+wBKgrpFRAfMfEOfZOYbRPSY\nOnUI4LYiuAtEdCnO9xiAD7bILypBUYPXmflwQ+9lJ2Gf0TTs81mObf2MNkVyD64zmJlvqsOnATyl\njq8KqRHRLQCfAvDosVdoMBjOJCZJLpqEj0wMucbMLyGYqmWgYSnxxfk/zsyfkHNatUXVd7CuKWsw\nGAyCSZKT4MAKuIkGqZWmqkb02d2MJCnnDgC8IAEMNc8yglt1nWcZ9hlNwz6f5djKz2gjKSQlmcW0\nD01e+zqlRAIVQnDRBwcEsnxejbsIIKm8iedv5Yd/P2Gf0TTs81mObf2MiJk3M1EgrosAbgA4QO5b\nexHBtL0aCfCV4vabzPxIHHsRIZABBFO5GXgwGAyGVbAxkjMYDIbTCCvrMpwpENG1FcasXL2za1jx\n89mqqqRNVjzcU8QP8hIa5vBxxu4K1vx8rgB4BiEX8TqAp4u0np2DcoOMJalrrFS9s0tY8/PZqqqk\nrTFXiehl9Yd3ASEK2/zDW2fsrmDNz+fytjqRjwsi4qkvaPQtX2Hmx9S5zzPzF9+XBZ4wln0+ccxW\n/f1shbnaKhvDyP8464zdFZzF93wPMVq9cxKLOaW4QESXojl/5bSb81tBcljvD+8s/pGu+5636o/0\nPmOt6p0ziqvM/ImYAvZxhKqkU4tt8cmt84d3Fv9I133PVjo3jiNV75wlbFtV0rYouXX+8M7iH+la\n77n8IwVwYGouYe3qnbOESGgvl+dPK8EB20Ny6/zhncU/0pXf8zb+kd5r6IqcZdU7ZxFFxdKRqpJO\nEltBcuuUjZ3FP9I1y+q27o90E4jk/kx8faXod3gFwHeq46ckTw4hLUd3ydlJrPr5xP8Mb8bO3pcR\n2qGd6s9nm1JIViobWzZ2V7Hm52Olc4Yzg60hOYPBYDgKtsJcNRgMhqPCSM5gMOw0jOQMBsNOw0jO\nYDDsNIzkDAbDTsNIzmAw7DSM5AwGw07DSM5gMOw0/n+byNOviH3a6QAAAABJRU5ErkJggg==\n", 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Mw2iGiiQKR4qAczSwAYoJsHGHf4CEUGZIOG4S/zqD7LJ2b5FyrDqW+2hyy9w3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"text/plain": [ "" "" ] }, "metadata": {}, ... ... @@ -346,6 +351,13 @@ "# plotting deformed unit cell with total displacement u = Eps*y + v\n", "plot(0.5*(dot(Eps, Expression((\"x[0]\",\"x[1]\"), degree=1))+v), mode=\"displacement\", title=case)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { ... ...
 ... ... @@ -8,7 +8,7 @@ "\n", "## Introduction\n", "\n", "In this tour will show how to perform periodic homogenization of linear elastic materials. The considered 2D plane strain problem deals with a skewed unit cell of dimensions $1\\times \\sqrt{3}/2$ consisting of circular inclusions (numbered $1$) of radius $R$ with elastic properties $(E_r, \\nu_r)$ and embedded in a matrix material (numbered $0$) of properties $(E_m, \\nu_m)$ following an hexagonal pattern. A classical result of homogenization theory ensures that the resulting overall behavior will be isotropic, a property that will be numerically verified later." "This tour will show how to perform periodic homogenization of linear elastic materials. The considered 2D plane strain problem deals with a skewed unit cell of dimensions $1\\times \\sqrt{3}/2$ consisting of circular inclusions (numbered $1$) of radius $R$ with elastic properties $(E_r, \\nu_r)$ and embedded in a matrix material (numbered $0$) of properties $(E_m, \\nu_m)$ following an hexagonal pattern. A classical result of homogenization theory ensures that the resulting overall behavior will be isotropic, a property that will be numerically verified later." ] }, { ... ... @@ -30,7 +30,7 @@ { "data": { "text/plain": [ "" "" ] }, "execution_count": 1, ... ... @@ -41,7 +41,7 @@ "data": { "image/png": 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"text/plain": [ "" "" ] }, "metadata": {}, ... ... @@ -233,9 +233,12 @@ "Solving Exx case...\n", "Solving Eyy case...\n", "Solving Exy case...\n", "[[65267. 17338. 81.]\n", " [17338. 65451. 79.]\n", " [ 81. 79. 24009.]]\n" "[[65266.54 17337.7 81.36]\n", " [17337.72 65450.73 79.01]\n", " [ 81.36 79.01 24008.79]]\n", "[[65266.54 17337.69 81.35]\n", " [17337.69 65450.73 79. ]\n", " [ 81.35 79. 24008.79]]\n" ] } ], ... ... @@ -259,14 +262,16 @@ " Sigma[k] = assemble(sum([stress2Voigt(sigma(v, i, Eps))[k]*dx(i) for i in range(nphases)]))/vol\n", " Chom[j, :] = Sigma\n", "\n", "print(np.array_str(Chom, precision=0))" "print(np.array_str(Chom, precision=2))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It can first be verified that the obtained macroscopic stiffness is indeed symmetric and that the corresponding behaviour is quasi-isotropic (up to the finite element discretization error). Indeed, if $\\lambda^{hom} = \\mathbb{C}_{xxyy}$ and $\\mu^{hom} = \\mathbb{C}_{xyxy}$ we have that $\\mathbb{C}_{xxxx}\\approx\\mathbb{C}_{yyyy}\\approx \\mathbb{C}_{xxyy}+2\\mathbb{C}_{xyxy} = \\lambda^{hom}+2\\mu^{hom}$." "It can first be verified that the obtained macroscopic stiffness is indeed symmetric and that the corresponding behaviour is quasi-isotropic (up to the finite element discretization error). Indeed, if $\\lambda^{hom} = \\mathbb{C}_{xxyy}$ and $\\mu^{hom} = \\mathbb{C}_{xyxy}$ we have that $\\mathbb{C}_{xxxx}\\approx\\mathbb{C}_{yyyy}\\approx \\mathbb{C}_{xxyy}+2\\mathbb{C}_{xyxy} = \\lambda^{hom}+2\\mu^{hom}$.\n", "\n", "> **Note:** The macroscopic stiffness is not exactly symmetric because we computed it from the average stress which is not stricly verifying local equilibrium on the unit cell due to the FE discretization. A truly symmetric version can be obtained from the computation of the bilinear form for a pair of solutions to the elementary load cases." ] }, { ... ... @@ -324,7 +329,7 @@ { "data": { "text/plain": [ "" "" ] }, "execution_count": 8, ... ... @@ -333,9 +338,9 @@ }, { "data": { "image/png": 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9wrhohqontcxUICg7KdwXs9WBcbefBf8bIQs6OPKYs8MMQ2E+APz5r/1rIx/A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\n", 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Mw2iGiiQKR4qAczSwAYoJsHGHf4CEUGZIOG4S/zqD7LJ2b5FyrDqW+2hyy9w3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\n", "text/plain": [ "" "" ] }, "metadata": {}, ... ... @@ -346,6 +351,13 @@ "# plotting deformed unit cell with total displacement u = Eps*y + v\n", "plot(0.5*(dot(Eps, Expression((\"x[0]\",\"x[1]\"), degree=1))+v), mode=\"displacement\", title=case)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { ... ...
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